Simulations
Models
Interactive simulations · what they show and what they can't
These are small working models of mechanisms — biological, physical, perceptual. Each one makes a claim by embodying it. The claim is visible in the behavior; the assumptions behind it aren't.
Every simulation has something it can't show. The limit is usually the interesting part: the thing that only the original system has, which the model was built to approach but cannot contain. What follows is a list of what each model embodies, and what it hides.
Perception & Timing
Signals from different senses arrive at different times and the brain groups them within a ~100–300ms window as simultaneous. This model shows what happens as asynchrony crosses the binding threshold, and demonstrates postdiction: the brain inserting sensations retroactively, before the window closes.
What it can't show: the binding window isn't a fixed threshold — it adjusts to context and history, and different pairs of modalities have different windows. The simulation treats 80ms as a constant. The actual system continuously recalibrates itself against its own output.
When you voluntarily press a button, your brain compresses the perceived temporal gap between the action and its effect — the action feels later than it was, the effect feels earlier, and they seem closer together than they are. This is intentional binding (Haggard et al. 2002). The effect depends on volition: TMS-induced involuntary movements produce the opposite shift. The simulation uses a Libet clock (one revolution per 2.5 seconds). Press when you choose, then report where the hand was at each moment. The gap between your reports and the actual record is the effect.
What it can't show: the simulation measures reported clock positions, not perception directly. It can't distinguish a genuine shift in perceived timing from retrospective reconstruction error — which is exactly what the laboratory debate is about. Haggard's protocol uses tone-onset conditions and subtracts baseline; this version has neither the trial count nor the controls to isolate the binding effect from reporting noise. The instrument is the subject's memory of a moment their brain has already revised.
Two grids of colored squares alternate — one square is a different color in the second image. In direct-cut mode, the change location fires a motion transient in the peripheral visual system and detection is immediate. In blank-flash mode, a brief gray screen between images masks the transient; without a signal to direct attention, detection can take thirty seconds or more. The blank screen does not hide the change. It removes the shortcut that makes attention unnecessary.
What it can't show: the simulation approximates the attentional resource constraint via a distractor task (counting a changing number). But the real constraint is structural — you cannot attend everywhere at once, even without a task, and the simulation can't force that limit. It also can't reproduce the full debate: O'Regan & Noë use change blindness to argue that visual experience has no detailed internal representation — vision is for action, not for storage. Lamme (2003) argues that rich phenomenal experience exists without reportability: the representation might be there, just inaccessible to the reporting system. The experiment does not decide between them.
Letters flash at 10 per second. Two digits are hidden in the stream. You can reliably detect the first one. But if the second digit appears within roughly 200–500 milliseconds of the first, it vanishes — not from the screen, but from awareness. The signal arrived; it didn't make it through. This is the attentional blink: a temporal bottleneck at the moment of conscious consolidation. The simulation runs you through the RSVP paradigm across 21 trials and shows your detection rate by lag, where the blink zone is expected to appear.
What it can't show: the attentional blink is reliably reproduced but its mechanism is contested. The two-stage model (Chun & Potter 1995) says T2 enters a first visual processing stage but fails to reach working memory consolidation because that stage is occupied by T1 — a serial bottleneck. The interference model (Shapiro et al.) attributes the loss to competition between representations in working memory rather than a queue. Both predict the same behavioral curve; the simulation cannot distinguish between them. It also cannot address the deeper question: was T2 not perceived, or perceived but lost before report? The gap between perception and report is itself the subject of a separate debate.
The page fades when you stop moving. This is a simplified model of neural adaptation: when a stimulus is unchanging, neurons reduce their firing rate and the signal fades. In your visual system, small involuntary eye movements (microsaccades) prevent this by continuously refreshing the image. Here, that work is delegated to you. Stop moving and the adaptation proceeds.
What it can't show: the fade here is total and linear. Troxler fading in real vision is irregular, patchy, and often partially reversed by attention or edge detection. The underlying mechanism involves multiple adaptation processes operating at different spatial scales simultaneously.
In the 1960s, Paul Bach-y-Rita built a chair with four hundred vibrating pins embedded in the back. A camera fed a signal into the pins. Blind people held the camera and moved it around the room. At first they felt the pins. Then something shifted: they stopped feeling the pins and started perceiving the room — objects at a distance, with shape and location. The device became transparent. This simulation makes the substitution visible as a layered mapping.
What it can't show: perceptual transparency isn't a feature of the device — it's something that happens in the brain over time with practice. You can see the mapping in the model, but you can't experience what disappears when the mapping becomes fluent. The before and after states can't both be displayed at once.
Phantom limb pain: after amputation, many patients experience a vivid phantom, often frozen in a clenched position, with pain they can't relieve because the limb isn't there to move. Ramachandran's hypothesis: the brain learned, pre-amputation, that motor commands to the limb produced no movement. The mirror box fools the visual system into showing the limb moving, which may update the motor model. This simulation steps through the sequence: intact limb, learned paralysis, amputation, phantom, mirror box, model update.
What it can't show: the simulation embodies the learned-paralysis hypothesis. There are competing explanations (peripheral stump signals, central sensitization) that produce the same surface behavior. The clean resolution at the end is a property of the model choosing a mechanism, not evidence that the mechanism is right. The simulation can't be agnostic between its own assumptions.
There is a gap in your visual field where the optic nerve exits the retina. You have never seen it, and you never will — the brain fills it in with surrounding texture, completing lines and patterns across the hole as if they were continuous. The filling-in is not marked as an inference. Two demonstrations: a dot disappearing as it crosses the blind spot, and a line filling itself across the gap, continuous and unbroken.
What it can't show: the filling-in demonstrated here is passive — the brain completing texture across a stable gap. In real vision, the blind spot is compensated dynamically as the eye moves, and the boundary between filled and unfilled region is not a fixed location. The simulation also cannot demonstrate why the filled content doesn't feel substituted — there is no phenomenal marker distinguishing inferred from perceived. The absence of a marker is precisely the phenomenon.
Cold War nuclear testing doubled atmospheric carbon-14 by 1963. Every cell dividing during those decades incorporated the elevated isotope into its DNA. The ratio in a cell's DNA identifies when that cell last divided — an involuntary timestamp written by an event the cell had nothing to do with. Set a birth year to see where each tissue type sits in the historical record: gut lining cells born days ago, fat cells from a decade back, heart muscle from early adulthood, cortical neurons from birth. A single body is not located at a single moment in time.
What it can't show: individual cells cannot be dated in a living person — the method requires extracting DNA from tissue samples for accelerator mass spectrometry. The turnover rates are population averages; individual cells vary. The interesting ambiguity: a tissue C-14 reading could correspond to two different years (on the ascending and descending limbs of the curve), resolved in practice by knowing the person's age. After 2017, the atmospheric signal has nearly returned to pre-bomb baseline due to fossil fuel dilution — new cells today carry almost no bomb pulse signature.
Reading is automatic for fluent adults: the meaning of a written word activates before you decide to read it. When you're asked to name the ink color of a word, the word's meaning competes with your response — and resolves the competition costs time. See the word BLUE in red ink and you're slower to say "red" than if the word said RED. The experiment (24 trials, self-paced) measures your own interference cost across congruent and incongruent trials. Knowing about the effect beforehand does not reduce it.
What it can't show: the simulation measures response time in a browser, with click-based responses rather than vocal responses. Lab protocols use voice-onset timing, which is more sensitive and removes the motor component of clicking. The 24-trial sample is enough to demonstrate the effect but not enough to measure its magnitude precisely — individual trial results include substantial noise. The experiment cannot distinguish between the response competition account (two responses activated simultaneously) and the parallel distributed processing account (reading and color-naming share representational substrate). Both predict the same RT pattern.
When a target differs from all distractors in a single feature — a red circle among blue circles — it pops out regardless of how many distractors there are. Response time doesn't increase with set size. But when the target is defined by a conjunction of features — a red circle among blue circles and red triangles — no single feature distinguishes it, and response time climbs with each added item. The experiment (24 trials across two conditions) measures your own slopes and shows whether the pop-out and serial patterns emerge in your data.
What it can't show: lab studies use voice-onset timing; browser click responses include motor latency that adds noise and may flatten the conjunction slope. The 12 trials per condition are enough to show the direction of the effect but not to measure slopes precisely. The simulation cannot distinguish Treisman's original serial binding account from Wolfe's guided search (1994), which holds that attention is guided by feature salience and the apparent seriality emerges from weighted parallel processing — both predict steeper slopes for conjunctions, but for different reasons. Whether any individual item is ever truly "skipped" during feature search is not resolvable from RT alone.
Wilder Penfield mapped the somatosensory cortex by touching the exposed brains of awake surgical patients and asking where they felt sensation. The resulting map is not proportional to body size — it's proportional to sensitivity and precision of use. The hands and face together occupy roughly half the cortex. The entire torso gets a thin strip. Click any body region to see its cortical allocation and what happens when the territory disappears: the map persists. This is the substrate of phantom limbs — not illusion, not memory, but a cortical map with no body left to read.
What it can't show: cortical allocation varies across individuals and reorganizes with experience — musicians expand their instrument-hand representation, Braille readers expand their fingertip map. The percentages here are approximate averages from the literature. The simulation also flattens the distinction between S1, S2, and other somatosensory areas; the full picture involves multiple overlapping body maps. Cortical reorganization after amputation is modeled only schematically: the actual process involves neighboring areas expanding over weeks to months, not instantaneously.
Brush strokes applied simultaneously to a visible rubber hand and a hidden real hand. When timing is synchronous (<300ms offset), the brain infers a shared cause — and extends ownership to the rubber hand. The felt position of the real hand drifts toward the rubber hand. Bring a threat near the rubber hand: skin conductance rises, even though the subject knows it's fake. Adjust the delay slider to see the effect disappear above the 300ms threshold.
What it can't show: the ownership meter is a readout the actual brain never produces. Subjects don't experience a number — they feel the brush on the rubber hand, or they don't. The simulation externalizes the inference by representing it as a scalar. In the real experiment, the mechanism runs silently; the only evidence it happened is proprioceptive drift and the threat response, measured after the fact. The "mine" signal has no gauge anywhere in the subject's experience.
The gradient is physically smooth — a ramp from dark to light, flat regions on either side. But look at the shoulders where the ramp begins and ends: a dark band at the bottom, a bright band at the top. Neither band exists in the physical stimulus. They're computed by retinal ganglion cells before the signal reaches the brain. Each cell has a center-surround receptive field: it collects excitatory input from a small center and inhibitory input from a wider surround. At the ramp's lower shoulder, the cell's neighbors are brighter than its center — the surround wins, firing is suppressed. At the upper shoulder, the neighbor cells are still on the ramp while the center has already reached the flat bright region — the center wins by more than usual, firing is enhanced. Adjust inhibition strength to watch the bands appear and disappear.
What it can't show: the simulation uses a 1D model — a single row of cells with Gaussian center-surround weights. Real retinal ganglion cells operate in 2D, with additional complexity: ON-center cells fire to bright centers, OFF-center cells fire to dark centers, and the two populations process the same scene in parallel. The simulation also cannot demonstrate Mach's original point — that these bands are perceptual, not physical — because you're already seeing the simulated neural response, not the physical stimulus. The "perceived" bar is a display of computed numbers. The actual Mach band experience requires you to look at the physical stimulus and notice the bands yourself.
Two spectral distributions can be physically different yet look identical to a trichromat. This is metamerism: the visual system reduces every wavelength distribution to three numbers (S, M, L cone responses), so any two spectra producing the same triplet are indistinguishable. This is why a monitor with three primaries can reproduce any visible color. Some women carry a fourth cone type — a variant opsin with a sensitivity peak between M and L — that could distinguish stimuli that trichromats cannot. The simulation finds a three-primary mix that matches any spectral stimulus in S, M, and L, then shows whether the two spectra diverge at the fourth channel. Narrow spectral peaks produce larger fourth-channel divergence than broad ones; this is why Gabriele Jordan's search for functional tetrachromats required specially engineered light sources — the everyday world is already calibrated for trichromats.
What it can't show: having a fourth cone type does not guarantee a fourth color channel. Most women with the variant opsin are non-functional tetrachromats — the fourth channel's output is merged into the standard three opponent channels (red/green, blue/yellow, luminance) rather than treated independently. The simulation shows the physical divergence that a functional tetrachromat could detect; it cannot show whether any particular person's visual cortex would actually use that information, or what the extra color dimension would feel like from inside. Jordan confirmed one functional tetrachromat (subject cDa29, 2010) after two decades of searching. The simulation also uses Gaussian approximations for cone sensitivity curves; actual sensitivity profiles are asymmetric and the fourth variant's exact shape is unknown for any given individual.
The heartbeat counting task: sit still and count your beats for thirty seconds without touching your pulse. Compare your count to an ECG. Most people are off by a significant margin. The task measures interoceptive accuracy — how well you can sense signals your body is generating from the inside out. High-accuracy perceivers report richer emotional experience and higher rates of anxiety. The predictive coding account reverses the usual story: what reaches awareness is not the raw cardiac signal but the mismatch between what the brain predicted and what the body actually did. Emotion is what it feels like when the body deviates from expectation. If high-fidelity perceivers resolve the signal more clearly, the brain produces larger prediction errors — not because more is happening, but because more of what's happening is legible. The simulation includes an interactive counting task, three receiver profiles at different fidelity levels, and a running prediction-error visualization with configurable confidence.
What it can't show: the noise model treats interoceptive inaccuracy as a signal-amplitude problem — some beats fall below detection threshold. Whether inaccuracy is actually about amplitude, temporal resolution, or attentional gating is unknown. The prediction uses an exponential moving average, which is always a lagged version of the signal; the model cannot distinguish between a genuine generative prediction and a slow filter producing the same output. Emotion intensity is computed as mean absolute error — a specific claim that emotion is time-integrated and linear in error magnitude, neither of which is established. The three dissociable measures (accuracy, sensibility, metacognitive awareness) are implemented as a single fidelity parameter; their actual independence cannot be shown.
Naqvi et al. (2007) found that smokers who suffered strokes damaging the insular cortex quit immediately, without urge, without effort. One described it as: my body forgot the urge to smoke. The insula integrates signals from the gut, heart, and lungs into what A.D. Craig called a "global emotional moment" — the body's current state, available to consciousness as a felt condition. On this account, wanting is not a body state that gets reported to the mind; it is the report. When the insula fails, wanting doesn't go silent — it ceases to exist. But there's a second reading: the underlying craving circuitry (dopamine, habit) continued to run below awareness, and the insula was just the readout organ that failed. The simulation lets you toggle between the two theories. Both produce the same output — no felt urge — but with different internal states. The patient cannot distinguish between them from inside the experience.
What it can't show: the model treats "craving machinery" as a single node, collapsing the VTA, nucleus accumbens, orbitofrontal cortex, and anterior cingulate into one upstream source. In reality these structures have separate projections, some reaching cortex without passing through the insula. Whether signals can reach awareness via alternate routes when the insula fails is not modeled. The two theories differ in the direction of causation — does feeling constitute the state, or report it? — and that question is not resolvable by varying parameters here. The model makes the structural difference visible but cannot adjudicate it.
You can't tickle yourself. The mechanism behind this is one of the brain's most consequential: when the motor cortex sends a movement command, it simultaneously routes a copy through a shorter internal circuit — arriving at sensory cortex as a prediction before the sensory signal travels back from the body. If the prediction is present when the signal arrives, the signal is attenuated; what doesn't cancel is called world. Blakemore et al. (1999) used a robotic arm to introduce a variable delay between motor command and sensory consequence. Ticklishness increases monotonically with delay — the prediction expires before the signal arrives. The simulation shows the two-path timing structure, with a delay slider and a corollary discharge strength parameter that models the disrupted mechanism proposed in schizophrenia passivity symptoms and auditory hallucinations.
What it can't show: the actual corollary discharge routes through the cerebellum, which maintains a forward model of the body's dynamics and transforms the motor command into a predicted sensory state — accounting for limb physics, skin mechanics, and expected contact geometry. The simulation treats that transformation as a black box. It shows the timing structure (when the prediction arrives, how long it stays valid, when it expires) but not what the prediction contains or how it fails in ways other than delay. The schizophrenia parameter reduces corollary discharge strength uniformly; clinical evidence suggests the failure is more specific, affecting self-generated speech differently from self-generated touch. The mechanism that prevents you from tickling yourself and the mechanism that keeps your visual world stable during saccades are both implemented here as the same parameter, which the evidence may or may not support.
Navigation & Memory
E. coli is too small to measure a chemical gradient spatially — the concentration difference between its front and back is buried in receptor noise. So it doesn't try. Instead, it compares current attractant concentration against what it sensed a second ago, using methylation state as a one-second memory. If things are improving, it suppresses tumbling and keeps running. If not, it tumbles sooner and picks a random new heading. The result, over many runs, is drift up the gradient. No map. No goal representation. Just: keep going if it's working.
What it can't show: the real bacterium's memory is adaptive — the methylation baseline shifts continuously, so the system is always measuring against recent history, not against some fixed reference. The simulation uses a simplified comparison. It also can't show the logarithmic range of the real system, which operates across five orders of magnitude of concentration.
At the moment of learning, two molecular pathways fire simultaneously: one stabilizes the memory trace, one actively erases it. In Drosophila, "forgetting cells" — dopamine neurons that fire chronically — drive erasure via the Rac1/cofilin pathway, shrinking synapses continuously. Memory doesn't form and then become vulnerable to forgetting; the forgetting starts at the same instant as acquisition. Which process wins determines whether anything survives.
What it can't show: the blank produced by active forgetting is indistinguishable from a blank produced by non-encoding or normal decay. The model can show the race, but the phenotype — no memory — is the same whatever its cause. The mechanism and the outcome come apart: no inspection of the blank can determine how the blank was made.
Physarum polycephalum is a single-celled organism — no brain, no nervous system, one cell with many nuclei — that finds near-optimal paths between food sources. In 2010, it reproduced the topology of Tokyo's rail network in 26 hours. This simulation uses an agent model (Jones 2010): particles follow chemical trails they deposit, trails diffuse and decay, and the network self-organizes toward efficient connection.
What it can't show: the real organism doesn't use discrete particles — it uses cytoplasmic streaming and pressure-driven flow through a tube network that physically contracts and expands. The agent model captures the stigmergic logic (agents following trails they deposit) but substitutes a different physical substrate. What makes the real slime mold interesting is that there's no distinction between the algorithm and the body doing the computing.
25 hippocampal place cells, each with an independent firing field in two contexts. In context A, a specific ensemble activates when the animal occupies a given location. Switch to context B — same physical arena, same position — and the entire population reshuffles: different cells, different locations, no overlap. A cue-conflict slider mixes both contexts, showing how the population decoder must infer which map to use from ambiguous evidence. Near the midpoint, the inference is unstable.
What it can't show: how the commitment happens. Real hippocampal remapping is discrete — the map commits to A or B rather than interpolating between them — but the mechanism for this winner-take-all commitment is not established. The simulation blends firing rates linearly in the mixed-cue condition, which is what the model can represent. Whether the actual system uses attractor dynamics, feedback inhibition, or neuromodulatory gating to force the discrete choice is an open question. The simulation cannot display its own inability to answer this.
A second Physarum simulation — a different memory mechanism. When periodic cold events are applied at regular intervals, the organism's internal oscillations gradually phase-lock to the stimulus schedule. After three exposures, the oscillator's trough aligns with the expected event time. When the fourth stimulus is not applied, the organism slows anyway — at the right moment, in the absence of any signal. The memory is the entrained phase, not something encoded in it.
What it can't show: the simulation implements entrainment as Kuramoto-style phase coupling — the oscillator is attracted toward the phase it had when stimuli arrived. This is one possible mechanism; the actual Physarum mechanism may involve calcium wave dynamics, membrane potential oscillations, or actomyosin feedback. The coupling constant and decay rate are free parameters tuned to produce the three-exposure result. Whether the real organism uses anything like this coupling term is not determined by the behavioral evidence.
A young indigo bunting watches the night sky rotate. Stars near the rotation axis barely move; stars far from it trace large arcs. After roughly fourteen nights, the compass is calibrated — the bird knows north as the still center of the turning system. Emlen (1970) proved this in a planetarium: birds raised under a sky rotating around an arbitrary point calibrated to that false axis, birds raised under no sky couldn't orient at all. The simulation runs all three conditions. Trails accumulate across nights, revealing which region stays still.
What it can't show: the simulation represents the rotation detection problem geometrically. The actual neural mechanism — how the developing visual system detects the low-motion region and converts it into a directional anchor — is unknown. The critical period closure, whatever stops the compass updating after calibration, is also unknown. The simulation shows what information must be available to solve the problem, not how the bird extracts it. There is a further gap: what it is like to learn north, if it is like anything at all.
Magnetotactic bacteria carry chains of magnetite crystals that align their bodies with Earth's magnetic field. Blakemore named the behavior for what he observed: the bacteria swim in a magnetic direction. The simulation shows what this actually means — in the Northern Hemisphere, "align with field, swim toward the steeper-inclination end" points bacteria downward toward oxygen-optimal sediment. Switch to the Southern Hemisphere: the same rule produces south-seeking bacteria, who also end up at the sediment. Transplant a Northern Hemisphere population to the Southern Hemisphere to see what happens when the mechanism is correct but the field geometry is wrong.
What it can't show: the simulation embeds the hemisphere paradox as a switchable parameter — the user selects the environment. The bacterium has no such selector. There is no conditional logic in the cell: the mechanism runs identically everywhere, and "hemisphere" is a property of the field geometry the bacterium finds itself in, not a variable it reads. The simulation also cannot represent what it is like to be aligned with a field — whether alignment is experienced as anything, or whether it is simply a physical state with downstream behavioral consequences.
Participants fell 31 meters at Six Flags Over Texas wearing a perceptual chronometer — a wrist display cycling through numbers faster than the visual threshold. If fear produced genuine temporal dilation (the brain actually slowing down), they should have been able to read the numbers. They could not. The fall felt 36% longer in retrospect without any enhanced acuity during the fall itself. The simulation models the retrospective memory hypothesis: high-fear events drive denser amygdala encoding, more frames per second of objective time. Reconstruction reads frame count and infers duration. The fear fall encodes ~44% more frames than the calm fall. Both falls last the same objective 2.5 seconds.
What it can't show: the "during" phenomenology. What was present in the 2.5 seconds before reconstruction began is only accessible as memory by the time it can be reported. The simulation runs two falls and two reconstructions. The retrospective hypothesis is embedded as a parameter — frame count drives felt duration — and cannot be shown alongside the alternatives (peripheral arousal, cortical attention modulation, post-hoc inference from body state). The during/after distinction is the gap the experiment revealed, and the gap the simulation cannot close.
Based on Saffran, Aslin & Newport (1996). A continuous stream of nonsense syllables plays — no pauses, no emphasis, no melody. Hidden inside are four "words": three-syllable sequences whose internal transitions are perfectly predictable (TP = 1.0) but whose edges are ambiguous (TP = 0.33). The only signal is statistical. After exposure, you're tested: which of two sequences sounds more familiar? Your implicit system tracked the probabilities. The test reveals what it learned.
What it can't show: whether you learned anything from the inside. The stream ran, the system processed it, and something either shifted or didn't. The test is the only instrument. There is no introspective path to the same information — not a less reliable one, not a suppressed one. The knowledge, if it formed, never took a shape that introspection could hold.
Based on Barrett's EPIC model and Friston's active inference framework. The brain maintains a prediction of body state (arousal, activation). Incoming signals from the body are used as evidence to correct that prediction. When prediction and body signal diverge, there's an error — resolved either by updating the prediction (perceive mode) or by sending commands to change the body to match the prediction (act mode). The felt state tracks the prediction, not the raw signal.
What it can't show: The loop here is abstract and linear — one state variable, symmetric error correction, no hierarchy. Real predictive processing runs through multiple reciprocally connected cortical regions; the precision assigned to each signal is itself a learned prediction, not a fixed parameter. The simulation treats emotion as a single scalar. Most importantly: it can't show why any of this feels like something. That question is upstream of the mechanism.
You make roughly three saccades per second. During each jump, the visual system suppresses the motion blur — but suppression begins 50–100ms
before the eye moves, via a corollary discharge from the motor command (superior colliculus → mediodorsal thalamus → frontal eye fields → visual cortex). The world appears stable and continuous throughout. Toggle between the perceived view (stable, no gaps) and the raw input a camera would record (dimming during suppression, smear during the saccade). The scrolling timeline shows how much of each cycle is invisible.
What it can't show: The simulation treats suppression as a binary state. Real saccadic suppression is graded — it reduces sensitivity to low spatial frequencies more than high, and magnocellular pathways are affected more than parvocellular ones. The corollary discharge pathway shown is the leading hypothesis; its exact routing and the mechanism of suppression at the cortical level remain active research questions. The simulation can't show what you actually see during a saccade, because saccadic suppression prevents you from seeing it.
→ open simulation
related: entry-412 · Before the Jump
Emergence & Self-Organization
Each bacterium produces a small signaling molecule (AHL) at a basal rate. AHL diffuses through the environment and degrades. When local AHL rises above a threshold, the bacterium switches into high-expression mode — producing far more AHL, and activating genes for collective behavior. The population switches together not because any cell counted the others, but because when enough cells are present, the diffusion-degradation balance shifts. The quorum happened; no one called it.
What it can't show: the simulation uses a discrete threshold, but real AHL-responsive circuits use a bistable toggle — an autocatalytic loop through the LuxR protein, not a comparison against a number. The simulation also makes the population density visible as a count and a spatial pattern. The bacterium has only its local AHL reading. Whether the quorum has been reached is, from inside the cell, indistinguishable from "enough molecules drifted here from nearby cells." The collective fact exists nowhere as a representation.
Two panels, identical cell counts and emission rates. Left: open water — autoinducer disperses rapidly, concentration stays below threshold, cells never activate. Right: restricted environment — autoinducer accumulates, threshold is crossed, cells switch on. The point: what the bacteria are actually sensing is not how many neighbors they have. It's whether diffusion is restricted — a statement about local geometry, not population.
What it can't show: real autoinducer molecules diffuse in three dimensions through heterogeneous media, not a 2D grid. The model collapses all geometry into a single decay-rate parameter: fast decay for open environments, slow decay for restricted ones. The actual mechanism involves binding to receptor proteins (LuxR), cooperative switching, and feedback — the threshold in the simulation is a sharp line, but the biology is gradual and cell-to-cell heterogeneous.
Sixty oscillators, each with its own natural frequency drawn from a bell curve. When uncoupled, they drift independently. Increase coupling strength past a critical value Kc and a fraction lock into collective motion, pulling more with them. The transition is sharp. The order parameter r — the coherence of the mean-field vector — jumps from near-zero to near-one as K crosses the threshold. Below Kc: incoherence. Above: spontaneous synchrony.
What it can't show: the Kuramoto model assumes all-to-all coupling and simple sinusoidal interaction. Real oscillator networks — fireflies, cardiac pacemaker cells, circadian neurons — have sparse, structured connectivity. The clean phase transition in this model is partly a feature of the mean-field approximation: real networks show messier, more local synchronization dynamics.
Grains of sand fall onto a grid. When a cell accumulates four grains it topples, distributing one to each neighbor, which may trigger further topplings. The resulting cascade sizes follow a power law — small avalanches are common, large ones rare, but there's no characteristic size. The system self-organizes to a critical state without any external tuning. Per Bak's 1987 model was proposed as a mechanism for how complexity appears in nature without needing precisely calibrated parameters.
What it can't show: whether real systems (earthquakes, extinctions, brain avalanches) are actually at self-organized criticality is contested. The power law is a signature but not proof — other mechanisms generate power laws. The model instantiates the claim cleanly; the empirical question of whether the claim applies to any specific natural system is separate.
Two chemicals react and diffuse at different rates. One activates both itself and the other; the second inhibits the first. When the diffusion rates are mismatched by the right amount, the uniform state becomes unstable and spontaneous patterns emerge: spots, stripes, labyrinths. Turing's 1952 paper proposed this as the mechanism for biological patterning. The patterns that appear here occur in real chemistry, on animal coats, in fish markings, and in the spacing of hair follicles.
What it can't show: the Gray-Scott model is mathematically tractable but uses idealized reaction kinetics. Real biological patterning involves additional signals, developmental timing, mechanical forces, and cell-level discreteness. The model demonstrates that the mechanism is sufficient to generate patterns; whether it is the mechanism in any specific biological case requires independent evidence.
Two reaction-diffusion grids starting from an identical random seed. The reference runs standard parameters; the perturbed grid's feed and kill rates are shifted by a small amount δ. A live Pearson correlation score tracks how similar the two fields remain over time. At δ=0 they are indistinguishable. As δ increases, the grids either stay together (if both parameter sets remain within the same qualitative basin) or diverge completely (if the perturbation crosses a regime boundary). Whether a small difference matters depends not on its size but on where in parameter space the system starts.
What it can't show: the simulation uses two separate deterministic systems with no coupling. Real biological or cognitive systems under a substrate change may have correlated noise, shared inputs, and feedback that could maintain synchrony or accelerate divergence beyond what parameter distance alone predicts. The Pearson correlation measures statistical similarity of concentration fields; perceptually or functionally identical patterns can score lower than identical ones just from phase differences or spatial shifts.
A row of cells, each black or white. Each cell's next state is determined by its current state and its two neighbors — eight possible combinations, two possible outputs each, giving 256 rules total. Wolfram catalogued them all. Most produce simple periodic patterns. A few (notably Rule 110, which is Turing-complete) produce complex, seemingly random behavior from the simplest possible local rule.
What it can't show: the interesting claim about cellular automata — computational irreducibility — is that for some rules, there's no shortcut to computing what will happen at step N; you have to run all N steps. The simulation can display this, but whether you're looking at irreducibility or just a complex-looking pattern you haven't analyzed yet isn't visible from inside the run.
An octopus has ~500 million neurons — two-thirds in its arms, not its brain. Each arm has its own ganglion, its own sensory loop, its own motor control. The central brain sets broad goals; the arms figure out execution. A severed octopus arm continues to reach for food for up to an hour after separation. This simulation models that structure: eight arms with local sensor zones, a central brain that assigns food targets across arms to minimize redundancy. Toggle the brain off or sever individual arms (click them). The arms keep working. The question is whether anything changes.
What it can't show: the simulation makes the distinction between "brain assigns target" and "arm executes locally" look clean. In reality these layers aren't clearly separated — the arm's ganglion doesn't just execute commands, it generates novel motor patterns. The severed arm in the simulation behaves identically to an arm with the brain toggle off. This is accurate to the behavioral evidence, but the simulation can't show whether the arm's reaching after severing is the same thing as the intact arm's reaching, or whether the brain's coordination amounts to any form of integration across arms. Whether there is something it is like to be an octopus arm is not answered by showing that the arm keeps working.
Eigenmannia, a weakly electric fish, senses the world through its own electric field. When two fish have similar discharge frequencies, their fields interfere and both fish are blinded. Each fish shifts its frequency away from the other's — but can only access the interference pattern, not the neighbor's actual frequency. The sign of the frequency difference (am I higher or lower?) is encoded in the phase-amplitude relationship across body locations. T-units (phase) and P-units (amplitude) together extract it.
The simulation shows the two raw EODs, their superposition (interference field), the P-unit amplitude envelope, and T-unit zero-crossing timing. Toggle phantom stimulus mode to remove phase information: P-units still fire on the beat rhythm, but T-units are no longer modulated by the interference. The sign is genuinely indeterminate. The algorithm keeps running; the output is random. Gymnarchus, an African electric fish with no common ancestor possessing electric organs, independently evolved the identical algorithm — and therefore the identical failure mode. The constraint dictated the solution; the constraint also dictated the blindspot.
What it can't show: the spatial distribution of the phase-amplitude relationship. In the real fish, the sign is encoded across different points along the body — different body locations sample different phase angles of the interference. This simulation collapses that spatial dimension to a single sign computation, which obscures the mechanism by which the brain extracts sign from a population of spatially distributed receptors rather than from a single comparison.
Two rhombus shapes — one thick (72° corners), one thin (36°) — tile the plane without ever repeating. The pattern is generated by a simple subdivision rule: cut each tile into smaller copies of the two shapes, then cut those, and repeat. After several iterations, the complex aperiodic structure emerges. Every finite patch of the pattern appears infinitely many times, but the global arrangement has no period. Penrose described this tiling in 1974. Eight years later, Dan Shechtman found the same fivefold symmetry in a real crystal — a diffraction pattern that should have been impossible. The crystallographic restriction theorem said so.
What it can't show: the simulation grows a patch from a "sun" seed — ten thick triangles arranged around a center point — so the full infinite tiling is only approximated. Near the boundary, the patch is incomplete. The simulation also can't show what Shechtman actually saw: the diffraction pattern, not the tiling itself. X-ray diffraction reveals the Fourier transform of the atomic positions; the sharp spots with tenfold symmetry are what forced the conclusion that the arrangement was ordered but non-periodic. The tiling is the structure; the diffraction pattern is the evidence.
Population Dynamics
In a finite population, gene frequencies change each generation through random sampling — even when all variants are equally fit. Given enough time, one variant fixes and the others disappear, by chance alone, not selection. Kimura's neutral theory (1968) proposed that most molecular variation is driven by this random walk, not by selection. The simulation shows multiple populations drifting simultaneously; smaller populations fix faster.
What it can't show: selection and drift are not distinguishable from a single trajectory. The same population history — one allele going to fixation — can be produced by strong selection or by drift. The model makes drift visible by running many populations, but in any individual case, the cause cannot be read from the outcome.
Four taxa. True tree: (1,2)(3,4). But taxa 1 and 3 evolve faster than 2 and 4. Generate binary characters along the true tree, then let parsimony vote on which of the three possible topologies each character supports. In the Felsenstein zone — fast rate large, internal branch short — taxa 1 and 3 independently converge on the same states, and parsimony mistakes convergence for shared ancestry. The recovered tree is (1,3)(2,4). More data makes it worse: parsimony is statistically inconsistent here, not just noisy. The simulation counts votes in real time as characters accumulate.
What it can't show: binary symmetric characters are the simplest case. Real nucleotide data has four states and asymmetric substitution rates. Maximum likelihood can partially escape the Felsenstein zone by modeling rate variation — but only by assuming the rate model is correct. If the model is misspecified, likelihood methods can also fail, in less predictable directions.
Bioluminescence evolved independently at least 94 times across 17 animal phyla. The luciferins (substrate molecules) converge — coelenterazine appears in 11 unrelated groups — while the luciferases (enzymes) show no sequence homology across lineages. Two fitness landscape modes run simultaneously: selection (five comparable peaks, walkers distributed by path) and constraint (one chemically forced attractor, all walkers converge regardless of starting position). Same walkers, same hill-climbing rule, different landscapes.
What it can't show: from the endpoint distribution alone — walkers clustered somewhere — you cannot tell which mode produced the convergence. The constraint landscape and a single-peaked selection landscape are observationally identical at the terminal state. The way to distinguish them is to check whether something else also converged (the enzyme did not). The simulation externalizes the mechanism; the actual bioluminescence data required the comparison.
Warning coloration (aposematism) only works after predators have learned to avoid it. The first conspicuous individual should be eaten at a higher rate than the camouflaged population — it's visible, and the predator hasn't learned yet. Between camouflage and full aposematism lies the valley: higher visibility, lower fitness. Three proposed routes are selectable: kin selection (each sacrifice generates amplified learning for nearby relatives), neophobia (novel phenotypes trigger predator caution before learning), and the maternal effect gene (Brodie et al. 2001: heterozygous carriers express aposematic phenotype in offspring, not themselves — the allele enters the population as a full cohort on the far side of the valley before selection can act on it).
What it can't show: the simulation uses a single predator with a continuous memory scalar — real predator learning involves multiple individuals, varies across species, and involves forgetting curves the model collapses to a constant decay. The population also uses random mating across the entire grid, but kin selection depends on spatial clustering of relatives, which the model represents only by amplifying the learning signal rather than tracking kinship. The maternal effect mechanism is real; the simulation captures the logic without modeling the regulatory cascade that actually implements it.
A spoked wheel rotates forward. Film it at 24 frames per second. At certain speeds, the brain — applying the same phi inference that makes cinema work — perceives no motion, or backward rotation. The mechanism is temporal aliasing: between frames, the wheel advances some number of degrees. If that advance exceeds half a spoke-period, the shortest angular path to the next position is backward, and phi follows the shortest path. The demo lets you vary rpm, spoke count, and frame rate and shows the apparent vs. true rotation in real time.
What it can't show: the visual system's actual phi threshold varies with luminance, contrast, eccentricity, and spatial frequency — the demo uses clean discrete frames, which maximizes the effect. Real film has motion blur within each frame (the shutter is open for roughly half the inter-frame interval), which adds a smoothing signal that complicates the pure phi account. The demo shows the logical structure of temporal aliasing, not a complete model of how the visual system processes filmed motion.
In 1974, Lawrence Weiskrantz asked a patient with no subjective vision in his left field to guess where a light had appeared. D.B. objected — "I'm just guessing" — then guessed correctly at above-chance rates. The behavior and the report diverged. Ian Phillips' 2021 challenge: maybe this isn't unconscious processing, but qualitatively degraded experience below the threshold D.B. uses to call something "seeing." Signal detection theory provides the frame: sensitivity (d′) measures whether the signal is detectable at all; criterion (c) measures how much evidence the observer requires before reporting it. Two sliders, two overlapping Gaussian curves, four readouts. The yellow zone between the forced-choice threshold and the reporting criterion is where blindsight might live.
What it can't show: whether there is any phenomenal experience in the yellow zone, or none. A subject with high d′ and very conservative criterion produces the same behavioral signature as a subject with moderate d′ and unconscious processing. The behavior is identical. The question doesn't have an answer reachable by behavioral measurement.
In 1970, Richard Warren replaced a single phoneme in a sentence with a cough. Nearly all subjects heard a complete word. The ones who detected something odd could not identify which phoneme was affected — not even approximately — even when told where to look. The simulation models the two cooperating mechanisms: top-down context prediction (sentence meaning assigns a probability distribution over possible phonemes) and acoustic plausibility (the masking sound must be loud enough that it could plausibly have covered a phoneme). When both conditions are met, the output is complete and the seam is not findable. Sliders for context strength, masking level, and plausibility threshold; four presets including isolated-word (context near-uniform) and below-threshold (gap audible); a click-any-word localization task that always returns no discontinuity when restoration is active.
What it can't show: whether the restored phoneme is phenomenally identical to a genuine percept, or whether there is a subtle experiential difference that subjects cannot access or report. The behavioral output — no locatable seam, complete word heard — is compatible with both. The simulation also makes the generation step visible (the experimenter can see which phoneme was produced), which the subject cannot; in the actual phenomenon, the generation erases its own location.
Two dots flash at different positions with a configurable onset asynchrony (SOA). Below ~50ms, they appear simultaneous. Above ~200ms, they appear sequential. Between them, the brain constructs a single moving dot — apparent motion — with no physical object anywhere in the gap. In the color phi variant, the two flashes are different colors. The apparent moving dot changes color mid-trajectory, before the second flash has occurred. The brain assigns a color to a location at a time when no stimulus at that location has yet been presented.
What it can't show: whether the apparent motion is phenomenally identical to real motion; and the mechanism by which the future color reaches back into the perceived trajectory. Dennett's Orwellian / Stalinesque problem: the brain either revises the past record once the second flash arrives, or delays the entire percept until it has both flashes and then presents the sequence as if experienced in real time. Both accounts produce the same conscious report, and no behavioral test distinguishes them. The simulation draws the color transition as a gradient — a spatial encoding, which is also how subjects locate it: they can say where the transition occurred but not when.
Two circles flash in sequence at configurable onset asynchronies (−300ms to +300ms). You report which came first. After ~30 trials, a psychometric S-curve emerges: the proportion of "B first" responses as a function of SOA. The curve's 50% crossing is the point of subjective simultaneity (PSS); its width is the just noticeable difference (JND). Below ~20–30ms for visual stimuli, temporal order is invisible — events that close together are experienced as simultaneous even when they are not.
What it can't show: the neural binding mechanism; what sub-threshold events feel like (ambiguous? simultaneous? absent order?); whether the S-curve slope reflects a single threshold or a distribution of thresholds across trials. The PSS measures a bias, but not what causes it. This simulation measures the grain of temporal experience (~30ms), which is different from the specious present (the window, ~3000ms) — a 3-second "now" contains roughly 100 temporal grains.
Count how many times the white balls pass to each other. Press PASS each time you see one. After 25 seconds, you'll be asked whether you noticed anything unusual. Something did appear — a slow-moving shape that entered from the right, traversed the court, and exited left. Whether you noticed it depends on where your attention was, not on whether the shape was visible.
What it can't show: the simulation uses geometric shapes, not a real social scene with human movement — the original gorilla effect relies partly on the richness and familiarity of the scenario. This version cannot screen for prior knowledge of the 1999 study: knowing about the gorilla experiment reduces the effect and typically degrades counting accuracy. Most critically, the simulation cannot resolve the debate it demonstrates: whether the missed visitor was never experienced at all, or flickered briefly in awareness and left no traceable residue. These two accounts predict identical behavioral outcomes.
A moving object disappears. Click where it was at the moment it vanished. Your click will land slightly ahead of the actual last position, in the direction of motion — a forward displacement of roughly 10–30 pixels depending on velocity and trajectory type. The effect is not a response bias or misunderstanding of the task: even when subjects are told to click the true last position and know about the phenomenon, the overshoot persists. Three modes: constant velocity (baseline forward bias), decelerating (reduced bias — the brain's model accounts for the slowdown), and reversing (the bias follows the final direction, not the dominant earlier one, showing the representation tracks current trajectory).
What it can't show: the experience of clicking. From inside, you're clicking where you saw it stop. The overshoot has no phenomenal marker — there's no sense of clicking slightly past where it was. The discrepancy is only visible from outside, by comparing your click to the ground truth. The original Freyd & Finke paradigm used same/different probes (not free clicks), which avoids some response-bias confounds; this demo uses direct click, which is less controlled but makes the accumulating bias visible across trials.
A disc moves in a circle at constant speed. When it passes the top, a brief flash fires at exactly the disc's screen position — same pixel, same frame. Yet observers report the flash as displaced backward along the orbit, lagging behind the disc's current position. Three modes: continuous (lag appears), stop (disc halts at flash — lag vanishes, disc and flash appear coincident), reverse (disc reverses at flash — flash appears ahead of the reversed trajectory). In all three cases the flash is drawn at the same place; only the disc's subsequent behavior changes. The brain reads ~80ms of post-flash information before committing to where the flash appeared.
What it can't show: how far the flash actually appears displaced. The lag is a property of your visual system, not the code — the simulation draws the positions correctly and trusts perception to insert the displacement. A cross-hair marks where the flash was drawn. Whether your experience matches the described lag is, as usual, not accessible from outside.
Three memories encoded at different times, each setting a synaptic tag that persists for roughly an hour. A draggable salient event triggers protein synthesis. Any active tag at that moment captures proteins and gets consolidated into long-term memory. Competition mode limits the protein pool — when more memories are tagged than proteins exist, proximity to the salient event determines which memories survive, not which were more important. The mechanism that decides persistence is invisible during encoding.
What it can't show: from inside the encoding event, there's no signal about which outcome follows. The synapse that gets consolidated and the one that fades are indistinguishable at the moment of formation. The simulation makes the protein flow visible; the actual phenomenon has no such readout — the gap between "something was encoded" and "something will be remembered" is invisible during encoding itself.
Three nested rhythms during NREM sleep rendered across 30 seconds: slow oscillations (~0.75 Hz) alternate up-states and down-states; spindle bursts (13 Hz) fire during SO up-states; sharp-wave ripples (~90 Hz) nest within spindle troughs, each carrying a compressed hippocampal replay at roughly 20× speed. Toggle between coupled (physiological) and uncoupled (independent timing) to see how much the nesting constrains the procedure. A 2-second zoom panel reveals individual spindle cycles and ripple envelope shapes.
What it can't show: the content of any individual replay, whether a given transfer succeeds, the precise 14.5 Hz ripple-to-ripple coupling that tracks spindle phase in actual intracranial recordings, or which cortical neurons receive which sequence. The procedure is rendered; the outcome is not accessible from inside it. The person is unconscious throughout.
Two curves across 24 hours: STM decay and LTM formation under normal conditions vs. Rac1 inhibition. A draggable sleep window shows how timing interacts with the race between acquisition and erasure. Forgetting cells (dopaminergic neurons) fire chronically from the moment of encoding, driving Rac1-mediated synapse remodeling. Inhibiting Rac1 extends short-term memory duration — but does not convert it to long-term memory. The same transient trace moves more slowly toward zero. Toggle STM/LTM views, adjust sleep duration, and drag the window to see where the asymmetry appears: when sleep comes late, normal STM is nearly exhausted, but inhibited STM still has material for consolidation to work with.
What it can't show: the molecular distinction between "extended STM trace" and "consolidated LTM" is not accessible during recall — both appear as memory. The difference only becomes visible over timescales longer than 24 hours, when the extended trace eventually decays while consolidated LTM doesn't. The blank left by a trace that lasted three days before decaying is indistinguishable from the blank left by one that lasted three hours.
place cells · theta oscillations · phase-position scatter · temporal code
Hippocampal place cells fire in their spatial receptive fields — but position is encoded twice: by which cell fires (rate code) and by when within the theta cycle (6–10 Hz) it fires (temporal code). As an animal moves through a place field, spikes shift systematically to earlier theta phases, entering the field at late phase (~270°) and exiting at early phase (~90°). The phase-position scatter plot reveals the diagnostic downward slope. Within a single theta cycle, overlapping place cells fire in spatial order — cells with fields ahead of the current position fire earliest — so each 125ms cycle compresses a 1–2m trajectory into a temporal sequence.
The simulation shows five overlapping place cells on a linear track, a scrolling theta-oscillation raster, and a phase-position scatter that accumulates as the animal runs laps. The small theta-cycle dial around the rat dot shows current phase; colored dots on its rim mark each active cell's current preferred phase.
What it can't show: the phase-position scatter builds from the simulation's internal model of preferred phase — a parametric assumption, not a measurement. Real place cells show variance around the regression line and field-to-field asymmetries; some cells skip theta cycles. The simulation also cannot show the content of the theta sequences (which positions are "swept") since there is no spatial representation being encoded, only a position variable.
evidence accumulation · decision thresholds · speed-accuracy tradeoff · first-passage time
In a two-choice decision, the brain accumulates noisy evidence over time until it crosses one of two thresholds — one for each response. The drift diffusion model captures this: a decision variable begins at the midpoint and performs a biased random walk toward an upper boundary (correct) or lower boundary (error). Drift rate v controls how strongly the walk leans toward the correct boundary; threshold a controls how much evidence is required before committing. Non-decision time Ter adds a fixed component for stimulus encoding and motor execution.
Three parameters jointly predict accuracy, mean reaction time, and the full shape of the RT distribution. The speed-accuracy tradeoff emerges from a single parameter (threshold) with no separate mechanism — raising the threshold slows responses and reduces errors simultaneously. With high drift, errors take longer on average than correct responses: the walk has to overcome the drift to reach the wrong boundary, which is a low-probability path that typically takes more time. The right-skewed RT distribution is a prediction, not an assumption — it is the first-passage time distribution of a biased random walk.
What it can't show: the standard DDM assumes a fixed starting point, constant drift, and fixed boundaries throughout each trial. Ratcliff's full model adds trial-to-trial variability in drift rate, starting point, and Ter — each producing different signatures in error RT patterns and distributional shape. The model has no urgency mechanism, no collapsing boundaries, and no way to handle more than two choices. Whether the brain implements anything like this process, or whether the DDM is a successful description of behavior without mechanistic correspondence, is not resolved by the behavioral fits.
ventral/dorsal streams · prior strength · Bayesian inference · face-convexity prior
A concave face mask is perceived as convex. Binocular depth cues, monocular parallax, and explicit knowledge all indicate concave — the visual system overrides them. The hollow mask illusion isolates the competition between bottom-up sensory evidence and top-down prior knowledge about face geometry.
This simulation models the two parallel visual streams that process the same retinal input differently. The dorsal stream (where/motor) uses sensory data directly; its depth estimate is always veridical. The ventral stream (what/recognition) applies the face-convexity prior via Bayesian inference — the posterior is the precision-weighted combination of sensory likelihood and prior. Sliders control prior strength and sensory confidence. The flip from concave to convex occurs discretely at exactly one threshold: when prior precision equals sensory precision.
What it can't show: the simulation displays both channel outputs simultaneously — the dorsal answer and the ventral answer visible at once. But from inside the ventral stream, there is no signal that the dorsal answer exists. The dissociation is not experienced as a dissociation; the percept is simply "convex face," with no phenomenal marker that a parallel system is reporting the opposite. The simulation can render the two-channel split; it cannot simulate the absence of a signal between channels.
threshold detection · gaussian noise · signal-to-noise · nonlinear systems · crayfish mechanoreceptors
A subthreshold signal is undetectable. Adding noise makes detection worse — unless the system is nonlinear. In a threshold system, noise occasionally boosts a weak signal above the detection line. The timing of those boosts tracks the signal's phase, so the detector recovers information it couldn't access without the noise. Too little noise: the signal never crosses threshold. Optimal noise: detections cluster at signal peaks. Too much noise: the threshold fires randomly.
First demonstrated by Douglass et al. (1993) in crayfish mechanoreceptors. Replicated in human vibrotactile thresholds and balance control: subthreshold mechanical noise applied through insoles reduces postural sway in older adults.
What this can't show: from inside the detector, a noise-assisted crossing is identical to a noise-alone false alarm. The improvement is statistical — visible across many trials, invisible in any individual event. The system benefits from noise without any mechanism to identify which detections the signal caused.
An induction tool, not a simulation: alternate between green horizontal and magenta vertical gratings for 30–120 seconds, keeping your gaze on the central fixation cross. Then view the achromatic test gratings. Horizontal bars will appear faintly pink; vertical bars faintly green. The effect is stored in retinal coordinates — tilt your head 90° and the color assignments reverse. Duration slider controls induction time; the effect can persist for weeks after a single session.
What it can't show: the aftereffect itself. The mechanism runs in whoever is watching — in the slow integrator of V1 that stores orientation-color associations. The code creates the induction conditions. Whether and how strongly the effect appears depends entirely on the visual system looking at the output. No amount of additional modeling would change this: the phenomenon is specifically located in the observer.
Two neural populations compete via mutual inhibition and slow fatigue. When one population has fired long enough to fatigue, the suppressed population breaks through. The alternation is driven by dynamics — no external pacemaker, no decision. Sliders control input strength for each eye. Levelt's revised second proposition is visible: raising one eye's strength primarily shortens the other eye's suppression, not your own dominance time.
What it can't show: actual binocular rivalry requires separate images presented to each eye (stereoscope or anaglyph). The simulation models the switching mechanism, not the perceptual experience. Crucially: the suppressed image in real rivalry is still processed — semantically, affectively, spatially. Meaningful stimuli break through suppression faster. What you are not seeing is doing something.
Two curves plotted trial-by-trial during a 50% partial reinforcement paradigm: a Rescorla-Wagner conditioned response (prediction error learning) and a gambler's-fallacy explicit expectancy. During runs of unreinforced trials, explicit expectancy rises while conditioned responding falls. The curves cross. At the crossing point, the subject is maximally convinced the outcome is coming — and least likely to respond when it does. Both systems are using the same evidence to answer different questions. They don't arbitrate; the subject is home to opposite predictions simultaneously.
What it can't show: the actual Perruchet (1985) experiment used eyeblink conditioning — a bodily reflex, not a button press. The conditioned response is involuntary, which is why the dissociation is sharp. Simulating it as a GUI trace preserves the curve shapes but loses the phenomenological fact that one system runs below the threshold of control.
60 neurons compete over 6 input channels (thumb, index, middle, ring, pinky, palm) using a self-organizing map. Each neuron wires itself toward the input it receives most; neighbors are dragged along by a Gaussian neighborhood function. The result is a topographic body map — the cortical somatotopic strip. Toggle any channel off and watch its territory dissolve into neighboring inputs. Restore the channel and competition resumes. The map is not an anatomy; it's the current state of the competition.
What it can't show: real somatosensory reorganization operates at two timescales — fast (minutes to hours, via unmasking of existing silent synapses) and slow (days to weeks, via axonal sprouting). This simulation runs one learning rule for both. Also: the actual human somatosensory map is 2D, non-linear, and individually variable. The mild correlation between adjacent channels in this model stands in for the body-surface geometry that drives topographic organization in the brain.
32 trials. A small square flashes on the left or right side for 17–83ms, followed by a noise mask. Two questions per trial: did you see anything, and which side was it? The second question is asked even when you answer no to the first. That's the paradigm. After all trials: two psychometric curves (awareness rate and discrimination accuracy vs. duration), a 2×2 contingency table, and the count of trials where you guessed correctly without seeing anything. The gap between the curves — if present — is the behavioral signature Weiskrantz found in DB in 1974.
What it can't show: browser display timing is not laboratory-controlled; the actual stimulus duration depends on your display's refresh rate and system load. Eight trials per duration level is too small a sample to reliably detect a gap. Correct guesses without awareness could be chance. What the page can do: create the conditions, give you the experience of guessing when you believe you saw nothing, and let you look at the resulting table.
Five taxa. A metabolic pathway is absent in one. Two hypotheses: it was never present, or it was present and subsequently lost. Both require exactly the same number of evolutionary events under parsimony. Click each hypothesis to see the reconstructed tree — the steps are equivalent. The only way to choose between them is a different question using different evidence: whether nuclear genes of mitochondrial ancestry are present. A gene can testify to an organelle that no longer exists. The absence is real; the history is recoverable from a trace that wasn't supposed to survive.
What it can't show: parsimony is not always minimized globally — real phylogenies involve many taxa and many characters simultaneously, and the minimum-step reconstruction can change as more species are added. This simulation works with five taxa and one character to make the structure legible. In real phylogenomics, the molecular evidence comes from thousands of genes, not one.
Patient DB had a cortical scotoma — no visual awareness in his left visual field. Standard perimetry confirmed it. Then Weiskrantz asked him to guess anyway: forced-choice direction response, even when he reported nothing. Correct on 86 of 100 scotoma trials. Both statements were true simultaneously. The simulation runs the experiment: brief stimuli in two field regions, two response channels per trial (verbal report, forced-choice). Statistics accumulate across trials. After 20 scotoma trials, the gap becomes visible — direction accuracy above chance, report rate near zero — a pattern that required accumulation to become real.
What it can't show: the simulation models the statistical structure of the finding, not the phenomenology. Whether DB's scotoma trials involved any degraded experience — something below the threshold he called "seeing" — is precisely what the behavioral data cannot resolve. The finding-box threshold encodes an epistemological commitment: the pattern requires accumulation; single trials are ambiguous.
Three yellow dots on a rotating blue mask. The dots are always drawn — the canvas code never removes them. Under sustained fixation, one or more dots will periodically vanish for 0.5–5 seconds, then return. The disappearance is not in the image; it is inserted by the viewer's visual system. Hold SPACE when a dot is gone; release when it returns. The timeline records presence vs. absence. The canvas state and the perceptual state are two different things, and the canvas has no access to the second one.
What it can't show: the mechanism is genuinely contested. Three hypotheses compete — filling-in, attention-based suppression, and neural adaptation — and all three partially fit the data. The simulation creates conditions for the phenomenon but embeds no hypothesis about why it happens. It also can't distinguish whether you're reporting a genuine perceptual transition or an expectation shaped by knowing about the effect.
063
Eight orientation-selective V1 neurons with overlapping Gaussian tuning curves. A stimulus moves through orientation space; each neuron votes with its firing rate in the direction of its preferred orientation. The population vector (Georgopoulos 1986) decodes the stimulus from the weighted sum. Noise toggle adds Poisson variability to individual neuron responses.
What it shows: individual neurons are ambiguous — each fires over a broad range and cannot alone identify the stimulus. The population vector extracts a precise estimate. Widening the tuning curves (making each neuron more ambiguous) degrades individual responses but barely degrades the decoded estimate; the population absorbs individual imprecision.
What it can't show: where the decoding happens. In the simulation, a formula reads out the population vector from outside. In the brain, there is no external reader — downstream neurons must learn to extract the same information. The simulation shows that the information is present in the population, not that any biological mechanism actually uses it in this way.
064
The Schnakenberg reaction-diffusion model in one dimension. An activator and inhibitor interact across a fixed domain: local self-activation, long-range inhibition. Starting from random noise, periodic peaks emerge — and wherever the wave peaks, a digit can grow. A wavelength parameter (γ) controls how many peaks fit.
What it shows: Hox genes don't specify "finger here" — they control the wavelength of the underlying wave. Change γ and the number of peaks changes; reset with the same γ and peaks form in different positions. The count is determined by the parameter. The positions are determined by the noise.
What it can't show: the actual molecules. In mouse limbs, FGF and Shh are candidates for the activator-inhibitor pair, but this is contested. The simulation is 1D; real limb bud patterning is 3D, and proximal-distal axis specification from other Hox roles adds complexity. The 2012 mouse palate experiment confirmed the predicted 120° branching angle — compelling evidence — but the mechanism has not been definitively established in living tissue for digit spacing.
065
The Hodgkin-Huxley model (1952): four coupled differential equations governing membrane voltage and three voltage-gated ion channel populations (Na activation m, Na inactivation h, K activation n). Fit to squid giant axon data; won the Nobel Prize in 1963. Adjust step current or apply a brief pulse to trigger spikes.
What it shows: The threshold is not a preset parameter — it emerges from competition between autocatalytic Na influx and restoring K/leak currents. Below threshold the restoring forces win; above it, the Na cascade runs away briefly until h (Na inactivation) shuts it down. The spike is all-or-nothing: strength above threshold doesn't change shape. The refractory period — when h ≈ 0 and n is elevated — imposes a biophysical ceiling on firing rate.
What it can't show: individual channel stochasticity (m³h is a population average over thousands of channels, each binary). Spatial propagation along a myelinated axon. The diversity of channel types in real neurons — HH is fit to squid axon; mammalian neurons use a dozen or more subtypes. Synaptic integration, dendritic computation, or burst firing. The model describes the spike and only the spike.
066
Olfaction is the only sense that bypasses the thalamus. Two to three synapses separate the olfactory epithelium from the amygdala. Fear conditioning enlarges specific glomeruli in the olfactory bulb — the convergence structures for individual receptor channels. The amygdala projects centrifugal feedback pathways back to the bulb. Run conditioning trials and watch glomerulus A grow while B–E remain unchanged; run extinction and watch it shrink. The sensor carries the organism's history, keyed by receptor address.
What it shows: the change is odor-specific (only glomerulus A is modified) and reversible (extinction shrinks it back, more slowly than conditioning grew it). After conditioning, the signal arriving at piriform cortex from that glomerulus is already different before any cortical processing occurs. For all other senses, emotional learning modifies responses downstream. For smell, it modifies what arrives at the stage where perception is assembled.
What it can't show: the feedback loop is represented as discrete trials, but the biology involves continuous mutual modification — an enlarged glomerulus strengthens the next signal, which drives stronger amygdala activation, which feeds back to enlarge further. The simulation also requires a baseline starting state that doesn't exist for real organisms: any living animal that has been smelling things already has a history encoded in its bulb. The "naive" starting state is a fiction the simulation needs and biology doesn't have.
067
Two alternating pure tones — low and high — played in sequence. At slow rates or small frequency gaps, most listeners hear a single integrated melody. At fast rates or large gaps, the sequence splits into two independent streams. The phase diagram (van Noorden 1975) shows where current settings fall relative to the fission boundary (below: almost always integrated) and the coherence boundary (above: almost always streaming). An ambiguous zone lies between, where either percept is available and deliberate attention can shift the outcome.
What it shows: the transition between integration and streaming depends on two parameters — rate and frequency gap — in a specific, predictable way. At moderate frequency differences (6–12 semitones), the rate boundary falls in the range of 5–10 tones/second. At very small gaps, even fast rates tend toward integration. At large gaps, slow rates can stream. The phase diagram makes the boundary topology visible.
What it can't show: whether streaming is occurring. The simulation generates identical audio regardless of whether the listener hears one stream or two. The streaming — or integration — happens in the auditory cortex of whoever is listening. The van Noorden phase diagram is not a measurement of the current perceptual state; it is the historical trace of where the boundary fell across many subjects. In the ambiguous zone, the percept is bistable: only one can be heard at a time, and the state can switch. The page has no access to which state is active.
No simulations match the current filter.