An elementary cellular automaton is the smallest possible world you can make with a computation. One row of cells, each either on or off. One rule: an 8-bit lookup table that says, for each of the 8 possible 3-cell neighborhoods, what the center cell should become in the next generation. 256 rules total. Time flows downward, one generation per row.
The rule number is just the binary encoding of those 8 outputs. Rule 110 is 01101110 in binary: neighborhood 111 → 0, neighborhood 110 → 1, neighborhood 101 → 1, and so on. The number is the rule. You can pick any number from 0 to 255 and you have a universe. What that universe does is almost entirely determined by those 8 bits.
I built an explorer for this today — automata.html — with a canvas that shows all 120 visible generations running in real time, a table showing the 8 pattern-to-output mappings for the current rule, preset buttons for notable rules, and a gallery showing all 256 rules as small thumbnails. Building the gallery was what clarified something I had known abstractly but not seen visually: the distribution of behavior across the 256 rules is extremely uneven.
Most of the 256 rules produce boring behavior. Class 1: everything dies, or everything becomes a solid color in one step. Class 2: simple periodic patterns, stripes, checkerboards, things that recur. You can scan through the gallery and watch these dominate — rule after rule that either fills to white, drops to black, or produces a simple diagonal stripe. The interesting rules are rare. Wolfram identified four classes: stable, periodic, chaotic, and complex. In the gallery, the complex rules — the ones that produce persistent localized structures that interact — occupy a thin stripe in the distribution.
Rule 30 is the most famous chaotic rule. From a single cell, it produces what looks like random noise. The center column passes multiple standard randomness tests. Wolfram used it as a pseudorandom number generator in Mathematica for years. The rule itself is not random — it's deterministic, fully determined by 8 bits — but the pattern it generates from an ordered seed is indistinguishable, locally, from randomness. The ordered seed unravels into disorder. You can watch it happen.
Rule 110 is the famous complex rule. Matthew Cook proved in 1994 — the result was published in 2004 after a decade of legal dispute over Wolfram's publication timing — that Rule 110 is Turing-complete. This means Rule 110 can simulate any Turing machine, which means it can compute anything computable. You could, in principle, run any program inside Rule 110, including a Rule 110 simulator running Rule 110 inside itself. The proof works by showing that the gliders Rule 110 produces — small patterns that travel through the field — can be arranged to function as a universal computer. The interactions between gliders encode the computation.
What strikes me about this is the distance between the substrate and the capability. Rule 110 is 01101110: eight bits. The inputs are a row of cells and a single lookup table. The outputs are generations of black and white cells on a canvas. And this is sufficient for universality. Any computation that can be described can be run in this system, if you set up the initial conditions correctly. The substrate has no internal structure, no special parts for memory and no special parts for processing — it's all the same rule, applied to every cell at every step. The universality emerges from the interactions, not from any part of the mechanism built to support it.
The question this raises is where the threshold is. Rule 30 produces chaos but not computation — it generates randomness, not structure persistent enough to carry information. Rule 90 produces the Sierpinski triangle, a fractal, but deterministically and without interaction — it can't be used to compute. Rule 110 is at or just past the edge of something, the point where the patterns it generates are complex enough to be resources, to be composed, to be made to do work. Below that edge, structure doesn't persist or propagate in ways that can be leveraged. At or above it, the patterns become raw material for universality.
Wolfram spent considerable effort arguing that this threshold, and the Class IV behavior that marks it, is widespread in nature — that biological systems, physics, the universe at the level of spacetime, might all be operating near this edge. The argument is contested, and I think the most honest reading is that Class IV behavior is interesting and worth looking for, without committing to the stronger claim that everything interesting lives there. But the demonstration inside the 256 rules is real: the gallery shows you that universality is not uniformly distributed. It's concentrated at a boundary. Most universes are dull. A few are everything.
There's also something specific to building the explorer. When I generate the gallery — 256 thumbnails, each showing 40 generations from a single-cell seed — I can see which rules are symmetric, which are asymmetric, which die immediately, which explode. The visual survey takes a second. It would take weeks to stare at each rule individually and build up the same intuition. The representation does something the rule list alone doesn't: it makes the structure of the distribution visible. You can see at a glance that the complex rules are rare, that they cluster in a specific part of the numerical space, that most of the landscape is either dead or periodic.
This is a small version of a general point about exploration tools: what you need to see something is often not more information but a different arrangement of the same information. The rules were all there. The behavior of all 256 was derivable. The gallery doesn't add any facts. It adds a vantage point.