lateral inhibition · so1omon.net

The gradient below is physically smooth — luminance ramps from dark to light with flat regions on either side. There are no bands. But look at where the ramp meets the flat regions: a dark stripe at the bottom of the ramp, a bright stripe at the top. Those bands don't exist in the physical stimulus. They're computed by the retina before the signal reaches the brain.

physical stimulus

perceived (neural response) — drag inhibition to zero to disable bands

response profile

inhibition strength 0.65

surround radius 18 cells

Mach bands detected at the ramp shoulders — darker at bottom, brighter at top. Both bands are artifacts of lateral inhibition. The retina is computing where the luminance slope changes, not where luminance is high or low.

mechanism

Each retinal ganglion cell has a center-surround receptive field: it collects light from a small central area (excitatory) and is inhibited by activity in a wider surrounding ring. The cell fires in proportion to how much brighter its center is than its surround.

Midway along the ramp: center is bright, but so is the surround → moderate response.
At the top shoulder (ramp meets bright flat): center is bright, surround is partly still on the ramp → center wins by more → fires stronger than the flat region.
At the bottom shoulder (dark flat meets ramp): center is dark, but surround is partly on the ramp (brighter) → inhibition wins by more → fires weaker than the flat region.

The result: a dark band that doesn't exist and a bright band that doesn't exist, at the exact locations where the slope of the luminance gradient changes.

This was first described by Ernst Mach in 1865. He proposed a mechanism involving mutual inhibition between retinal cells — an inference from a perceptual phenomenon. The cellular mechanism (center-surround receptive fields in retinal ganglion cells) wasn't confirmed until Kuffler's 1953 microelectrode recordings.

what the cell is computing

The center-surround response approximates a second derivative of the luminance profile — not luminance itself, and not the first derivative (edges), but where the rate of change is itself changing. The Mach bands mark exactly those inflection points.

This is what the visual system sends to the brain: not a copy of the world's luminance, but a compressed representation of its structure — boundaries, gradients, sudden changes. The flat regions carry almost no signal once lateral inhibition has run. The edges carry everything.

The implication: what feels like "seeing brightness" is already a highly processed derivative. The Mach bands aren't a bug. They're the readout of the computation, made visible at the seam.

step vs. trapezoid

A sharp step (no ramp) produces a single edge response — the boundary appears enhanced, the interior suppressed, but no Mach bands. Mach bands require a region of changing slope: the ramp's start and end are precisely where the second derivative spikes.

In the multi-ramp pattern, every slope change produces a pair of bands. The physical pattern has no bands anywhere; the perceived pattern is a sequence of enhanced edges wherever the slope structure changes. Try it above.