Reverse Reverse

Philosophy — the image genuinely does not know. Take a cloud of dots on the surface of a sphere, turn it about the vertical axis, and draw it with an orthographic camera: no perspective, every dot the same size and the same brightness whatever its depth, nothing hidden behind anything. Now mirror the whole thing in depth, so every point at z moves to −z, and turn it the other way. The two produce pixel-identical images, forever, because the projection throws away the coordinate the two versions differ in. This is not an artist's trick or a near-miss; it is an exact algebraic degeneracy. What you see when you look at it is therefore not a reading of the evidence — the evidence is silent — it is a construction your visual system commits to and then defends. Wallach and O'Connell called the general phenomenon the kinetic depth effect in 1953: a flat moving shadow spontaneously acquiring a solid three-dimensional form. The reversals are the interesting part. A perceptual system that had merely computed the answer would not keep changing it. The flips look much more like a system that has to pick a winner among equals, gets bored of its winner, and picks again — which is roughly what the bistable-perception literature has converged on, and which is why watching yourself do it feels like catching your own mind mid-sentence.

Technique — what it costs to keep the image honest. Almost every piece of graphics code you would write by reflex is a depth cue, and any one of them silently ends the illusion. Perspective divide: a cue. Scaling dots with distance: a cue. Fog, shading, occlusion, z-sorting with opaque fills, a drop shadow, antialiasing that happens to differ front and back: all cues. So the renderer here is deliberately impoverished. Projection is orthographic — (x, y, z) → (x, y), no divide. At cue = 0 every dot in a cloud is emitted into a single path and filled once, at one radius and one alpha, so there is no per-dot state that could leak depth; a wire is stroked as one path at one width; the silhouette is the nonzero-winding union of every triangle in the mesh filled flat, which is why it has no interior line at all. The mesh is not depth-sorted at cue = 0 because with a single flat colour the sort order is unobservable. Every loop is animated from phase = (t mod period) / period and never from an accumulated delta, so the frame at phase 0 is bit-identical to the frame at phase 1 and a recording of one period loops without a seam. And the cue dial is the same code path with the terms switched on: scale = 1/(1 − cue·k·z) for perspective, radius × (1 + cue·z·k) for size, alpha falling off with depth, lambert shading mixed in by cue for the silhouette. At cue = 0 each of those expressions is exactly its identity, which is the property that makes the claim checkable rather than aspirational.

Aesthetics — a training instrument, not a poster. The temptation with these shapes is to make them beautiful, and beauty here means texture, and texture means cues. So the palette is one colour of dot on one colour of ground, and the only chromatic decisions in the whole site are the two percept colours — cyan for leftward, amber for rightward — used in the timeline strip and on the drill's target arrow so that "what I saw" and "what I was asked for" are the same two colours everywhere. The timeline strip is the piece that changed how the thing feels to use: once your reported percept is drawn as a band of colour over ninety seconds, you stop experiencing flips as events and start seeing your own bistability as a texture, with a characteristic dwell time that visibly shortens as you get better at forcing it. The silhouette is the one stimulus that gets its own paper-white ground, because a silhouette has to be the dark thing; that is the whole point of a silhouette, and it is the oldest of these illusions in popular form — Nobuyuki Kayahara's spinning dancer, 2003. The arrow and the chair are the same construction with the paper the other way up: a flat light fill on the dark ground, no outline and no interior edge, so all you are given is a shape that widens and narrows.

Honest weaknesses. The nine are not equally good, and the page order is the honest order. The arrow is first because it is the loop that went round this week and because it is the cleanest case in the set: an arrow is mirror-symmetric about its own vertical plane, so its depth-mirror is the same arrow, and the two readings are the same picture rather than two theories about a picture. The chair is that trick applied to an object you have opinions about, and it is noticeably stickier for exactly that reason. Sphere and cylinder are the lab standards and they flip freely for almost everyone. The cube is a Necker cube in motion and flips readily but the flip is as much a figural reversal as a motion reversal, which is a slightly different phenomenon wearing the same coat. The ring is the crispest of the lot for some people and stubborn for others, because thirty-two dots on one ellipse is very little evidence and the percept can lock. The silhouette depends heavily on the shape: this one is a lathe-turned vessel with a spout, which reverses well when the spout is near the edges of its sweep and rather less well when it is pointing straight at you. The last one is the honest failure. It is named dual-axis after Frank Force's 2019 Best Illusion of the Year, in which a single loop reads as spinning about a vertical axis and about a horizontal one; what is shipped here is a tennis-ball-seam curve turning about an axis that leans out of the screen, so its two readings are "leaning towards me" and "leaning away" — a real second axis, but not the vertical-versus-horizontal read that makes Force's version famous. The README says why the obvious constructions do not get there. Finally: none of this measures your percept. It records the key you pressed. Every number on the site is a number about your reporting, which lags the flip by a reaction time and can be wrong on purpose, and there is no way around that in a browser.