Cut by φ, forever.
Start with a fat rhomb (72° / 108°) and a thin one (36° / 144°). Robinson's rules slice each into halves of the same two kinds — the fat half breaks into three smaller pieces, the thin into two — and every edge shrinks by a factor of φ = 1.6180339…, the golden ratio. Then you cut again.
That is all the canvas above is doing. Each time the camera closes in by one factor of φ, every rhomb in view subdivides once and the tally in the corner ticks up a generation. The construction has no bottom; the zoom has no end.
The rule that forbids repetition.
The two rhombs alone would happily tile like wallpaper. Penrose forbade it with a decoration: two arcs cross every tile, cutting each edge at 1/φ and 1/φ² of its length. Tiles may only meet where the arcs continue across the joint.
That single local constraint has a global consequence — no arrangement that obeys it ever settles into a repeating block. Watch the field: every thirteen seconds the arcs surface in gilt, knit across the tiles, and sink back into the lapis.
Everywhere familiar, nowhere identical.
Conway proved the paradox: circle any patch of this tiling and the same patch appears again infinitely often — never farther away than a couple of its own diameters. Yet slide the whole plane any distance, in any direction, and it will not line up with itself. Not once.
The witness is in the corner of the screen. The count of fat to thin rhombs drifts toward φ as the field deepens — and φ is irrational, so no finite repeating block could ever produce it.
Craftsmen at the Darb-i Imam shrine in Isfahan laid girih strapwork with this deep structure in 1453, five centuries before Roger Penrose published his rhombs in 1974 and de Bruijn caught them in a pentagrid in 1981. The pattern was never invented. It was found, twice.