π around 360 on three axes — the turn that never closes

Three turns, one on each axis, each cycling its own 360°. Combine them and trace the point. When the three rates are rational — like 3:2:1 — the path comes home: it closes into a knot and retraces forever. When even one ratio is irrational — anything carrying π — the path never closes and never repeats; it winds densely, filling the torus, because π is irrational and no whole number of turns ever lands back on the start. That is the honest correction to the seed: it is not π-the-angle that wanders (π radians is just 180°, it closes) — it is the irrational ratio that never returns. Then flip on scaling: add a contraction, rotate-and-shrink, and the same winding collapses inward into a self-similar spiral — the move that turns a turn into a fractal. One engine, two infinities, one contraction apart.

Bridge-Burners LLC · Fiddler · rational closes · irrational (π) fills · scaling folds it self-similar · the turn, the torus, the carpet · self-testing