The Pentagram Map — Infinite Zoom

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Projective dynamics  ·  convex pentagons

Join each vertex to its second neighbours; the short diagonals cut out a smaller polygon. Iterate forever. A pentagon returns to its own projective class after one step, so the whole tower is powers of a single projective matrix h — no construction is ever repeated.

Labelled class  ·  returns every 5

Periods, in steps

Generator  · 

Run

Order

Seed

Show

Drag a vertex  ·  5 / 6 to switch  ·  space to hold  ·  R to reseed