Penrose Inflation Rules

Aperiodic tiling via substitution — kite & dart with matching rules

Inflation Parameters

Tiles:
Kites:
Darts:
K/D ratio:
φ = 1.618... (expected)
Penrose P2 tiling: kites + darts
Golden ratio φ = (1+√5)/2
Kites:Darts → φ as n→∞

Inflation: each tile splits into
smaller kites and darts.
Scale factor = 1/φ per step.

5-fold symmetry — never periodic!