Interlace Patterns Emerging in a Penrose-Type Islamic Design

Year: 2024 Authors: Joseph I. Cline

Core claim

Applying a simple Girih rule to an aperiodic Penrose P2 tiling yields infinitely varied closed-loop interlace patterns with complex knotting and self-similarity.

Topics

Penrose tiling, Girih decoration, interlace patterns, self-similarity, mathematical knots

Domains

aperiodic tilings, symmetry groups, knot theory, self-similarity, golden ratio, Islamic geometric art, strapwork, ornamental pattern design

Methods

tiling decoration rule, strand analysis, crossing count, symmetry inspection, computer-generated tilings

Media

Penrose P2 tiling, kite and dart tiles, black line strapwork, fig code, rendered diagrams

Source status

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