Aperiodic Monotile Substitutions

This repository includes several notebooks to generate supertiles of the Hat/Spectre monotiles by L system and substitution rules.

Content

• DynamicSubstituion.nb. - A dynamic module to visualize the construction of hat supertiles.
• HatSubtitution_LSystem_Intro.nb - All analysis about derivation of L system rules to generate the fractal boundary of any-level supertile of the Hat monotile.
• LSystemBoundarSubstitution_Hat.nb - The boundary substitution for the supertiles of the Hat prototile.
• LSystemBoundarSubstitution_Spectre.nb - The boundary substitution for the supertiles of the Spectre prototile.
• Substitution_Code_Spectre.nb - Use code to represent the tile rather than graphics primitive to do substitution, which is more efficient.
• Substitution_Hat_Visual.nb - Generate different visualizations including figures and videos.
• Substitution_Hat_Analysis.nb - Analyze the subtitution process in detail at one section, and count the number of different metatiles.

Related Links

• Hat tiling: fractal subtitution. Wolfram Community
• An aperiodic monotile
• A chiral aperiodic monotile