A Truchet Tiling Hidden in Ammann-Beenker Tiling

Year: 2023 Authors: Pierre Gradit; Vincent Van Dongen

Core claim

The [1:0] limit of the integer-parameterized Ammann-Beenker projection produces a Truchet tiling equivalent to patterns described in corner percolation and hitomezashi literature.

Topics

Ammann-Beenker tiling, Truchet tilings, integer projection, limit-case patterns, visual equivalence

Domains

aperiodic tilings, Pell sequence, Beatty sequence, 4D lattice projection, mod 2 arithmetic, mathematical art, pattern design, textile-inspired design

Methods

deflation, [[methods/parametric-x-y-projection|parametric [x:y] projection]], transparency checking, visual comparison, syntactic equivalence

Media

Truchet tiles, square and rhombus tiles, 4D integer lattice, digital images, software-generated tilings

Source status

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