Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Return a substitution tiling
ResourceFunction["AlgebraicSubstitutionTiling"][tiling,steps] with the given tiling system specified by tiling, return the state after steps substitutions. 
Show a starting kite after two substitution steps with the Penrose kites and darts tiling system:
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With steps=0, the substitution tiling itself is shown, as with the Penrose kites and darts tiling system:
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Show the pinwheel tiling with an alternate start:
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Show the numerically approximated second step of all namesupported tilings:
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The Penrose kites&darts tiling system with the root, algebraic points in terms of that root, polygon substitutions and polygon types:
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A chord tiling with a plastic constant (ρ) root, algebraic points in terms of ρ, polygon substitutions and polygon types:
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Show polygons of every step as a layered graphic:
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The psiquad substitution tiling is based on the Narayana cow sequence constant, ψ≈1.465571231876768, also called the supergolden ratio, shown here with sixteen levels of substitution:
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The rhoquad substitution tiling is based on the plastic constant, ρ≈1.324717957244746, shown here with thirteen levels of substitution on top of the initial tile:
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Use numeric approximation to show and compare growth with alternate starting positions for the Penrose rhombs and the GodrècheLançon binary tiling systems:
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Tilings from the blog article Shattering the Plane with Twelve New Substitution Tilings Using 2, φ, ψ, χ, ρ:
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One of many variants of a tiling based on a root of χ^{4}χ1=0:
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Counts of the triangles of different sizes in the above tiling:
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Wolfram Language 11.3 (March 2018) or above
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