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‎README.md

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[![View Pixel Grid on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/69490-penrose-rhombus-tiling)
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# Penrose Rhombus Tiling
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This repository contains MATLAB functions for visualizing a type of Penrose tiling. Penrose tilings are non-periodic and self-similar. The particular tiling implemented here, called P3, is constructed from a pair of rhombuses, a thin one and a thick one.
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![](doc/penrose-screen-shot.png)
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Copyright 2019 The MathWorks, Inc.

‎aTriangle.m

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function t = aTriangle(Apex,Left,Right)
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%aTriangle Representation of type A triangle in table form.
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% t = aTriangle(apex,left,right) returns a type A triangle represented as
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% a one-row table. The triangle vertices (apex, left, and right) are
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% complex numbers. If one of the triangle vertices is empty, it is
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% computed automatically.
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%
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% EXAMPLE
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% Compute a type A triangle with apex at (0,1) and left base vertex at
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% (0,0) in the complex plane.
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%
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% t = aTriangle(1i,0,[])
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% Copyright 2018 The MathWorks, Inc.
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[Apex,Left,Right] = isoscelesTriangle(Apex,Left,Right,36);
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Type = categorical("A");
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t = table(Apex,Left,Right,Type);

‎apTriangle.m

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function t = apTriangle(Apex,Left,Right)
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%aTriangle Representation of type A-prime triangle in table form.
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% t = aTriangle(apex,left,right) returns a type A-prime triangle
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% represented as a one-row table. The triangle vertices (apex, left, and
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% right) are complex numbers. If one of the triangle vertices is empty,
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% it is computed automatically.
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%
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% EXAMPLE
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%
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% Compute a type A-prime triangle with apex at (0,1) and left base vertex
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% at (0,0) in the complex plane.
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%
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% t = apTriangle(1i,0,[])
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% Copyright 2018 The MathWorks, Inc.
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[Apex,Left,Right] = isoscelesTriangle(Apex,Left,Right,36);
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Type = categorical("Ap");
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t = table(Apex,Left,Right,Type);

‎bTriangle.m

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function t = bTriangle(Apex,Left,Right)
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%bTriangle Representation of type B triangle in table form.
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% t = bTriangle(apex,left,right) returns a type B triangle represented as
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% a one-row table. The triangle vertices (apex, left, and right) are
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% complex numbers. If one of the triangle vertices is empty, it is
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% computed automatically.
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%
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% EXAMPLE
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% Compute a type B triangle with apex at (0,1) and left base vertex at
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% (0,0) in the complex plane.
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%
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% t = bTriangle(1i,0,[])
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% Copyright 2018 The MathWorks, Inc.
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[Apex,Left,Right] = isoscelesTriangle(Apex,Left,Right,108);
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Type = categorical("B");
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t = table(Apex,Left,Right,Type);

‎bpTriangle.m

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function t = bpTriangle(Apex,Left,Right)
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%bpTriangle Representation of type B-prime triangle in table form.
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% t = bpTriangle(apex,left,right) returns a type B-prime triangle
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% represented as a one-row table. The triangle vertices (apex, left, and
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% right) are complex numbers. If one of the triangle vertices is empty,
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% it is computed automatically.
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%
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% EXAMPLE
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%
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% Compute a type B-prime triangle with apex at (0,1) and left base vertex
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% at (0,0) in the complex plane.
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%
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% t = bpTriangle(1i,0,[])
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% Copyright 2018 The MathWorks, Inc.
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[Apex,Left,Right] = isoscelesTriangle(Apex,Left,Right,108);
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Type = categorical("Bp");
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t = table(Apex,Left,Right,Type);

‎decomposeATriangle.m

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function out = decomposeATriangle(in)
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%decomposeATriangle Decompose type A triangle.
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%
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% t = decomposeATriangle(in) decomposes a type A triangle into a type A
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% and a type B-prime triangle. The input is a one-row table as returned
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% by aTriangle, and the output is a two-row table.
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% Copyright 2018 The MathWorks, Inc.
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out = [ ...
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aTriangle(in.Left,in.Right,[])
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bpTriangle([],in.Apex,in.Left) ];

‎decomposeApTriangle.m

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function out = decomposeApTriangle(in)
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%decomposeApTriangle Decompose type A-prime triangle.
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%
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% t = decomposeApTriangle(in) decomposes a type A-prime triangle into a
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% type A-prime and a type B triangle. The input is a one-row table as
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% returned by apTriangle, and the output is a two-row table.
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% Copyright 2018 The MathWorks, Inc.
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out = [ ...
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apTriangle(in.Right,[],in.Left)
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bTriangle([],in.Right,in.Apex) ];

‎decomposeBTriangle.m

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function out = decomposeBTriangle(in)
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%decomposeBTriangle Decompose type B triangle.
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%
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% t = decomposeBTriangle(in) decomposes a type B triangle into a type A
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% triangle, a type B triangle, and a type B-prime triangle. The input is
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% a one-row table as returned by bTriangle, and the output is a three-row
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% table.
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% Copyright 2018 The MathWorks, Inc.
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t_b = bTriangle([],in.Right,in.Apex);
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t_a = aTriangle(t_b.Apex,in.Apex,[]);
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t_bp = bpTriangle(t_a.Right,in.Left,t_a.Apex);
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out = [t_b ; t_a ; t_bp];
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‎decomposeBpTriangle.m

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function out = decomposeBpTriangle(in)
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%decomposeBpTriangle Decompose type B-prime triangle.
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%
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% t = decomposeBpTriangle(in) decomposes a type B-prime triangle into a
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% type B-prime triangle, a type A-prime triangle, and a type B triangle.
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% The input is a one-row table as returned by bpTriangle, and the output
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% is a three-row table.
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% Copyright 2018 The MathWorks, Inc.
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t_bp = bpTriangle([],in.Apex,in.Left);
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t_ap = apTriangle(t_bp.Apex,[],in.Apex);
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t_b = bTriangle(t_ap.Left,t_ap.Apex,in.Right);
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out = [t_bp ; t_ap ; t_b];
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‎decomposeTriangles.m

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function out = decomposeTriangles(in)
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%decomposeTriangles Decompose a table of A, A', B, and B' triangles.
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%
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% decomposeTriangles decomposes each triangle in the input table and
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% returns all the decomposed triangles together as a new table.
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%
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% EXAMPLE
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% Starting with an A triangle, successively apply triangle
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% decomposition three times and display the result.
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%
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% t = aTriangle(1i,0,[]);
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% for k = 1:3
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% t = decomposeTriangles(t);
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% end
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% showLabeledTriangles(t)
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% Copyright 2018 The MathWorks, Inc.
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c = cell(height(in),1);
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for k = 1:height(in)
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t_k = in(k,:);
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switch in.Type(k)
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case "A"
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c{k} = decomposeATriangle(t_k);
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case "Ap"
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c{k} = decomposeApTriangle(t_k);
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case "B"
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c{k} = decomposeBTriangle(t_k);
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case "Bp"
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c{k} = decomposeBpTriangle(t_k);
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end
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end
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out = cat(1,c{:});

‎doc/PenroseRhombusTiling.mlx

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