5
Using ArrayPad + Fold + Nest + MatrixPlot
ClearAll[padMat]
padMat = Fold[ArrayPad[#, RotateLeft[{{0}, {Length @ #, 0}}, #2 - 1], 1 + Max @ #] &,
#, {1, 2}] &;
Examples:
With[{n = 6}, MatrixPlot[Nest[padMat, {{1}}, n] /. x_Integer :> ColorData[97][x],
ImageSize -> 600, Frame -> False, Mesh -> All]]
Grid @ Partition[#, 3] & @ ...
4
We can also use affine transformations of the unit rectangle to get the desired picture:
ClearAll[rectangleCoords]
rectangleCoords[n_] := Module[{mod = Mod[Range[0, n - 2], 2],
sy = 2^Floor[Range[0, n - 2]/2], rcoords = {{0, 0}, {1, 1}}},
Through[(Reverse @ Prepend[Identity][AffineTransform[{{{#, 0}, {0, #2}}, {##3}}] & @@@
(Transpose[{(1 + ...
1
We can also recursively divide the bottom-right rectangle into three rectangles as follows:
ClearAll[threerects, step, rectlist]
threerects = # /. Rectangle[{a_, b_}, {c_, d_}] :>
{Rectangle[{a, (b + d)/2}, {c, d}],
Rectangle[{a, b}, {a + c, b + d}/2],
Rectangle[{(a + c)/2, b}, {c, (b + d)/2}]} &;
Graphics[MapIndexed[{{Red, Green,...
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