Cantor dust

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Incomprehensible, non-Wolfram Research-approved code:

start = {{0.0, 1.0}};

dropmid[{s_, f_}] :=

	With[{third = (f - s)/3.0}, {{s, s + third}, {f - third, f}} ];

trcorn = Map[ Transpose,
	NestList[ Function[Flatten[Map[ dropmid, # ], 1]],
		start, 4 ]];

allcorn = Map[
              Map[ Function[Outer[ List, #, # ]], # ]&,
           trcorn];

arr = Map[
       Map[ Apply[ Rectangle, # ]&,
        Transpose[ Map[ Flatten[#, 1]&, # ] ] ]&, allcorn];

Show[ GraphicsArray[
	DiagonalMatrix@Map[Graphics[#, AspectRatio -> 1]&, arr]],
	AspectRatio -> Automatic ]

Designed and rendered using Mathematica 2.2 for the Apple Macintosh.

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