シェルピンスキーのカーペット（Mathematicaショートフラクタルシリーズ） ref: http://qiita.com/butchi_y/items/3b164bb8e25dad7763cc

file0.txt

sierpinskiCarpet[x_] := ArrayFlatten[x /. {
  0 -> {
   {0, 0, 0},
   {0, 0, 0},
   {0, 0, 0}
  },
  1 -> {
   {1, 1, 1},
   {1, 0, 1},
   {1, 1, 1}
  }
}]
ArrayPlot[Nest[sierpinskiCarpet, 1, 5], PixelConstrained -> 1, Frame -> False]

file1.txt

In[1] = sierpinskiCarpet[1]
Out[1] = {{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}

file2.txt

  1 -> {
   {1, 1, 1},
   {1, 0, 1},
   {1, 1, 1}
  }

file3.txt

In[2] = sierpinskiCarpet[sierpinskiCarpet[1]]
Out[2] = {{1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 1, 1, 0, 1, 1, 0, 1}, {1, 1, 1, 
  1, 1, 1, 1, 1, 1}, {1, 1, 1, 0, 0, 0, 1, 1, 1}, {1, 0, 1, 0, 0, 0, 
  1, 0, 1}, {1, 1, 1, 0, 0, 0, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 
  1}, {1, 0, 1, 1, 0, 1, 1, 0, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1}}

file4.txt

ArrayPlot[sierpinskiCarpet[sierpinskiCarpet[1]]]

file5.txt

{{{{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}, {{1, 1, 1}, {1, 0, 1}, {1, 1, 
    1}}, {{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}}, {{{1, 1, 1}, {1, 0, 
    1}, {1, 1, 1}}, {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}, {{1, 1, 1}, {1,
     0, 1}, {1, 1, 1}}}, {{{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}, {{1, 1, 
    1}, {1, 0, 1}, {1, 1, 1}}, {{1, 1, 1}, {1, 0, 1}, {1, 1, 1}}}}

file6.txt

ArrayPlot[Nest[ArrayFlatten[#/.{0->ConstantArray[0,{3,3}],1->{{1,1,1},{1,0,1},{1,1,1}}}]&,1,5]]

file7.txt

ArrayPlot[
  Nest[
    ArrayFlatten[
      #/.{
        0 -> ConstantArray[0,{3,3}],
        1 -> {{1,1,1},{1,0,1},{1,1,1}}
      }
    ]&,
    1,
    5
  ],
  PixelConstrained->1,
  Frame->False
]

file8.txt

Graphics[Raster[Nest[
  ArrayFlatten[
    #/.{
      1 -> ConstantArray[1,{3,3}],
      0 -> {{0,0,0},{0,1,0},{0,0,0}}
    }
  ]&,
  0,
  5
]]]