Simple Fractal square

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I am working on a math question about infinite series, and one of the question images is below.



iterations of subdividing a square



Each new white square has an area that is 1/4 of the previous square.



Always looking to learn elegant ways to create things using Mathematica, and in this case, probably recursion as well?



I know it's not complicated, but any help with the process would be appreciated.



Having a NICE diagram really helps with creating a better response.
(questions about sums of areas of white, black, etc.)






graphics recursion iteration







share|improve this question

























    up vote
    3
    down vote

    favorite












    I am working on a math question about infinite series, and one of the question images is below.



    iterations of subdividing a square



    Each new white square has an area that is 1/4 of the previous square.



    Always looking to learn elegant ways to create things using Mathematica, and in this case, probably recursion as well?



    I know it's not complicated, but any help with the process would be appreciated.



    Having a NICE diagram really helps with creating a better response.
    (questions about sums of areas of white, black, etc.)






    graphics recursion iteration







    share|improve this question























      up vote
      3
      down vote

      favorite









      up vote
      3
      down vote

      favorite











      I am working on a math question about infinite series, and one of the question images is below.



      iterations of subdividing a square



      Each new white square has an area that is 1/4 of the previous square.



      Always looking to learn elegant ways to create things using Mathematica, and in this case, probably recursion as well?



      I know it's not complicated, but any help with the process would be appreciated.



      Having a NICE diagram really helps with creating a better response.
      (questions about sums of areas of white, black, etc.)






      graphics recursion iteration







      share|improve this question













      I am working on a math question about infinite series, and one of the question images is below.



      iterations of subdividing a square



      Each new white square has an area that is 1/4 of the previous square.



      Always looking to learn elegant ways to create things using Mathematica, and in this case, probably recursion as well?



      I know it's not complicated, but any help with the process would be appreciated.



      Having a NICE diagram really helps with creating a better response.
      (questions about sums of areas of white, black, etc.)






      graphics recursion iteration




      graphics recursion iteration






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 1 hour ago









      Tom De Vries

      1,6351224




      1,6351224




















          2 Answers
          2






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          up vote
          3
          down vote













          coords = 0, 0, 0, 1, 1, 1, 1, 0;
          tf = Composition[TranslationTransform[1/2, 0], ScalingTransform[1/2, 1/2]]
          rects = NestList[tf /@ ## &, coords, 4];
          Graphics[ EdgeForm[Black], Rectangle,
          FaceForm[Gray], Polygon@#, FaceForm[White], Polygon@#2 & @@@ 
          Transpose[rects, Most /@ rects], FaceForm[White], Polygon[Last@rects]]


          enter image description here






          share|improve this answer





























            up vote
            1
            down vote













            n = 100;
            T1 = Developer`ToPackedArray[-1., 0., -0.5, 0., -0.5, 0.5];
            T2 = Developer`ToPackedArray[-0.5, 0.5, 0., 0.5, 0., 1.];
            Graphics[
             Polygon[Table[0.5^k T1, k, 0, n]],
             Polygon[Table[0.5^k T2, k, 0, n]]
             ]


            enter image description here





            share




















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              2 Answers
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              active

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              2 Answers
              2






              active

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              active

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              up vote
              3
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              coords = 0, 0, 0, 1, 1, 1, 1, 0;
              tf = Composition[TranslationTransform[1/2, 0], ScalingTransform[1/2, 1/2]]
              rects = NestList[tf /@ ## &, coords, 4];
              Graphics[ EdgeForm[Black], Rectangle,
              FaceForm[Gray], Polygon@#, FaceForm[White], Polygon@#2 & @@@ 
              Transpose[rects, Most /@ rects], FaceForm[White], Polygon[Last@rects]]


              enter image description here






              share|improve this answer


























                up vote
                3
                down vote













                coords = 0, 0, 0, 1, 1, 1, 1, 0;
                tf = Composition[TranslationTransform[1/2, 0], ScalingTransform[1/2, 1/2]]
                rects = NestList[tf /@ ## &, coords, 4];
                Graphics[ EdgeForm[Black], Rectangle,
                FaceForm[Gray], Polygon@#, FaceForm[White], Polygon@#2 & @@@ 
                Transpose[rects, Most /@ rects], FaceForm[White], Polygon[Last@rects]]


                enter image description here






                share|improve this answer
























                  up vote
                  3
                  down vote










                  up vote
                  3
                  down vote









                  coords = 0, 0, 0, 1, 1, 1, 1, 0;
                  tf = Composition[TranslationTransform[1/2, 0], ScalingTransform[1/2, 1/2]]
                  rects = NestList[tf /@ ## &, coords, 4];
                  Graphics[ EdgeForm[Black], Rectangle,
                  FaceForm[Gray], Polygon@#, FaceForm[White], Polygon@#2 & @@@ 
                  Transpose[rects, Most /@ rects], FaceForm[White], Polygon[Last@rects]]


                  enter image description here






                  share|improve this answer














                  coords = 0, 0, 0, 1, 1, 1, 1, 0;
                  tf = Composition[TranslationTransform[1/2, 0], ScalingTransform[1/2, 1/2]]
                  rects = NestList[tf /@ ## &, coords, 4];
                  Graphics[ EdgeForm[Black], Rectangle,
                  FaceForm[Gray], Polygon@#, FaceForm[White], Polygon@#2 & @@@ 
                  Transpose[rects, Most /@ rects], FaceForm[White], Polygon[Last@rects]]


                  enter image description here







                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited 4 mins ago

























                  answered 14 mins ago









                  kglr

                  167k8188390




                  167k8188390




















                      up vote
                      1
                      down vote













                      n = 100;
                      T1 = Developer`ToPackedArray[-1., 0., -0.5, 0., -0.5, 0.5];
                      T2 = Developer`ToPackedArray[-0.5, 0.5, 0., 0.5, 0., 1.];
                      Graphics[
                       Polygon[Table[0.5^k T1, k, 0, n]],
                       Polygon[Table[0.5^k T2, k, 0, n]]
                       ]


                      enter image description here





                      share
























                        up vote
                        1
                        down vote













                        n = 100;
                        T1 = Developer`ToPackedArray[-1., 0., -0.5, 0., -0.5, 0.5];
                        T2 = Developer`ToPackedArray[-0.5, 0.5, 0., 0.5, 0., 1.];
                        Graphics[
                         Polygon[Table[0.5^k T1, k, 0, n]],
                         Polygon[Table[0.5^k T2, k, 0, n]]
                         ]


                        enter image description here





                        share






















                          up vote
                          1
                          down vote










                          up vote
                          1
                          down vote









                          n = 100;
                          T1 = Developer`ToPackedArray[-1., 0., -0.5, 0., -0.5, 0.5];
                          T2 = Developer`ToPackedArray[-0.5, 0.5, 0., 0.5, 0., 1.];
                          Graphics[
                           Polygon[Table[0.5^k T1, k, 0, n]],
                           Polygon[Table[0.5^k T2, k, 0, n]]
                           ]


                          enter image description here





                          share












                          n = 100;
                          T1 = Developer`ToPackedArray[-1., 0., -0.5, 0., -0.5, 0.5];
                          T2 = Developer`ToPackedArray[-0.5, 0.5, 0., 0.5, 0., 1.];
                          Graphics[
                           Polygon[Table[0.5^k T1, k, 0, n]],
                           Polygon[Table[0.5^k T2, k, 0, n]]
                           ]


                          enter image description here






                          share











                          share


                          share










                          answered 6 mins ago









                          Henrik Schumacher

                          42.8k261127




                          42.8k261127



























                               

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