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up vote 2 down vote favorite

I want to add a quarter circle to delimit the evolution of the 2D CA with code 746 (which is almost circular) like it's shown here

I tried what's shown below, but I can't get the Epilog to show, why?

Manipulate[ ArrayPlot[
  (ca = CellularAutomaton[
      {746, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}},
      {Table[1, {5}, {1}], 0}, {{{steps}}}])
   [[1 ;; Floor[Dimensions[ca][[1]]/2], 
    Floor[Dimensions[ca][[2]]/2] ;; -1 ]]
  ,

  ImageSize -> {460, 330}, Frame -> False, 
  Epilog -> {Circle[{0, 0}, 1, {0, Pi/2}]}], {{steps, 100}, 1, 1000, 
  1, Appearance -> "Labeled"}]
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up vote 3 down vote accepted

Try this:

Manipulate[
 ArrayPlot[(ca = 
     CellularAutomaton[{746, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 
          2}}}, {1, 1}}, {Table[1, {5}, {1}], 0}, {{{steps}}}])[[1 ;; 
     Floor[Dimensions[ca][[1]]/2], 
    Floor[Dimensions[ca][[2]]/2] ;; -1]], ImageSize -> {460, 330}, 
  Frame -> False, AspectRatio -> 1, 
  Epilog -> {Red, Thick, 
    Circle[{0, 0}, Scaled[1], {0, Pi/2}]}], {{steps, 100}, 1, 1000, 1,
   Appearance -> "Labeled"}]

circle

It shows the circle. The original radius was just not large enough on the scale of the plot. I replaced it by a scaled quantity so that it always extends to the end.

share|improve this answer
up vote 2 down vote

One can use the DataRange option of ArrayPlot.

Manipulate[
 ArrayPlot[
   (ca = CellularAutomaton[{746, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}},
      {Table[1, {5}, {1}], 0},
      {{{steps}}}])[[1 ;; Floor[Dimensions[ca][[1]]/2],
    Floor[Dimensions[ca][[2]]/2] ;; -1]],
  ImageSize -> {460, 330},
  DataRange -> {{0, 1}, {0, 1}},
  Frame -> False, 
  Epilog -> {Red, Circle[{0, 0}, 1, {0, Pi/2}]}], {{steps, 100}, 1, 
  1000, 1, Appearance -> "Labeled"},
 {ca, ControlType -> None}]

Mathematica graphics

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