bakersmap.wl

precision := 1000
bakers[x_, y_] := Piecewise[{
   {
    {2 x, y/2}, 0 <= x <= 1/2},
   {
    {2 - 2 x, 1 - y/2}, 1/2 <= x <= 1}
   }
  ]
ColorUtil[x_] := Piecewise[{
   {Red, 0 <= x <= 1/6},
   {Orange, 1/6 < x <= 2/6},
   {Yellow, 2/6 < x <= 3/6},
   {Green, 3/6 < x <= 4/6},
   {Blue, 4/6 < x <= 5/6},
   {Purple, 5/6 < x <= 6/6}
   }]
(*original points*)
UnitSquare := 
 SortBy[Table[{RandomReal[], RandomReal[]}, {i, 1, precision}], 
  First]
BakeTheSquare[sq_] := Table[bakers[c[[1]], c[[2]]], {c, sq}]

SquareSize := Length[UnitSquare]


(*is this part necessary?*)
(*gen data*)
For[n = 0, n < 30, n++,
 Export["bakers_iteration_" <> ToString[n] <> ".mx",
  Nest[BakeTheSquare, UnitSquare, n]
  ]
 ]
(*import*)maps := 
 Table[Import["bakers_iteration_" <> ToString[n] <> ".mx"], {n, 0, 29}]
(*draw points*)
coloured = Table[
  Table[
   {
    ColorUtil[c/SquareSize],
    Point[
     maps[[n]][[c]]
     ]
    },
   {c, 1, Length[maps[[n]]]}
   ],
  {n, 1, Length[maps]}
  ]

coloures := Table[
  ColorUtil[maps[[1]][[c]][[1]]],
  {c, 1, Length[maps[[1]]]}
  ]

retraction[start_, end_, t_] := end*t + (1 - t) start
(*The final guy tm*)
frames := Table[
  Graphics[
   {
    Text["Iteration: " <> ToString[Floor[n]], {0.5, -.05}],
    PointSize -> Large,
    {Black , Rectangle[{-0.02, -0.02}, {1.02, 1.02}]},
    Point[ 
     retraction[maps[[Floor[n]]], maps[[Floor[n + 1]]], Mod[n, 1]],
     VertexColors -> coloures
     ]
    }],
  {n, 1, 29, .05}
  (*{t,0,1}*)
  ]

gif = ListAnimate[frames, 60] /. 
  HoldPattern[
    AppearanceElements -> _] -> (AppearanceElements -> None)

Table[
 Export["bakers/bakers_" <> ToString[i] <> ".svg", frames[[i]]],
 {i, 1, Length[frames]}
 ]