Thanks, Brad. That's closer to what I want, but Lucas V. B. has gone ahead and done something that does the job perfectly. So I think I'll use his video in my talk, provided I can figure out how to display a .webm file from within PowerPoint (or convert it to an .mp4). Thanks, Jim On Sat, Aug 3, 2019 at 12:50 PM Brad Klee <bradklee@gmail.com> wrote:
Hi Jim,
Just create a parallelogram and use parameter "or" to change the origin:
(* slightly revised, v0.2 *)
TriVerts = Sqrt[3] {Sin[2 Pi #/3], Cos[2 Pi #/3]} & /@ Range[3];
poly[time_, or_] := Switch[{time >= 1/3, time <= -1/3}, {True, _}, Polygon[or + # & /@ (TriVerts (1 - time))], {_, True}, Polygon[or + # {1, -1} & /@ (TriVerts (time + 1))], {_, _}, Polygon[{ poly[1/3 + 2 time, or - {1, Sqrt[3]/3}][[1, 1]], poly[1/3 + 2 time, or - {1, Sqrt[3]/3}][[1, 3]], poly[1/3 + 2 time, or + {0, 2/Sqrt[3]}][[1, 2]], poly[1/3 + 2 time, or + {0, 2/Sqrt[3]}][[1, 1]], poly[1/3 + 2 time, or + {1, -1/Sqrt[3]}][[1, 3]], poly[1/3 + 2 time, or + {1, -1/Sqrt[3]}][[1, 2]]}]]
G[time_, or_] := Graphics[{EdgeForm[Thick], { ColorData["TemperatureMap"][time/2], poly[1/3 + (2/3) time, {0, 0} + or]}, { ColorData["TemperatureMap"][1/2 + time/2], poly[-1 + (2/3) time, {2, 2 Sqrt[3]/3} + or]}, Blend[{ColorData["TemperatureMap"][1 - time], Green}, 2 (1/4 - (1/2 - time)^2)], poly[1/3 time, {1, Sqrt[3]/3} + or] }, PlotRange -> {{-2, 4}, {-2, 3}}]
ListAnimate[G[#/100, {0, 0}] & /@ Range[0, 100]]
ListAnimate[Show[Table[ G[#/100, {2*i + j, Sqrt[3] j}], {i, 0, 5}, {j, 0, 5}], PlotRange -> {{-4, 20}, {-2, 13}}, ImageSize -> 800] & /@ Range[0, 100]]
To explain relation to Z^3, you can also draw a cube and put the RGB color gradient directly onto the faces of the cube.
Cheers --Brad
On Sat, Aug 3, 2019 at 6:43 AM James Propp <jamespropp@gmail.com> wrote:
I was able to run it just now and it looks good. Thanks, Brad! Unfortunately I'm not enough of a Mathematica-wizard to modify Brad's
code
to give me what I want, namely, a morphing tessellation. I need the visuals to convey the sense that the pattern repeats throughout the whole plane.
Jim
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