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[GIF] Derange (Deforming a plain weave)

Posted 2 years ago
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Deforming a plain weave

Derange

I always find weaving patterns a challenge, since the way my brain wants to think of them (as a collection of long strands passing over and under other long strands) doesn't usually match with what I can easily make Mathematica do (since there's no consistent way of layering the strands).

In any case, when I saw this, it was more obvious than usual how to recreate it fairly easily (using short strands). Once I'd done that, I just played around until I got an animation I liked.

Here's the (slightly ugly) code:

DynamicModule[{f, cols, angle},
 f = π Piecewise[{{0, # < 0}, {1/2 - 1/2 Cos[#], 0 <= # < π}, {1, # >= π}}] &;
 cols = RGBColor /@ {"#EEEEEE", "#00ADB5", "#303841"};
 Manipulate[
  Graphics[
   {Thickness[.02],
    Table[{angle = f[(θ - π (i + j + 10)/20)];
      Blend[cols[[{1, 2, 1}]], angle/π],
      Line[({i, j} + RotationMatrix[angle].#) & /@ {{-.7, 0}, {.7, 0}}],
      Line[({i + 1, j} + RotationMatrix[angle].#) & /@ {{0, -.7}, {0, .7}}]},
     {i, -4, 4, 2}, {j, -4, 4, 2}],
    Table[{angle = f[(θ - π (i + j + 10)/20)];
      Blend[cols[[{1, 2, 1}]], angle/π],
      Line[({i, j} + RotationMatrix[-angle].#) & /@ {{-.7, 0}, {.7, 0}}],
      Line[({i + 1, j} + RotationMatrix[-angle].#) & /@ {{0, -.7}, {0, .7}}]},
     {i, -5, 5, 2}, {j, -5, 5, 2}]},
   PlotRange -> 4.75, ImageSize -> 540, Background -> cols[[3]]],
  {θ, 0, 2 π}]
 ]
6 Replies

I really enjoy this, thanks a lot for sharing! This is a sort of dynamic transition between order and chaos, a wave of disorder rolling and passing. The change of color emphasizes the contrast.

@Marina Shchitova Thanks! That's definitely what I was going for.

enter image description here - another post of yours has been selected for the Staff Picks group, congratulations !

We are happy to see you at the tops of the "Featured Contributor" board. Thank you for your wonderful contributions, and please keep them coming!

Not sure if you are following Wolfram social media, but these from time to time are appearing there, very nice!

https://www.facebook.com/wolframresearch/posts/10153689401698795

https://twitter.com/WolframResearch/status/715259835655163905

@Vitaliy Kaurov Very cool. Thanks for letting me know!

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