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plotting - Make a beautiful Moiré effect


How do I make the following Moiré pattern?


moiré pattern


I tried:


A = Plot[Table[n, {n, 1, 30}], {x, 0, 31}, 
GridLines -> {Table[n, {n, 1, 30}], None}, 
GridLinesStyle -> AbsoluteThickness[1.2], PlotStyle -> Gray, 
Axes -> False, AspectRatio -> 1]
B = Rotate[A, -30 Degree]

C = Rotate[A, -60 Degree]

Answer



I feel that once you start with Moire patterns, there's no ending. The way I would replicate these is by making a grid into a function (like @JasonB) but also parametrise the angle of rotation into it:


lines[t_, n_] := 
  Line /@ ({RotationMatrix[t].# & /@ {{-1, #}, {1, #}}, 
        RotationMatrix[t].# & /@ {{#, -1}, {#, 1}}} & /@ 
      Range[-1, 1, 2/n]) // Graphics;

So that you can vary the number of lines n and rotation parameter t as well. Now your image is (more or less):


lines[#, 40] & /@ Range[0, π - π/3, π/3] // Show


enter image description here


And you can play more with these two parameters. Here's what you get if you superimpose grids with very small relative angle differences:


lines[#, 100] & /@ Range[-π/300, π/300, π/300] // Show

enter image description here


Or randomising the spacing and angle of each grid:


lines[Cos[# π/30], #] & /@ RandomInteger[{1, 20}, 9] // Show

enter image description here



and -as an overkill- harmonically varying these two effects results in great gif potential


gif = Table[Show[{lines[0, Floor[10 + 9 Cos[t]]], lines[-2 π/3 Cos[t], 20], 
    lines[+2 π/3 Cos[t], 20]}, 
   PlotRange -> {{-1.5, 1.5}, {-1.5, 1.5}}, 
   ImageSize -> 200], {t, -π/2, π/2 - π/70, π/70}];
Export["moire.gif", gif]

enter image description here


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