17
Nov
04

Crackle

Here is a technique for generating periodic cellular textures using Voronoi diagrams.
(* runtime: 8.5 minutes *)
n = 275; SeedRandom[0]; nodes = Table[Random[], {100}, {2}];
dist[p1_, p2_] := Module[{d = Map[If[# > n/2, n - #, #] &, Abs[p2 - p1]]}, d.d];
DensityPlot[Module[{dlist = Sort[Map[dist[{j, i}, #] &, nodes]]}, dlist[[2]] -dlist[[1]]], {i, 1, n}, {j, 1, n}, PlotPoints -> n, Mesh -> False, Frame -> False];

Mathematica’s ComputationalGeometry package can also be used to generate Voronoi diagrams, Delaunay triangulation, and convex hulls. This is useful for mesh generation:
(* runtime: 5 seconds *)
<< DiscreteMath`ComputationalGeometry`; SeedRandom[0]; nodes = Table[Random[], {100}, {2}];
DiagramPlot[nodes, PlotRange -> {{0, 1}, {0, 1}}];
PlanarGraphPlot[nodes];
PlanarGraphPlot[nodes, ConvexHull[nodes]];

POV-Ray also has a built-in function for this:
// runtime: 0.5 second
camera{orthographic location <0,0,-4> look_at 0 angle 90}
plane{z,0 pigment{crackle color_map{[0 rgb 0][0.5 rgb <0,1,0>][1 rgb 1]}} finish{ambient 1}}

Link: Cellular Texture Tutorial – by Jim Scott

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