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Conway's game of life is a 2D, two-state, outer totalistic, cellular automaton. I guess the natural thing is to try such CAs in 3D. Here's the evolution of one such CA: twos = Array[2 &, {3, 3}]; twosWithOne = twos; twosWithOne[[2, 2]] = 1; outerTotalisticCA3D[ruleNumber_Integer, duration_Integer, init_List] := CellularAutomaton[ {ruleNumber, ...


In version 10.0.0 the PlotStyle -> Thickness method shown by cormullion does not appear to work. Instead we can use the undocumented Extrusion option: ContourPlot3D[x y z == 0.05, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, Extrusion -> 0.1]


In Version 10, we can compute the convex hull using ConvexHullMesh p = {{2, 1, 6}, {4, 3, 0}, {5, 2, 5}, {3, 5, 4}} chull = ConvexHullMesh[p] Which we can style using HighlightMesh Show[HighlightMesh[chull, Labeled[1, "Index"]], Graphics3D[{Red, Sphere[p, 0.1]}]]


In Version 10 there is such a function. Meet RegionMember. We take your Cylinder primitive as an example: cyl = Cylinder[] Let's create some points: pts = RandomReal[{-1.5, 1.5}, {100, 3}]; Now we create a RegionMemberFunction that can be used repeatedly on various points. mf = RegionMember[cyl] We apply mf to the set of points and give them ...


In Version 10, there is now the built-in ConvexHullMesh to do exactly this. pos = Position[DiskMatrix[{12, 10, 8}], 1]; To get the 3D convex hull: ConvexHullMesh[pos]


It seems that regularly-spaced mesh parallel to the axes--not the mesh used to create the graphics--can only be drawn for "*Plot" type graphics (and not Graphics3D). Here is my attempt to draw it. Note that I don't know how to combine both types of meshes in one plot--I tried to use BoundaryStyle but it only drew the outline of the shape without the line ...

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