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edited Nov 18, 2015 at 20:56

user484

Here's a function to create a random scalar field:

randomFunction3D[xrange_, yrange_, zrange_] := Interpolation[ Flatten[Table[{{x, y, z}, RandomReal[{-1, 1}]}, Evaluate@{x, Sequence @@ xrange}, Evaluate@{y, Sequence @@ yrange}, Evaluate@{z, Sequence @@ zrange}], 2], Method -> "Spline"]

Now instead of drawing a sphere with constant radius $x^2+y^2+z^2=r^2$, let's make the "radius" vary randomly over space, so we get an irregular blobby shape:

SeedRandom[0]; f = randomFunction3D[{-3, 3}, {-3, 3}, {-3, 3}]; ContourPlot3D[ x^2 + y^2 + z^2 == (1 + 0.4 f[x, y, z])^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, Mesh -> None, PlotRange -> All, BoxRatios -> Automatic, Boxed -> False, Axes -> False]

You can also change the grid spacing to control the size of the bumps:

SeedRandom[0]; f = randomFunction3D[{-3, 3, 0.25}, {-3, 3, 0.25}, {-3, 3, 0.25}]; ContourPlot3D[ x^2 + y^2 + z^2 == (1 + 0.06 f[x, y, z])^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, Mesh -> None, PlotRange -> All, BoxRatios -> Automatic, Boxed -> False, Axes -> False]

You can have a lot of fun adding a bunch of different random fields with different scalings to create interesting effects, but I'll leave that as an exercise. For inspiration, see Ken Perlin's classic Making Noise talk.

Here's a function to create a random scalar field:

randomFunction3D[xrange_, yrange_, zrange_] := Interpolation[ Flatten[Table[{{x, y, z}, RandomReal[{-1, 1}]}, Evaluate@{x, Sequence @@ xrange}, Evaluate@{y, Sequence @@ yrange}, Evaluate@{z, Sequence @@ zrange}], 2], Method -> "Spline"]

Now instead of drawing a sphere with constant radius $x^2+y^2+z^2=r^2$, let's make the "radius" vary randomly over space, so we get an irregular blobby shape:

SeedRandom[0]; f = randomFunction3D[{-3, 3}, {-3, 3}, {-3, 3}]; ContourPlot3D[ x^2 + y^2 + z^2 == (1 + 0.4 f[x, y, z])^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, Mesh -> None, PlotRange -> All, BoxRatios -> Automatic, Boxed -> False, Axes -> False]

Here's a function to create a random scalar field:

randomFunction3D[xrange_, yrange_, zrange_] := Interpolation[ Flatten[Table[{{x, y, z}, RandomReal[{-1, 1}]}, Evaluate@{x, Sequence @@ xrange}, Evaluate@{y, Sequence @@ yrange}, Evaluate@{z, Sequence @@ zrange}], 2], Method -> "Spline"]

Now instead of drawing a sphere with constant radius $x^2+y^2+z^2=r^2$, let's make the "radius" vary randomly over space, so we get an irregular blobby shape:

SeedRandom[0]; f = randomFunction3D[{-3, 3}, {-3, 3}, {-3, 3}]; ContourPlot3D[ x^2 + y^2 + z^2 == (1 + 0.4 f[x, y, z])^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, Mesh -> None, PlotRange -> All, BoxRatios -> Automatic, Boxed -> False, Axes -> False]

You can also change the grid spacing to control the size of the bumps:

SeedRandom[0]; f = randomFunction3D[{-3, 3, 0.25}, {-3, 3, 0.25}, {-3, 3, 0.25}]; ContourPlot3D[ x^2 + y^2 + z^2 == (1 + 0.06 f[x, y, z])^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, Mesh -> None, PlotRange -> All, BoxRatios -> Automatic, Boxed -> False, Axes -> False]

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answered Nov 18, 2015 at 8:06

user484

Here's a function to create a random scalar field:

randomFunction3D[xrange_, yrange_, zrange_] := Interpolation[ Flatten[Table[{{x, y, z}, RandomReal[{-1, 1}]}, Evaluate@{x, Sequence @@ xrange}, Evaluate@{y, Sequence @@ yrange}, Evaluate@{z, Sequence @@ zrange}], 2], Method -> "Spline"]

Now instead of drawing a sphere with constant radius $x^2+y^2+z^2=r^2$, let's make the "radius" vary randomly over space, so we get an irregular blobby shape:

SeedRandom[0]; f = randomFunction3D[{-3, 3}, {-3, 3}, {-3, 3}]; ContourPlot3D[ x^2 + y^2 + z^2 == (1 + 0.4 f[x, y, z])^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, Mesh -> None, PlotRange -> All, BoxRatios -> Automatic, Boxed -> False, Axes -> False]