Suppose we have a 3D distribution of points, like the spherical ball example below :
Ball[num_]:=Table[
{
#1 Sqrt[1-#2^2]Cos[#3],
#1 Sqrt[1-#2^2]Sin[#3],
#1 #2
}
&[
Random[NormalDistribution[1, 0.5]],
Random[Real,{-1,1}],
Random[Real,{0,2Pi}]
],{num}]
Graphics3D[{AbsolutePointSize[2],Point[Ball[10000]]},Boxed->True,BoxRatios->{1,1,1},ImageSize->800,SphericalRegion->True]
This code produces the ball shown here :
Obviously, this ball has a spherical symmetry and could be considered as a "smooth" distribution (under the limit of an infinite set of points).
Now, I would like to randomly "erode" the distribution, to get something that look a bit like a fractal shape (think about how an eroded mountain could be obtain from a smooth hill). How can I do that ? What Mathematica procedures could modify the Ball distribution that act like a random eroding process ?
To me, "eroding" mean removing a randomly selected point, and several of its neighbors, then repeat the process several times.
Please, the suggestions should be compatible with Mathematica 7.0.