… and this is the code for generating animated GIFs using Spheres instead of Points:
n = 1000;
r := RandomInteger[{1, n}];
f := (#/(.01 + Sqrt[#.#])) & /@ (x[[#]] - x) &;
s := With[{r1 = r}, p[[r1]] = r; q[[r1]] = r];
x = RandomReal[{-1, 1}, {n, 3}];
{p, q} = RandomInteger[{1, n}, {2, n}];
Export["Dancing_Spheres.gif",
Table[
Graphics3D[
Rotate[{Yellow, Dynamic[If[r < 100, s]; Sphere[x = 0.995 x + 0.02 f[p] - 0.01 f[q], 0.04]]}, th, {0, 0, 1}],
ImageSize -> {700, 500}, Background -> Black, Boxed -> False, PlotRange -> 2],
{th, 0, 2 Pi, 0.03}]]
For two-dimensional animations, one can use the method explained in my discussion Visualizing Animated GIFs Along The Time Dimension With Image3D to keep track of the swarm’s complex dynamics.
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