Thanks, Rohit.

I was wondering what DynamicModule[] does. The documentation didn't make sense until I saw how you used it. If you don't know what the function is trying to do, it's hard to understand the documentation that tells you how to do that. As they say, if you don't know where you're going, any road will get you there. The DynamicModule[] documentation makes sense now.

The disappearing trails also keeps the time steps uniform since Mathematica doesn't have to do as much addition. Otherwise the model would start to slow down on my i7 after a few thousand steps.

The purpose is to give visual confirmation to an algebraic derivation of the diffusion equatioin from obvious logic of a random walk using average mean clear path.

I would never have tried to tackle Mathematica were it not for this commnity.

Thanks again, Rohit. Thanks to your help, I figured it out and got the model to look like I wanted (attached). The idea is to illustrate a random-walk derivation of the diffusion equation,.

Attachments:

Diffusion as ran...nb

Thanks, Rohit. I didn't even know AnglePath3D existed. This community is great. I'll get back to this thread after I've had a chance to implement these ideas later today.

Or, if you want straight lines joining the points rather than Henrik's nice interpolation.

Generate 5 3D paths with 1000 steps each using AnglePath3D. If you already have the list of points then this is not needed.

SeedRandom[123];   
randomPaths = Table[RandomReal[{-2 Pi, 2 Pi}, {1000, 3}], 5] // Map[AnglePath3D];

Colors for a path

colors = ColorData[112, "ColorList"];
color[n_] := colors[[Max[Mod[n, Length@colors], 1]]]

Plot the paths

Graphics3D[MapIndexed[{color@First@#2, Line[#1]} &, randomPaths], ViewPoint -> {0, 0, 2}]

Did you check out Plot3D[]?