Redone in 2016 -- see below the line for explanation and version from 15 years prior.

These could be cell centroids from a microscopy movie.

Projection of 100 paths and each path.

This is a maximum pixel projection of 100 random walks simulated with this macro in ImageJ.

This is a movie of the 100 paths.  randomwalk.avi [528 kb].

The color look up table is from blue to red to orange to yellow to white as the particle moves farther from its initial location.

All particles originate from the center.