Here are several java applets which illustrate the sample path behaviour of several important stochastic processes. The first, simple random walk, was written by me in 1998 while I was an undergraduate at the University of British Columbia. The others were written by Kevin Petrychyn, an undergraduate at the University of Regina who worked as an NSERC USRA student with me in Summer 2007 and 2008.
A related model is percolation. The first page contains a java applet for simulating percolation on the hexagonal lattice. It was written by Kevin Petrychyn as part of his NSERC USRA in Summer 2008. The second page contains several pictures of critical percolation on the hexagonal lattice available for download as well as Asymptote code for creating your own. The code was written by my colleague Edward Doolittle of the University of Regina.Simple Random Walk (SRW) Click here for the simulation
Brownian Motion (BM) Click here for the simulation
Schramm-Loewner Evolution (SLE) Click here for the simulation
Simple Random Walk (SRW) and Loop-Erased Random Walk (LERW) Click here for the simulation
Uniform Spanning Trees and Wilson's Algorithm Click here for the simulation
Percolation Click here for the simulation
Percolation Click here for the pictures