The Schramm Loewner Evolution is a "young" mathematical branch (1999) concerned with the conformally invariant stochastic process. This theory describes a class of random planar curves, obtained (by Schramm) by solving Lowener equations when the driving function (input) takes the form of brownian motion. Such curves are governed by "chi" which plays the role of the diffusion coefficient for the driving function. This matlab program (3 files: SLE.m, fz1.m, fz2.m) simulates such curves for any value of chi for various planar processes:
chi=0, vertical slit
chi=2, Loop Erased Random Walk (LERW)
chi =8/3, Self-Avoiding Walk
The SLE image (png file) represents a plot for n=50000 points and chi=2, the Loop Erased Random Walk (LERW) case.
Python app simulating percolation processes on square lattice of side L. The largest and second largest components evolution are shown from p=0 to p=1 for different size L of the square grid. https://pythonyx.pythonanywhere.com/percolation