# Math 303 - Explorations in Integrated Science

### Julia Sets

This MATLAB GUI iterates the quadratic map *f*(*z*) = *z*^{2}+ *c*, where *z* and *c* are complex numbers. The (filled in) Julia set is the set of initial conditions *z*_{0} such that successive iterates *z*_{1} = f(*z*_{0}), *z*_{2} = f(*z*_{1}), ..., *z*_{n+1} = f(*z*_{n}), ... remain bounded.

### Diffusion at the Microscopic Level

This MATLAB GUI simulates the random motion of *M* non-interacting particles on a grid. Each particle can only go up, down, left or right, with equal probability. All of the particles start their random walk from the origin, at the center of the box.