# Generating Images with Random Walks

The images below were produce by a small Haskell program using *random walks.* Random walk works like this. Start at position *(x0, y0)*.
Then add small random increments *dx* and *dy*, say in the range from -1 to +1 to get
*(x1, y1) = (x0 + dx, y0 + dy)*. Now generate new random numbers, also called
*dx* and *dy* in the same range. Let *(x2, y2) = (x1 + dx. y1 + dy)*. Do this
many times to get a “random” sequence of points. Draw a little square at each of these
points.

Random walk describes many physical phenomena, e.g., the diffusion of heat and the spread of perfume in still air. It also plays an important role in mathematical finance.

In the figures below, random walks were generated for a square region beginning at the origin. Several such images were generated, and one was chosen. The image was then cropped for artistic effect.

*Figure A: one random walk*

*Figure B: two random walks*