Self-Avoiding Random Walks

We modify the above random walk model by requiring the walk avoids itself. Not only is the random walk not allowed to immediately fold back onto itself, but also all sites which are occupied by the walk can not be accessed again. While in the pure random walk model all steps are independent of each other, here the future steps, with this modification, depend on the past. The walk immediately after the first step builds spatial correlation. A random walk with this modification is called a self-avoiding random walk (SAW).