Beyond random walks, there are many other systems based on discrete components in which randomness at a microscopic level also leads to continuous behavior on a large scale. The picture below shows as one example what happens in a simple aggregation model.
Behavior of a simple aggregation model, in which a single new black cell is added at each step at a randomly chosen position adjacent to the existing cluster of black cells. The system is a version of the so-called Eden model. The shape obtained is ultimately an almost perfect circle.