8.1 - Random Walk on a Fractal
30. Random Walk on a Fractal
The length of one step in Figure 8.2 as the distance from point A to point B. Then the distance from point A to point B'' is four steps. (From now on, we will call each intersection-where two or more lines meet-a point or a grid point.) What do we mean by a random walk on the gasket? If we are at point A or at either of the two point marked B'' in Figure 8.2(b), then we are connected to only two other points on the gasket. A random step from A or B'' will take us to one of the two nearest grid points, with a 0.5 probability of arriving at each point. If we are at any other point on the gasket, then we are connected to four other grid points. Then a random step will take us to one of these four nearest grid points, with a 0.25 probability of arriving at each point, just as in the case of the random walk on a square grid.