8.1  Random Walk on a Fractal
HandsOn Activities:
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 intersectionwhere two or more lines meeta 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.


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