8.3 - Diffusion on a Sierpinski Gasket

HandsOn Activities:

31. Resistance of a Fractal Network

32. Measuring the Resistance of the Sierpinski Gasket

33. Computing the Resistance of the Sierpinski Gasket

In the preceding section we learned that the average distance a random walker moves in a given length of time is determined by the connectivity of the points on the grid on which the walker moves. Although we studied a simple model, a random walk on a Sierpinski gasket, the results illustrate the behavior of random walkers in materials with complicated connections. Remember that the phenomenon of diffusion is explained using the model of random walkers. In fact, you have just studied diffusion on a fractal, in this case diffusion on the Sierpinski gasket.

In the following section we study the electrical resistance of the Sierpinski gasket, and how it varies with size. The experiments to be performed, and the behavior of the Sierpinski gasket made of resistors, is analogous to the behavior of the Sierpinski gasket made of pipes through which water flows. So if you have not studied electrical circuits yet, you can think of circuits as systems of water pipes.

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