I have to determine the fractal dimension of a random walk in 2D. How can I do that? I am first supposed to picture the random walk for 2D as in the following site. However, I am also asked to calculate the fractal dimension of it. How can I do that? What I only know, is: $$N = \epsilon^{-D}$$ where D is the number of dimensions, $\epsilon$ the scaling factor, and N the number of sticks of length $\epsilon^{-1}$needed to measure a line. After that, I am given the following formula for determining the fractal dimension: $$D = \lim_{i\rightarrow \infty}{\frac{\log{[N(\epsilon_i)/N(\epsilon_{i+1})]}}{\log{[\epsilon_{i+1}/\epsilon_i]}}}$$
How can I use this definition for my random walk?
Thanks!