Iterated function systems

If we have a space, S, with a set of transformations acting upon it, T and a probability distribution, μ over T, with an initial point, $x\in S$, the fractal generated by this iterated function system is defined as follows:

x₀=x and x_n+1=f_n+1(x_n) where f_n is an element chosen randomly from T with the probability distribution μ. The limit fractal is the set of points in S that are limit points of $\{x_{i}\}_{i=0}^{\infty }$ with probability 1.

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