The similarity dimension of the random iterated function system

In this paper we consider the properties of the random iterated function systems (RIFS) obtained using a generalization of the Chaos game algorithm. Used for the RIFS simulation R is a free software environment for statistical computing and graphics. The similarity dimension by the polygonal protofractals $Z = {z_j}, j = 1, 2,... , k$ nonmonotonically depends on the RIFS parameters $d_S(\mu|k )$ with an extreme value $\max_{0<\mu<\infty} d_S(\mu|k)=-\frac{\mathrm{ln}k}{\mathrm{ln}(1/(1+\mu))}$.