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In the 1988 textbook "Fractals Everywhere" M. Barnsley introduced an algorithm for generating fractals through a random procedure which he called "chaos game". Using ideas from classical theory of covering times Markov chains we prove asymptotic formula expected time taken by this to generate $\delta$-dense subset given self-similar fractal satisfying open set condition.

Abstract The search for novel topological quantum states has recently moved beyond naturally occurring crystalline materials to complex and engineered systems. In this work we generalize the notion of electronic random lattices in non-integer dimensions. By considering a class D tight-binding model on critical clusters resulting from two-dimensional site percolation process, demonstrate that th...