Abstract
We consider the iterated function system (IFS) fq(z)=z +q β , q ∈{(0,0),(1,0),(0,1)}. As is well known, for β = 2 the attractor, Sβ, is a fractal called the Sierpi´nski gasket (or sieve) and for β>2 it is also a fractal. Our goal is to study random β-transformations on the
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