Random β-transformation on fat Sierpinski gasket

Tingyu Zhang, Karma Dajani, Wenxia Li

We consider the iterated function system (IFS) $$f_{\vec{q}}(\vec{z})=\frac{\vec{z}+\vec{q}}{\beta },\vec{q}\in \{(0,0),(1,0),(0,1)\}.$$ As is well known, for $\beta =2$ the attractor, $S_{\beta }$,…