Periodic unique codings of fat Sierpinski gasket

Derong Kong, Yuhan Zhang

For $\beta >1$ let $S_{\beta }$ be the Sierpinski gasket generated by the iterated function system \[\left\{f_{α_0}(x,y)=\Big(\frac{x}β,\frac{y}β\Big), \quad f_{α_1}(x,y)=\Big(\frac{x+1}β, \fr…