Construction of a Dynamical System on the Sierpinski Gasket $SG(3)$

Classical Sierpinski gasket is one of the fundamental examples of self-similar sets. This set is also named as mod-$2$ Sierpinski gasket. In this study, we mention the mod-$3$ Sierpinski gasket and obtain this self-similar set by using the escape time algorithm with some special mappings. Then, we express a dynamical system on the mod-$3$ Sierpinski gasket with the help of the code representations of its points.