Plane quasicristal geometric structure in connotation Petersen graph colouring has been considered. Petersen graph can represented to be closed electric network (sell) contains $T$ - and $\Delta$-elements. For $Y$ -element volt-ampere characteristic being phase portrait on the plane has been defined. The modelling dynamic system for the $Y$ - element volt-ampere characteristic has been construction. It turns out to be the invariant four regions common boundary.The modelling propagate semi-dynamic system for the plane quasicristal has been constructed. The presence of the Peterson graph colouring and Wada basins have been shown.