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In this paper are investigated strictly self-similar fractals that arecomposed of an infinite number of regular star-polygons, also known asSierpinski $n$-gons, $n$-flakes or polyflakes. Construction scheme forSierpinsky $n$-gon and $n$-flake is presented where the dimensions of theSierpinsky $\infty$-gon and the $\infty$-flake are computed to be 1 and 2,respectively. These fractals are put in a general context and Iterated FunctionSystems are applied for the visualisation of the geometric iterations of theinitial polygons, as well as the visualisation of sets of points that lie onthe attractors of the IFS generated by random walks. Moreover, it is shown thatwell known fractals represent isolated cases of the presented generalisation.The IFS programming code is given, hence it can be used for furtherinvestigations.

Strictly self-similar fractals composed of star-polygons that are attractors of Iterated Function Systems