FRACTAL n-GONS AND THEIR MANDELBROT SETS
نویسندگان
چکیده
We consider self-similar sets in the plane for which a cyclic group acts transitively on the pieces. Examples like n-gon Sierpiński gaskets, Gosper snowflake and terdragon are well-known, but we study the whole family. For each n our family is parametrized by the points in the unit disk. Due to a connectedness criterion, there are corresponding Mandelbrot sets which are used to find various new examples with interesting properties. The Mandelbrot sets for n > 2 are regular-closed, and the open set condition holds for all parameters on their boundary, which is not known for the case n = 2. MSC classification: Primary 28A80, Secondary 52B15, 34B45
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تاریخ انتشار 2007