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Yoshiaki Araki

3D Quasi-Fuchsian Fractals

Abstract:

We introduce a new family of three dimensional quasi-fuchsian groups and the computer visualization of their limit sets as new fascinating fractal shapes which are natively embedded in the tree dimensional space. Very few examples of quaisfuchsian groups in three dimensional space are known, they had never been visualized. The limits set of fuchsian group can be defined as round sphere, and those of quasi-fuchsian group is just known as not round surfaces which topologically are equivalent to sphere, but no one knew how non-round they were. The limit sets are the first ever waiting "native" 3D fractal shapes which have richer nature of fractals than other known 3D fractals. The images can be found here

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