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Generating Self-Symmetrical Fractals by Hyperincursive Automata and Multiple Reduction Copy Machine

Daniel M. Dubois and Mathieu Belly

p. 95-115

    Abstract

    This paper shows that different algorithmic methods can generate self-symmetrical Sierpinski fractals. A first category deals with a hyperincursive generator based on a composition rule applied to a defined path in the frame. A second category of algorithms is based on a recursive generator obeying certain symmetries. This paper will consider generalised Sierpinski fractals generated by modulo 2 and modulo 3. Even and odd modulo give rise to very different properties of symmetry.

    Index

    Keywords

    Sierpinski gasket, fractal, recursive generator, hyperincursive frame, algorithms

    Text

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    References

    Bibliographical reference

    Daniel M. Dubois and Mathieu Belly, « Generating Self-Symmetrical Fractals by Hyperincursive Automata and Multiple Reduction Copy Machine », CASYS, 6 | 2000, 95-115.

    Electronic reference

    Daniel M. Dubois and Mathieu Belly, « Generating Self-Symmetrical Fractals by Hyperincursive Automata and Multiple Reduction Copy Machine », CASYS [Online], 6 | 2000, Online since 18 June 2024, connection on 10 January 2025. URL : http://popups.lib.uliege.be/1373-5411/index.php?id=156

    Authors

    Daniel M. Dubois

    Centre for Hyperincursion and Anticipation in Ordered Systems, CHAOS asbl, Institute of Mathematics, B37, University of Liège, Grande Traverse 12, B-4000 Liège, BELGIUM

    By this author

    Mathieu Belly

    Liège, BELGIUM

    Copyright

    CC BY-SA 4.0 Deed