Computer Graphics and Visualization • Publications

In Proceedings of AUTOMATA2021

Investigations of structures in the parameter space of three-dimensional Turing-like patterns

Martin Skrodzki, Ulrich Reitebuch, and Eric Zimmermann

Five of the seven possible Turing-like patterns in a three-torus, with the trivial cases of all DCs or all UCs not shown. The images show the isosurface separating DC (green) and UC (gray) cells. Patterns include sphere-like structures, (a) and (e), pipe-like structures, (b) and (d), and area-spanning structures (c)).

In this paper, we are interested in classifying the different arising (topological) structures of three-dimensional Turing-like patterns. By providing examples for the different structures, we confirm a conjecture regarding these structures within the setup of three-dimensional Turing-like pattern. Furthermore, we investigate how these structures are distributed in the parameter space of the discrete model. We found twofold versions of so-called "zero-" and "one-dimensional" structures as well as "two-dimensional" structures and use our experimental findings to formulate several conjectures for three-dimensional Turing-like patterns and higher-dimensional cases.

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Citation

Martin Skrodzki, Ulrich Reitebuch, and Eric Zimmermann, Investigations of structures in the parameter space of three-dimensional Turing-like patterns, In Proceedings of AUTOMATA2021, 2021.

BibTex

@inproceedings{bib:skrodzki:2021,
    author       = { Skrodzki, Martin and Reitebuch, Ulrich and Zimmermann, Eric },    
    title        = { Investigations of structures in the parameter space of three-dimensional Turing-like patterns },
    booktitle    = { In Proceedings of AUTOMATA2021 },
    year         = { 2021 },
    publisher    = { HAL },
    address      = { Marseille, France },
    url          = { https://publications.graphics.tudelft.nl/papers/344 },
}