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

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.

@InProceedings { SRZ21,
  author       = "Skrodzki, Martin and Reitebuch, Ulrich and Zimmermann, Eric",
  title        = "Investigations of structures in the parameter space of three-dimensional Turing-like patterns",
  booktitle    = "AUTOMATA2021",
  month        = "Jul",
  year         = "2021",
  publisher    = "HAL",
  address      = "Marseille, France",
  note         = "Available online at url{https://hal.archives-ouvertes.fr/hal-03270664/file/AUTOMATA2021-exploratory15.pdf}",
  url          = "http://graphics.tudelft.nl/Publications-new/2021/SRZ21"
}