Visualization of Developmental Processes by Extrusion in Space-Time

  • Hammel M
  • Prusinkiewicz P
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Abstract

Developmental processes in nature may involve complex changes in the topology, shape, and patterns of growing structures. Processes taking place in one or two dimen- sions can be visualized as objects in three-dimensional space, obtained by extruding the growing structures along a line or curve representing the progress of time. In this paper, we extend the notion of L-systems with turtle in- terpretation to facilitate the construction of such objects. This extension is based on the interpretation of the entire derivation graph generated by an L-system, as opposed to the interpretation of individual words. We illustrate the proposed method by applying it to visualize the develop- ment of compound leaves, a sea shell with a pigmentation pattern, and a filamentous bacteria. In addition to serving as visualization examples, these models are of interest on their own. The sea shell model uses an L-system to ex- press a reaction-diffusion process, thus relating these two models of morphogenesis. The model of bacteria, which is also of the reaction-diffusion type, sheds new light on one of the basic problems of morphogenesis, the forma- tion of equally spaced organs in a developing medium.

Author-supplied keywords

  • fractal
  • generative
  • l-system
  • modeling
  • plant
  • reaction-diffusion
  • sea shell
  • simulation
  • visualization

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  • ISSN: 07135424
  • PUI: 27894312
  • SCOPUS: 2-s2.0-0030354427
  • SGR: 0030354427

Authors

  • Mark Hammel

  • Przemyslaw Prusinkiewicz

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