On the Shape of Trees: Tools to Describe Ramified Patterns

  • J. Vannimenus
Part of the Springer Proceedings in Physics book series (SPPHY, volume 32)


“Trees”, i.e., loopless ramified patterns, appear everywhere — from botany to geology (river networks), from evolution (phylogeny) to physics — and it is no surprise that their mathematical description has been studied from many different viewpoints. Even within physics, such structures occur in completely unrelated situations, e.g., the Cayley tree which is used as a model to study phase transitions in high dimensions [1], the hierarchical structure of pure states in spin glasses [2], the “treeing” effects observed in the degradation of polyethylene [3] … My personal motivation comes from an interest in patterns observed during electric discharges [4], electrochemical deposition [5], some types of viscous flows [6], thin solid deposits [7] — one can give many more examples, and the problem of characterizing mathematically the “shape” of these trees arises naturally.


Binary Tree River Network Cayley Tree Eden Tree Sierpinski Gasket 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • J. Vannimenus
    • 1
    • 2
  1. 1.Laboratoire Louis Néel, CNRSGrenoble CedexFrance
  2. 2.Institut Laue-LangevinGrenoble CedexFrance

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