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Random Trees

Generate random critical Bienaymé (Galton-Watson) trees and display their free trees in a force-directed layout. Visit the page!

sample tree Displaying the free trees:

  • The free tree structure is animated via a hand-coded model with spring and repulsive forces.
  • Displayed beside each node is its multiplicity, i.e., the number of nodes in the free tree that look identical to it. The notion is more formally defined in the text.

Tree generation:

  • The user has a choice of offspring distribution between various binomial distributions, the geometric distribution and the Poisson distribution.
  • New Tree generates a Bienaymé tree with the selected offspring distribution (with limited size to avoid computational and visual overload)
  • Big Tree also generates such a tree, but conditioned to have large size!
  • You can draw your own tree using Draw Tree; the multiplicities of each node will be shown and updated as the tree is drawn. It will be animated once Done is clicked.

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Generate random critical Galton-Watson trees and display their free trees in a force-directed layout

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