GalleryBelow are some pictures and videos we produced as part of our research projects.
Aldous-Shields birth modelIn the paper "A diffusion limit for a class of randomly-growing binary trees", Aldous and Shields introduced a birth model as follows. Starting with single progenitor (generation zero), the population evolves such that each individual of generaltion n gives two births at once at rate \(\alpha^n\) and then dies immediately after giving births. That is, for an individual of generation n, \[P(\text{birth occurs between } t \text{ and } t+dt)=\alpha^ndt\] Below is the simulation of Aldous-Shields birth model with different values of \(\alpha\). The population is represented by dots on the square \([-10,10]\times[-10,10]\). The positions are uniformly distributed. Each individual remembers its generation in order to reproduce at the correct rate. The greener the dot, the later generation it is. See my presentation at the Faculty Advisory Council forum (BYUH). Simulation of Aldous-Shields birth model with \(\alpha=0.8, 1, 1.1\).
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