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Some mathematical riches from the living tree of life: multifractals, nearness spaces, and complex attractors
Probability| Speaker: | Kevin Hudnall, UC Davis |
| Location: | 2112 MSB |
| Start time: | Tue, Mar 3 2026, 1:10PM |
Description
We study a minimal stochastic model of the dynamic tree of life. The model is obtained by combining Galton–Watson branching with multiplicative contraction maps, yielding a branching-process random iterated function system. Successive branching across iterations of contraction maps induces a multiplicative cascade. The limiting random measure on the boundary of the cascade exhibits a nontrivial multifractal spectrum. The cascade does not single out a unique observer-independent metric on the boundary. Instead, its natural global structure is a graded nearness space defined through dimensionless scaling ratios. The nearness ratios can be computed using fractal and entropic quantities on the cascade boundary. Solutions organize into equivalence classes on the complex plane.