Coding the Information in Fractals

December 14, 2020

Jack Lutz and Neil Lutz

Professor Jack Lutz and Affiliate Assistant Professor Neil Lutz discovered a strong, information-theoretic connection between classical and algorithmic fractal dimensions.  This connection is analogous to Levin's famous coding theorem in algorithmic information theory.  The key to the connection was the identification of a class of "locally optimal" outer measures that include an important outer measure {\bf kappa} discovered earlier by the second author.  Details appear in the Lutzes' paper "Algorithmically Optimal Outer Measures," which is available on the arXiv and under journal review.

In a related news, Professor Jack Lutz has accepted an invitation to give a lecture on population-induced phase transitions in the Minisymposium on Applications of Stochastic Reaction Networks at the 2021 SIAM Conference on Applications of Dynamical Systems.

News Type: