Stan Palasek is a high school student from Tucson, Arizona studying the origin of complexity and information transfer in early life. His findings have made possible biomimicry of RNA dynamics in hydrothermal vent systems for the optimization of modern biotechnologies. He attends the Wolfram Summer School in hopes of further examining the computational side of this emergence of complexity. In his free time, Stan mostly studies mathematics. When he’s not studying mathematics, he enjoys statistics, Mexican food, politics, baseball, economics, lifting weights, and tutoring other students.
Project: Long-Time Tails in Cellular Automaton Information Flow
The dissipation of information about the initial conditions of a cellular automaton is examined. After a threshold, the information depletion curve transitions from an exponential to a power law in a manner reminiscent of the long-time tails observed in statistical physics and fluid mechanics. These decays are depicted below as the straight segments on log and log-log plots.
A closed form for the dissipation is derived based on the differential contributions of cells throughout the light cone and their empirical relationship to the mutual information.
Favorite Four-Color, Four State Turing Machine