Derandomized percolation machines

Date started: 2017
Leads: Alexander Holroyd, James Propp


The quincunx or Galton peg-board has a “derandomized” variant in which a ball is deflected left or right alternately rather than at random.  As with many such derandomized systems, this results in an almost perfect binomial distribution rather than a noisy one. Holroyd and Propp discovered a small change to the local rule that produces instead an almost perfect uniform distribution.  The resulting model can be seen as a derandomized version of critical site percolation, and also as a derandomized Polya urn, and generates fascinating patterns that are not yet fully understood. This project will design and make a mechanical implementation of this model.