Polyominoes on Twisted Cylinders
In this video we show how to enumerate polyominoes on twisted cylinders, and explain how to use them for setting lower bounds on the asymptotic growth rate of polyominoes in the plane.
The video shows the relation between polyominoes and twisted cylinders. First, it defines what polyominoes are, specifies possible uses of them, and mentions the best known lower and upper bounds on the asymptotic growth rate of polyominoes in the plane. It then illustrates the process of counting polyominoes on twisted cylinders by running the algorithm on a twisted cylinder of width 3. It also demonstrates how this process can be modeled by a finite automaton. Finally, the video shows how we compute the growth rate of polyominoes on twisted cylinders, and concludes with how this implies lower bounds on the respective rate in the plane.
This video belongs to the 22nd Annual Video and Multimedia Review of Computational Geometry, which is part of the 29th Annual Symposium on Computational Geometry.