HashLife
DDJ on how Gosper used a clever representation and memoization of multiple levels of calls to get a huge speedup:
Making a slow program fast can lead to both joy and frustration. Frequently, the best you can do is a low-level trick to double or maybe quadruple the speed of a program; for instance, many readers may have implemented John Conway’s “Game of Life” using bit-level operations for a significant speedup. But sometimes a whole new approach, combining just a few ideas, yields amazing improvements. A simple algorithm called “HashLife,” invented by William Gosper (“Exploiting Regularities in Large Cellular Spaces,” Physica 10D, 1984), combines quadtrees and memoization to yield astronomical speedup to the Game of Life. In this article, I evolve the simplest Life implementation into this algorithm, explain how it works, and run some universes for trillions of generations as they grow to billions of cells.
