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On Maximal Self-Avoiding Walks

Given a k × n grid, a self-avoiding walk (SAW) on that grid is a connected path that never touches the same square more than once and never doubles back on itself (note that some sources make the...

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Longest-Lived Soup Density in Conway's Game of Life

In Conway’s Game of Life, a simple way to learn about the general dynamics of the game are to study what happens to soup – patterns made up of a random assortment of ON and OFF cells. Two particularly...

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The Online Life-Like CA Soup Search

Today I’m “officially” announcing the Online Life-Like CA Soup Search, though some of the folks over at the ConwayLife.com forums have been helping me test it out for a couple of weeks now. As I...

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Longevity in Conway's Game of Life Revisited

A couple of weeks ago, I posted some intuition that suggested that, in Conway’s Game of Life, the longest-lived patterns should on average be those with density right around 37.5%. To test this...

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The Maximal Lifespan of Patterns in Conway's Game of Life

In a couple of recent posts, I argued that random patterns in Conway’s Game of Life tend, on average, to live longest when they have an initial density of 37.5% cells being alive. In this post, rather...

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How to compute hard-to-compute matrix norms

There are a wide variety of different norms of matrices and operators that are useful in many different contexts. Some matrix norms, such as the Schatten norms and Ky Fan norms, are easy to compute...

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