The Cook Book

Recipe for the week of April 17 - 23

A Puzzle Solution by Guest Chef Alex Day

I'll be at Dartmouth College this week giving the Kemeny Lectures on Wednesday, Thursday and Friday. Drop by if you get the chance; my talks will demo WinCA (see our soup from the week of Feb. 27).

During my absence the Kitchen is featuring a recipe by guest chef Alex Day ( Recall that for the past couple of weeks we have discussed a mystery graphic from the Turbo Pascal Programmer's Page. Contrary to the contention of several regular visitors to the Kitchen that tp.gif represents a kind of diffusion limited aggregation, I was convinced that competing oriented percolations generated the image. Such a random cellular automaton rule is the discrete-time analog of the competing contact processes studied by my colleague Claudia Neuhauser ( in her thesis.

Alex sent me this week's soup along with the source code that generated it, in both Basic and C versions. Rather remarkably, his algorithm can be formulated as either a ballistic aggregation rule or as a kind of directed contact interface; these two interpretations produce exactly the same dynamics, as confirmed by a separate program he has written to check the identity. It's probably best to let Alex explain the rule in his own words. His message to me, alex_day.txt contains concise descriptions of the two variants, all the source code, and a nice collection of references to books and articles on related matters. In retrospect, I must admit that Alex' solution to the puzzle seems preferable to the one proposed by me and a number of my colleagues...

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