What is Paterson’s Worms?

First discussed in Science 21 November 1969.

M.I.T. AI memo #290 by Michael Beeler 1973.

Paterson’s Worms according to Wikipedia

So a “Paterson Worm” is not a creature but rather a set of rules describing how an imaginary worm will crawl searching for food.  You can think of the rules as the worm’s DNA. The crawling worm will create very different patterns depending on its DNA. It is the created pattern that I will call a worm, or PW. There are different DNA implementations. I have used the numbers 1 to 5 in a DNA string of 26 “genes”.

Some PWs are very short, like this one

This is in fact the shortest one and created by two sets of DNA:

1 3…. ………. …..3….
1 5…. ………. 5………

A dot means any gene.

Some are very very long and there are some infinite ones as well. Here is one with a path length of 7524 showing a nice hexagon.

2 .3… .2.4.3..2. ..4…….

I hope you find this interesting and let me introduce a new dimension in PW creation. What will it look like when I let the color of the path change as the worm crawls? Here is one PW of length 9260 that starts off in red and ends in yellow and here is another PW of length 52549 with a different set of colors.

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