Paterson's worms

[BokaBB]

It seems to me there's not a thread for Paterson's worms (even more interestingly there's a Wikipedia page, but not a LifeWiki one), so here comes one for this almost forgotten kind of CA.

Some info: https://en.wikipedia.org/wiki/Paterson%27s_worms

Around half a dozen can be found on Golly.

[MEisSCAMMER]

Nitpick: "Paterson" is spelled with one T.
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This one appears to grow chaotically UNLESS you put another one on the same grid, in which case they seem to inevitably run into each other:

Code: Select all

x = 22, y = 11, rule = Worm-1042015
A10$21.A!

[GUYTU6J]

Here is another relevant link dated 20 years ago:
https://mathpuzzle.com/MAA/01-Paterson' ... 24_03.html
There is a complete inventory of worms comprised of 411 patterns with different sets of rules. Also note the comparison between Worms and CGoL.

As far as I see there are two possible issues if someone like Rowett is going to develop native supports for the family of rules in a cellular automata simulation program:
1)As is the case of Langton's Ant, it is supposed to have exactly one worm/ant//turmite/whatever you call the active element on a grid at a time. How do you define the behaviour of more than one of it meeting on a vertex?
2)Apart from a)looking up the table of enumeration and b)dynamically generating rules while running a pattern real-time, how do you tell whether a 7-digit (or less) number string is a valid rule in Sven Kahrkling's notation?