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Worm Paths
Fantastic patterns traced by programmed “worms”
Introduction
(this page)
Description & Rules
Examples
Scientific American reference
Mine vs. Gardner’s Notation
Pattern Inventory
Algorithms
LIFE Comparison
Introduction
What is it?
WORMS is a computer recreation akin to the likes of John Conway’s LIFE or fractal patterns.
What is it not?
The term “worms” is currently used in the context of computer viruses and other destructive programs. The definition used in this site, however, much predates this negative connotation. It is no more harmful than Tic-Tac-Toe.
Where does it come from?
It first appeared in the November, 1973 issue of Scientific American as a topic of Martin Gardner’s regular “Mathematical Games” section.
Paterson’s Worms
, as it was also refered to. After refining the definition of the “Worm Paths” class by John Horton Conway it was studied in-depth with the aid of a computer program by Michael Beeler, also of M.I.T.
What does it do?
WORMS is an exploration of geometric figures formed by recursively applying a set of simple rules.
What’s the goal?
The goal is to find a set of rules which generates the largest pattern. So far, eligible patterns have been traced to millions of line segments with no conclusive proof that they will eventually stop. We still don’t know what the largest pattern will ultimately be. Back in 1973 the record holder was thought to be one with a path length of
220,142
units. Since then I have found two larger patterns:
569,804
and
918,339
units.
How difficult is it?
Its description is no more complicated than the rules for Conway’s LIFE. Yet it can present a challenge to both novice and advanced programmers. It should probably be among the repertoire of all who are interested in puzzles and games.
Comments:
sven@accessv.com
… because it wasn’t on the Web – until this March 22, 1999
This site is under construction. Last updated: Feb 15/00