Ed Pegg, Jr., who runs http_mathpuzzl

Ed Pegg, Jr., who runs <a rel="nofollow" target="_blank" href="http://mathpuz...
Tim HuttonTim Hutton - 2013-02-05 17:22:07+0000 - Updated: 2013-02-05 17:29:31+0000
Ed Pegg, Jr., who runs mathpuzzle.com, has a challenge for us.

Turmites are little creatures that run around the grid. Langton's Ant is a simple turmite.

Golly can run turmites. Use Scripts/Python/Rule-
Generators/Turmite-gen.py. By default the script makes a random 2-state 2-color turmite, so just re-run it to see a new turmite.

Some turmites include a halting state. If they reach it then they will stop forever. The "Busy Beaver" game asks what machine runs the longest before halting.
Some Busy Beaver results for turmites can be found here:

Other turmites don't include a halting state and so run forever. But often they end up in repeating predictable behaviour. This is another kind of Busy Beaver game. For example, Langton's Ant makes a highway after 10000 steps. The turmite called "Worm Trails" (shown below) ends up getting trapped in a loop after 4.3 million steps:
Others seem to run forever, always random.

Ed asks us: What 2-state 2-color turmite runs the longest before becoming predictable? The current champion is Worm Trails, we think.

He defines 'predictable' to be: Traps, Highways, Spirals, Wedges and Sequences (like the counter), as shown here:
The turmite should start from an empty grid.

Send results to tim.hutton@gmail.com. I'll keep track of the current winner here:

Prize: If you find a new champion, you might get a mention on mathpuzzle.com.

Good luck!
Shared with: Public
Tim Hutton - 2013-02-06 21:50:35+0000 - Updated: 2013-02-06 21:50:47+0000
Update: New record holder is 18.22 million steps:
Tim Hutton - 2013-02-08 10:58:22+0000
Update: New record holder is 240 million steps:
Tim Hutton - 2013-02-11 12:37:03+0000
Update: New record holder is 7.735 billion steps:
David Moore - 2013-02-13 06:29:45+0000
Holy crap!

This post was originally on Google+