Ed Pegg, Jr., who runs <a rel="nofollow" target="_blank" href="http://mathpuz...
- 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.
http://www.conwaylife.com/forums/viewtopic.php?f=11&t=1029

Turmites are little creatures that run around the grid. Langton's Ant is a simple turmite.
http://en.wikipedia.org/wiki/Turmite
http://en.wikipedia.org/wiki/Langtons_ant

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.
http://golly.sourceforge.net/

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.
http://en.wikipedia.org/wiki/Busy_beaver
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:
http://www.maa.org/editorial/mathgames/mathgames_06_07_04.html
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
- 2013-02-06 21:50:35+0000 - Updated: 2013-02-06 21:50:47+0000
Update: New record holder is 18.22 million steps:
http://www.conwaylife.com/forums/viewtopic.php?f=11&t=1029
- 2013-02-08 10:58:22+0000
Update: New record holder is 240 million steps:
http://www.conwaylife.com/forums/viewtopic.php?f=11&t=1029#p7433
- 2013-02-11 12:37:03+0000
Update: New record holder is 7.735 billion steps:
http://www.conwaylife.com/forums/viewtopic.php?f=11&t=1029&p=7436#p7436
- 2013-02-13 06:29:45+0000
Holy crap!

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