Ed Pegg, Jr., who runs http_mathpuzzl
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:
http://code.google.com/p/ruletablerepository/wiki/TwoDimensionalTuringMachines
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:
http://code.google.com/p/ruletablerepository/wiki/TwoDimensionalTuringMachines#Non-halting_Busy_Beavers
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:
http://code.google.com/p/ruletablerepository/wiki/TwoDimensionalTuringMachines#Non-halting_Busy_Beavers
Prize: If you find a new champion, you might get a mention on mathpuzzle.com.
Good luck!
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:
http://code.google.com/p/ruletablerepository/wiki/TwoDimensionalTuringMachines
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:
http://code.google.com/p/ruletablerepository/wiki/TwoDimensionalTuringMachines#Non-halting_Busy_Beavers
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:
http://code.google.com/p/ruletablerepository/wiki/TwoDimensionalTuringMachines#Non-halting_Busy_Beavers
Prize: If you find a new champion, you might get a mention on mathpuzzle.com.
Good luck!
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