Langton's Ant
Multicolor extension of Langton's Ant cellular automaton program that finds highways and its period
It supports square and hexagonal grids
TODO
- Server
- Create server to submit ants tested by users
- Send rules to clients to test so that no rule is tested multiple times
- Verify rules by different clients
- Store rules tested and verified by each user for credit
- Prevent people from sending false data (trust system based on rule verification by other users)
- Webpage to visualize all the data
- Improve GUI
- Different work types:
- Check new rules
- Verify rules
- Approximate period of big highways
- Find exact period of big highways
- Algorithm to differentiate between highways/triangles/squares
- Hexagonal ant
- Parallel computing
Top highways with longest period
| Rule Number | Period | Rule String |
|---|---|---|
| 54787787 | 6518789812888 | RRLRLLRRLRRRRRRRRRLLLLRLRR |
| 34340555 | 3409034558708 | RRLRLLRRLRRRRRRRRRLRLLLLLR |
| 120192715 | 317869216552 | RRLRLLRRLRRRRRRRRLLRLRLLRRR |
| 5772148427 | 241836027556 | RRLRLLRRLRRRRRRRRRLRLLLLLLLRRLRLR |
| 45089076 | 200631077404 | LLRLRRLLRLLLLLLLLLLLRRLRLR |
| 15416631 | 117440512200 | RRRLRRLLRLRRRRLLRRLRLRRR |
| 52116791 | 113816934400 | RRRLRRLLRLRRRRLLRRLRRLLLRR |
| 5403410740 | 99463945900 | LLRLRRLLRLLLLLLRRLLLRLLLLRLLLLRLR |
| 13025588 | 66487151028 | LLRLRRLLRLLLLLRRLRRLLLRR |
| 22593844 | 28299602536 | LLRLRRLLRLLLLLRRLLLRRLRLR |
| 18858376907 | 26423448520 | RRLRLLRRLRRRRRRRRRLRLLLLLLRLLRRLLLR |
| 113508043 | 20009040104 | RRLRLLRRLRRRRRRRRRLLLLRRLRR |
| 96567604 | 14264116224 | LLRLRRLLRLLLLLLRRLLLLLRRRLR |
| 13730100 | 13498292016 | LLRLRRLLRLLLLLLRRLLLRLRR |
| 23723769547 | 7112124816 | RRLRLLRRLRRRRRRRRRLRLLLLLRRLLLLRRLR |
| 141229771 | 6902623604 | RRLRLLRRLRRRRRRRLRLRLRRLLLLR |
| 3539252 | 6740764524 | LLRLRRLLRLLLLLLLLRRLRR |
| 786123 | 5307264488 | RRLRLLRRLRRRRRRRRRLR |
| 31575506635 | 3886098700 | RRLRLLRRLRRRRRRRRRLRLLLLLRLRRLRLRRR |
| 3477339851 | 3289325504 | RRLRLLRRLRRRRRRRRRLLLLRLRRRRLLRR |
Biggest highways with unknown period
| Tested to # iters | Rule String | Rule number | Highway size | Estimated period | Real period | Rel. Error |
|---|---|---|---|---|---|---|
| 1.1e13 | RRLRLLRRLRRRRRRRRRLLLRLLRLR | 86245067 | >= 4707316320 | >=4.18492189e13 | ||
| 1e11 | LLRLRRLLRLLLLLLRRLLLR | 1147188 | >= 133671045600 | >=1.104122836656e15 | ||
| 1e13 | RRRLRRLLRLRRRRLLRRRLLRLR | 10960183 | 2^42*3 ?? | 3.77616273e16 ?? | ||
| 1.74e12 | RRRLRRLLRLRRRRRRRRRLR | 1572151 | 2^40*3 ?? | 5.64742157e15 ?? | ||
| 4.7e11 | LLRLRRRLRRLLLRRLLLLLLRLLRLRR | 220226420 | > 2^500 ?? | |||
| 7.6e11 | LLRLRRLLRLLLLLLLLLLRLRLR | 11010356 | >= 146880 | |||
| 1.4e12 | LLRLRRLLRLLLLLLLLRRRLLRLR | 21889332 | >= 1573560 | |||
| 1.5e10 | RRLRLLRRLRRRRRRRRRLRRLRLRR | 56360651 | >= 2364582528 | |||
| 4e11 | LLRLRRLLRLLLLLLLLRRRRRRLRLR | 92143924 | >= 886624056 | >=5.730524292850e12 | ||
| 96534219 | ||||||
| 5470519604 | ||||||
| 10369105611 | ||||||
| 16241131211 | >= 65597220 | |||||
| 25065946827 | ||||||
| 26106134219 | ||||||
| 28052291275 | ||||||
| 34763177675 | ||||||
| LLRLRRLLRLLLLLLLLLLLRRLRLR | 45089076 | 31460520 | 202740399826 | 200631077404 | 1.05% | |
| 5772148427 | 28301520 | 242294338124 | 241836027556 | 0.189% | ||
| 120192715 | 34543080 | 318476375254 | 317869216552 | 0.191% | ||
| RRLRLLRRLRRRRRRRRRLRLLLLLR | 34340555 | 478474920 | 3406262955480 | 3409034558708 | 0.081% | |
| RRLRLLRRLRRRRRRRRRLLLLRLRR | 54787787 | 777109320 | 6524244609340 | 6518789812888 | 0.083% |
How we found the huge highways
The rules that start with the same letters often behave very similar. When we find rules with a long period, we test the ones that start in the same way to find even longer highways.
Some functions that generate lots of highways
| functions | longest highway | longest highway period | % form highways | info |
|---|---|---|---|---|
| 16384n+16075 | RRLRLLRRLRRRRRRRRRLR | 5307264488 | 28.1% | biggest highway found |
| 16384n+15435 16384n+948 |
RRLRLLRLLLRRRRRRR | 320374420 | 10.7% | periods of around 1m |
| 8192n+8106 | LRLRLRLRRRRRRRLRRRRRLRLRR | 907904 | 94.9% | periods vary from 3k to 27k |
| 16384n+12892 | LLRRRLRLLRLLRRRLLRLLLRLRRLRLRLL RLLRLRLLLRRLLRRRRRLRRRRRLRLRLRR | 8797680 | 44.6% | got the rule from vmainen. Periods around 5k |
| 32768n+28757 | RLRLRLRLLLLLRRRRLLLR | 300078 | 24.1% | 20k - 300k |