User:Polygon/Page for testing: Difference between revisions
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(→Analysis by Shawn Ligocki: Added level 1) |
(Added level 2) |
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| Line 12: | Line 12: | ||
0^5 <A 212 22^n 52 5555 → <A 212 55 2 55^n+3 52 | 0^5 <A 212 22^n 52 5555 → <A 212 55 2 55^n+3 52 | ||
00 <A 212 22^n 2 52 5 → <A 212 55^n+2 52 | 00 <A 212 22^n 2 52 5 → <A 212 55^n+2 52 | ||
Level 2 | |||
Repeating the first rule above we get: | |||
0^∞ <A 212 22^n 55^k → 0^∞ 212 22^n+2k | |||
which let's is prove Rule 2: | |||
0^∞ <A 212 22^n 2 55 → 0^∞ <A 212 55^n+2 2 | |||
→ 0^∞ <A 212 22^2n+4 2 | |||
</pre> | </pre> | ||
Revision as of 16:42, 23 September 2025
1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch) is the current BB(2,6) champion. It was discovered on the 19th of May 2023 by Pavel Kropitz. It halts with a score > .
Analysis by Shawn Ligocki
https://www.sligocki.com/2023/05/20/bb-2-6-p3.html
Analysis
Level 1
These rules can all be verified by direct simulation:
00 <A 212 22^n 55 → <A 212 22^n+2
00 <A 212 22^n 2 55 → <A 212 55^n+2 2
0^5 <A 212 22^n 52 5555 → <A 212 55 2 55^n+3 52
00 <A 212 22^n 2 52 5 → <A 212 55^n+2 52
Level 2
Repeating the first rule above we get:
0^∞ <A 212 22^n 55^k → 0^∞ 212 22^n+2k
which let's is prove Rule 2:
0^∞ <A 212 22^n 2 55 → 0^∞ <A 212 55^n+2 2
→ 0^∞ <A 212 22^2n+4 2