https://wiki.bbchallenge.org/wiki/Cryptids Cryptids From BusyBeaverWiki Jump to navigation Jump to search A monstrous beaver in the style of HP Lovecraft with pink tentacles coming out of its mouth, 5 red spider eyes, horns on its head, elbows and tail, moss colored fur, sharp purple claws and webbed feet. Lovecraftian Beaver fan art made by Lauren Cryptids are Turing Machines whose behavior (when started on a blank tape) can be described completely by a relatively simple mathematical rule, but where that rule falls into a class of unsolved (and presumed hard) mathematical problems. This definition is somewhat subjective (What counts as a simple rule? What counts as a hard problem?). In practice, most currently known small Cryptids have Collatz-like behavior. In other words, the halting problem from blank tape of Cryptids is mathematically-hard. If there exists a Cryptid with n states and m symbols, then BB(n, m) cannot be solved without solving this hard math problem. The name Cryptid was proposed by Shawn Ligocki in an Oct 2023 blog post announcing the discovery of Bigfoot. Cryptids at the Edge This is a list of notable Minimal Cryptids (Cryptids in a domain with no strictly smaller known Cryptid). All of these Cryptids were "discovered in the wild" rather than "constructed". Name BB Machine Date Discoverer Note domain Bigfoot BB 1RB2RA1LC_2LC1RB2RB_---2LA1LA (bbch) Nov Shawn (3,3) 2023 Ligocki Hydra BB 1RB3RB---3LA1RA_2LA3RA4LB0LB0LA (bbch) May Daniel Yuan (2,5) 2024 Bonus BB 1RB3RB---3LA1RA_2LA3RA4LB0LB1LB (bbch) May Daniel Yuan Probviously cryptid (2,5) 2024 non-halting. Same as Hydra but starting iteration from @mxdys, 8 instead of 3 1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA June shown to be and with Antihydra BB(6) (bbch) 2024 a Cryptid termination by condition O > @racheline. 2E instead of E > 2O, hence the name Antihydra. Lucy's BB(6) 1RB0RD_0RC1RE_1RD0LA_1LE1LC_1RF0LD_---0RA Mar Racheline Probviously Moonlight (bbch) 2025 halting. Variant of 1RB1RC_1LC1LE_1RA1RD_0RF0RE_1LA0LB_---1RA Jul Hydra and BB(6) (bbch) 2024 mxdys Antihydra. Probviously non-halting. Similar random walk mechanism BB(6) 1RB1LD_1RC1RE_0LA1LB_0LD1LC_1RF0RA_---0RC Aug mxdys to Hydra, (bbch) 2024 Antihydra. Probviously non-halting. Similar random walk mechanism BB(6) 1RB0LD_1RC1RF_1LA0RA_0LA0LE_1LD1LA_0RB--- Sep Daniel Yuan to Hydra, (bbch) 2024 Antihydra. Probviously non-halting. Similar random walk mechanism BB(6) 1RB0LB_1LC0RE_1LA1LD_0LC---_0RB0RF_1RE1RB Nov Racheline to Hydra, (bbch) 2024 Antihydra. Probviously non-halting. Space BB(6) 1RB1LA_1LC0RE_1LF1LD_0RB0LA_1RC1RE_---0LD Jan mxdys Probviously Needle (bbch) 2025 non-halting. Has near-identical 1RB1RA_0RC1RC_1LD0LF_0LE1LE_1RA0LB_---0LC Jul behavior to 16 BB(6) (bbch) 2024 mxdys related BB(6) holdouts. Probviously halting. BB(6) 1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF Jul Racheline Probviously (bbch) 2024 halting. BB(6) 1RB0RE_1LC1LD_0RA0LD_1LB0LA_1RF1RA_---1LB Jul Racheline Probviously (bbch) 2024 halting. BB(6) 1RB0LC_0LC0RF_1RD1LC_0RA1LE_---0LD_1LF1LA Jul Racheline Probviously (bbch) 2024 halting. BB(6) 1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE Nov Racheline Probviously (bbch) 2024 halting. BB(6) 1RB---_0RC0RE_1RD1RF_1LE0LB_1RC0LD_1RC1RA Nov Racheline Probviously (bbch) 2024 halting. BB(6) 1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE Jul mxdys Probviously (bbch) 2025 halting. Probviously decidable. Estimated to have a 3/5 BB(6) 1RB1LE_0LC0LB_1RD1LC_1RD1RA_1RF0LA_---1RE Jul Racheline chance of (bbch) 2024 becoming a translated cycler and a 2 /5 chance of halting. The following machines have chaotic behavior, but have not been classified as Cryptids due to seemingly lacking a connection to any known open mathematical problems, such as Collatz-like problems. * 1RB1RE_1LC0RA_0RD1LB_---1RC_1LF1RE_0LB0LE (bbch) * 1RB0LD_1LC0RA_1RA1LB_1LA1LE_1RF0LC_---0RE (bbch) * 1RB0RB_1LC1RE_1LF0LD_1RA1LD_1RC1RB_---1LC (bbch) * 1RB---0RB0LA2RA_2LB2LA3RA4LB0LB (bbch) * 1RB3LA1LA1RA3RA_2LB2RA---4RB1LB (bbch) * 1RB3LA1LA1RA1RA_2LB2RA---4RB1LB (bbch) * 1RB3LB---4LA1RB_2LA4LA4LB3RB1RA (bbch) Analysis by @mxdys Larger Cryptids A more complete list of notable known Cryptids over a wider range of states and symbols. These Cryptids were all "constructed" rather than "discovered". Name BB Machine Announcement Date Discoverer Note domain The machine Wade's machine: https://codeberg.org/ajwade/turing_machine_explorer/ Wade, based halts if and ZF BB src/commit/ 2025 on work by only if (432) 33b30300054242201a95679aacf7e74312bd8803b0df9a85d2314095efd6804e CatIsFluffy Zermelo-Fraenkel and O'Rear set theory is inconsistent. The machine BB https://github.com/sorear/metamath-turing-machines/blob/master/ Matiyasevich halts if and RH (744) riemann-matiyasevich-aaronson.nql 2016 and O'Rear only if Riemann Hypothesis is false. The machine halts if and https://gist.github.com/anonymous/a64213f391339236c2fe31f8749a0df6 only if Machine code: Golbach's Goldbach BB(25) 2016 anonymous conjecture is 1RB1RD_1LC1RB_0RA1LC_0LQ1RE_0LF1RG_0LC1LF_0LF0LH_1LQ1LI_0RJ0LI_1RK0LJ_0RL0RS_1RL0RM_1RN1RM_0LO0LU_0LP1LO_1RH1LX_1LR1LQ_0RK0LT_1LR1RS_---1RC_1LV1LU_0LW0LJ_0RK0LW_1RY1LX_1RE1RY false. Its behavior has been verified in Lean.^[1] https://docs.bbchallenge.org/other/powers_of_two_5_4.txt The machine halts if and Machine code: only if the following BB 1RB3RA2RA1RB_0LC2RB1RA3RB_0LD1LC2LE3LC_3RE2RE---1RE_0RB1LE2LE3LE Tristan conjecture by Erdos (5,4) arxiv Jul Sterin Erdos is false: and BB https://docs.bbchallenge.org/other/powers_of_two_15_2.txt preprint 2021 (@cosmo) and "For all n > 8, (15) Damien Woods there is at Machine code: least one 2 in the base-3 1RB1RO_0RC0RC_0RD1RJ_0LE1RC_0LF1LK_0LG1LE_0LH1LF_1RI0LL_0RB1LK_1RC0RA_0LI1LN_1RM---_0RI0RO_0LK1LK_1LM1RA representation of 2^n" The machine halts if and only if the "weak Collatz conjecture" is false. The weak Collatz conjecture https://docs.bbchallenge.org/other/weak_Collatz_conjecture_124_2.txt states that the BB (unverified) iterated Collatz Weak (124) Jul Tristan map (3x+1) has Collatz and BB https://docs.bbchallenge.org/other/weak_Collatz_conjecture_43_4.txt 2021 Sterin only one cycle (43,4) (unverified) on the positive integers. Not independently verified, and probably easy to further optimise. Compilation of Bigfoot Bigfoot into 2 - BB(7) 0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB Bigfoot June @Iijil1 symbols, there compiled Comment 2024 was a previous compilation with 8 states Compilation of Hydra into 2 symbols, all confirmed by Shawn Ligocki. @Iijil1 provided 24 TMs which all Hydra - 0RB0LD_1LC0LI_1LD1LB_0LE0RG_1RF0RH_1RA---_0RD0LB_0RA---_0RF1RZ Discord June emulate the same compiled BB(9) message 2024 @Iijil1 behavior. File:Hydra 9 states.txt Previous compilation had 10 states, by Daniel Yuan, also confirmed by Shawn Ligocki . Beeping Busy Beaver Cryptids were actually noticed in the Beeping Busy Beaver problem before they were in the classic Busy Beaver. See Mother of Giants describing a "family" of Turing machines which "probviously" quasihalt, but requires solving a Collatz-like problem in order to actually prove it. They are all TMs formed by filling in the missing transition in 1RB1LE_0LC0LB_0LD1LC_1RD1RA_---0LA with different values. 1. | https://github.com/lengyijun/goldbach_tm Retrieved from "https://wiki.bbchallenge.org/w/index.php?title= Cryptids&oldid=4522" Categories: * Zoology * Cryptids Navigation menu Personal tools * Create account * Log in Namespaces * Page * Discussion [ ] English Views * Read * View source * View history [ ] More Search [ ] [Search] [Go] Navigation * Main page * Recent changes * Random page * All pages * Help about MediaWiki Tools * What links here * Related changes * Special pages * Printable version * Permanent link * Page information * This page was last edited on 13 October 2025, at 20:55. * Content is available under Creative Commons Attribution unless otherwise noted. * Privacy policy * About BusyBeaverWiki * Disclaimers * Creative Commons Attribution * Powered by MediaWiki