Cryptids: Difference between revisions

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'''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.
[[File:Lovecraft beaver.png|alt=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.|thumb|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.
If there exists a Cryptid with n states and m symbols, then BB(n, m) cannot be solved without solving this hard math problem.
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== Cryptids at the Edge ==
== Cryptids at the Edge ==


This is a list of Minimal Cryptids (Cryptids in a class with no strictly smaller known Cryptid). All of these Cryptids were "discovered in the wild" rather than "constructed".
This is a list of notable Minimal Cryptids (Cryptids in a [[:Category:BB_Domains|domain]] with no strictly smaller known Cryptid). All of these Cryptids were "discovered in the wild" rather than "constructed".


{| class="wikitable"
{| class="wikitable"
|-
|-
! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note
! Name !! BB domain !! Machine !! Date !! Discoverer !! Note
|-
|-
|[[Bigfoot]]
|[[Bigfoot]]
|[[BB(3,3)]]
|[[BB(3,3)]]
|{{TM|1RB2RA1LC_2LC1RB2RB_---2LA1LA|undecided}}
|{{TM|1RB2RA1LC_2LC1RB2RB_---2LA1LA|undecided}}
|[https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html BB(3, 3) is hard]
|Nov 2023
|Nov 2023
|[[User:Sligocki|Shawn Ligocki]]
|[[User:Sligocki|Shawn Ligocki]]
Line 24: Line 24:
|[[BB(2,5)]]
|[[BB(2,5)]]
|{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB0LA|undecided}}
|{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB0LA|undecided}}
|[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html BB(2, 5) is hard]
|May 2024
|May 2024
|Daniel Yuan
|Daniel Yuan
|
|
|-
|[[Bonus cryptid]]
|[[BB(2,5)]]
|{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB1LB}}
|May 2024
|Daniel Yuan
|Probviously non-halting.
|-
|-
|[[Antihydra]]
|[[Antihydra]]
|[[BB(6)]]
|[[BB(6)]]
|{{TM|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA|undecided}}
|{{TM|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA|undecided}}
|[https://discord.com/channels/960643023006490684/1026577255754903572/1256223215206924318 Discord message]
|June 2024
|June 2024
|<code>@mxdys</code>, shown to be a Cryptid by <code>@racheline</code>.
|<code>@mxdys</code>, shown to be a Cryptid by <code>@racheline</code>.
|Same as '''Hydra''' but starting iteration from 8 instead of 3 and with termination condition <code>O > 2E</code> instead of <code>E > 2O</code>, hence the name '''Antihydra'''.
|Same as '''Hydra''' but starting iteration from 8 instead of 3 and with termination condition <code>O > 2E</code> instead of <code>E > 2O</code>, hence the name '''Antihydra'''.
|-
|[[Lucy's Moonlight]]
|[[BB(6)]]
|{{TM|1RB0RD_0RC1RE_1RD0LA_1LE1LC_1RF0LD_---0RA}}
|Mar 2025
|Racheline
|Probviously halting.
|-
|
|[[BB(6)]]
|{{TM|1RB1RC_1LC1LE_1RA1RD_0RF0RE_1LA0LB_---1RA|undecided}}
|Jul 2024
|<code>mxdys</code>
|Variant of Hydra and Antihydra. Probviously non-halting.
|-
|
|[[BB(6)]]
|{{TM|1RB1LD_1RC1RE_0LA1LB_0LD1LC_1RF0RA_---0RC|undecided}}
|Aug 2024
|<code>mxdys</code>
|Similar random walk mechanism to Hydra, Antihydra. Probviously non-halting.
|-
|
|[[BB(6)]]
|{{TM|1RB0LD_1RC1RF_1LA0RA_0LA0LE_1LD1LA_0RB---|undecided}}
|Sep 2024
|Daniel Yuan
|Similar random walk mechanism to Hydra, Antihydra. Probviously non-halting.
|-
|
|[[BB(6)]]
|{{TM|1RB0LB_1LC0RE_1LA1LD_0LC---_0RB0RF_1RE1RB|undecided}}
|Nov 2024
|Racheline
|Similar random walk mechanism to Hydra, Antihydra. Probviously non-halting.
|-
|
|[[BB(6)]]
|{{TM|1RB1LA_1LC0RE_1LF1LD_0RB0LA_1RC1RE_---0LD|undecided}}
|Jan 2025
|<code>mxdys</code>
|Probviously non-halting.
|-
|
|[[BB(6)]]
|{{TM|1RB1RA_0RC1RC_1LD0LF_0LE1LE_1RA0LB_---0LC|undecided}}
|Jul 2024
|<code>mxdys</code>
|Has near-identical behavior to 16 related BB(6) holdouts. Probviously halting.
|-
|
|[[BB(6)]]
|{{TM|1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF}}
|Jul 2024
|Racheline
|Probviously halting.
|-
|
|[[BB(6)]]
|{{TM|1RB0RE_1LC1LD_0RA0LD_1LB0LA_1RF1RA_---1LB}}
|Jul 2024
|Racheline
|Probviously halting.
|-
|
|[[BB(6)]]
|{{TM|1RB0LC_0LC0RF_1RD1LC_0RA1LE_---0LD_1LF1LA}}
|Jul 2024
|Racheline
|Probviously halting.
|-
|
|[[BB(6)]]
|{{TM|1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE}}
|Nov 2024
|Racheline
|Probviously halting.
|-
|
|[[BB(6)]]
|{{TM|1RB---_0RC0RE_1RD1RF_1LE0LB_1RC0LD_1RC1RA}}
|Nov 2024
|Racheline
|Probviously halting.
|-
|
|[[BB(6)]]
|{{TM|1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE}}
|Jul 2025
|<code>mxdys</code>
|Probviously halting.
|-
|
|[[BB(6)]]
|{{TM|1RB1LE_0LC0LB_1RD1LC_1RD1RA_1RF0LA_---1RE}}
|Jul 2024
|Racheline
|Probviously decidable. Estimated to have a 3/5 chance of 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.
* {{TM|1RB1RE_1LC0RA_0RD1LB_---1RC_1LF1RE_0LB0LE|undecided}}
* {{TM|1RB0LD_1LC0RA_1RA1LB_1LA1LE_1RF0LC_---0RE|undecided}}
* {{TM|1RB0RB_1LC1RE_1LF0LD_1RA1LD_1RC1RB_---1LC|undecided}}
* {{TM|1RB---0RB0LA2RA_2LB2LA3RA4LB0LB|undecided}}
* {{TM|1RB3LA1LA1RA3RA_2LB2RA---4RB1LB|undecided}}
* {{TM|1RB3LA1LA1RA1RA_2LB2RA---4RB1LB|undecided}}
* {{TM|1RB3LB---4LA1RB_2LA4LA4LB3RB1RA|undecided}} [https://discord.com/channels/960643023006490684/1375584513777995957 Analysis by @mxdys]


== Larger Cryptids ==
== Larger Cryptids ==


A more complete list of all known Cryptids over a wider range of states and symbols. These Cryptds were all "constructed" rather than "discovered".
A more complete list of notable known Cryptids over a wider range of states and symbols. These Cryptids were all "constructed" rather than "discovered".


{| class="wikitable"
{| class="wikitable"
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! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note
! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note
|-
|-
|ZF
|[[Independence from ZFC|ZF]]
|BB(745)
|BB(745)
|O'Rear's machine: https://github.com/sorear/metamath-turing-machines/blob/master/zf2.nql
|style="width:30%;word-break:break-word"|O'Rear's machine: https://github.com/sorear/metamath-turing-machines/blob/master/zf2.nql
Riebel's analysis: https://www.ingo-blechschmidt.eu/assets/bachelor-thesis-undecidability-bb748.pdf
Riebel's analysis: https://www.ingo-blechschmidt.eu/assets/bachelor-thesis-undecidability-bb748.pdf
|
|
Line 57: Line 169:
|RH
|RH
|BB(744)
|BB(744)
|https://github.com/sorear/metamath-turing-machines/blob/master/riemann-matiyasevich-aaronson.nql
|style="width:30%;word-break:break-word"|https://github.com/sorear/metamath-turing-machines/blob/master/riemann-matiyasevich-aaronson.nql
|
|
|2016
|2016
Line 65: Line 177:
|Goldbach
|Goldbach
|BB(25)
|BB(25)
|https://gist.github.com/anonymous/a64213f391339236c2fe31f8749a0df6<nowiki/>
|style="width:30%;word-break:break-word"|https://gist.github.com/anonymous/a64213f391339236c2fe31f8749a0df6
<div class="toccolours mw-collapsible mw-collapsed">Machine code:<div class="mw-collapsible-content"><pre style="word-break:break-all">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</pre></div></div>
|
|
|2016
|2016
Line 71: Line 184:
|The machine halts if and only if [https://en.wikipedia.org/wiki/Goldbach%27s_conjecture Golbach's conjecture] is false. Its behavior has been verified in Lean.<ref>https://github.com/lengyijun/goldbach_tm</ref>
|The machine halts if and only if [https://en.wikipedia.org/wiki/Goldbach%27s_conjecture Golbach's conjecture] is false. Its behavior has been verified in Lean.<ref>https://github.com/lengyijun/goldbach_tm</ref>
|-  
|-  
| Erdős || BB(5,4) and
| Erdős
BB(15)
| BB(5,4) and BB(15)
|
|style="width:30%;word-break:break-word"|
https://docs.bbchallenge.org/other/powers_of_two_5_4.txt
https://docs.bbchallenge.org/other/powers_of_two_5_4.txt
 
<div class="toccolours mw-collapsible mw-collapsed">Machine code:<div class="mw-collapsible-content"><pre style="word-break:break-all">1RB3RA2RA1RB_0LC2RB1RA3RB_0LD1LC2LE3LC_3RE2RE---1RE_0RB1LE2LE3LE</pre></div></div>
https://docs.bbchallenge.org/other/powers_of_two_15_2.txt
https://docs.bbchallenge.org/other/powers_of_two_15_2.txt
<div class="toccolours mw-collapsible mw-collapsed">Machine code:<div class="mw-collapsible-content"><pre style="word-break:break-all">1RB1RO_0RC0RC_0RD1RJ_0LE1RC_0LF1LK_0LG1LE_0LH1LF_1RI0LL_0RB1LK_1RC0RA_0LI1LN_1RM---_0RI0RO_0LK1LK_1LM1RA</pre></div></div>
|| [https://arxiv.org/abs/2107.12475 arxiv preprint] || Jul 2021 || [[User:Cosmo|Tristan Stérin]] (<code>@cosmo</code>) and Damien Woods || The machine halts if and only if the following conjecture by Erdős is false: "For all n > 8, there is at least one 2 in the base-3 representation of 2^n"
|| [https://arxiv.org/abs/2107.12475 arxiv preprint] || Jul 2021 || [[User:Cosmo|Tristan Stérin]] (<code>@cosmo</code>) and Damien Woods || The machine halts if and only if the following conjecture by Erdős is false: "For all n > 8, there is at least one 2 in the base-3 representation of 2^n"
|-
|-
|Weak Collatz
|Weak Collatz
|BB(124) and BB(43,4)
|BB(124) and BB(43,4)
|https://docs.bbchallenge.org/other/weak_Collatz_conjecture_124_2.txt (unverified)
|style="width:30%;word-break:break-word"|https://docs.bbchallenge.org/other/weak_Collatz_conjecture_124_2.txt (unverified)
https://docs.bbchallenge.org/other/weak_Collatz_conjecture_43_4.txt (unverified)
https://docs.bbchallenge.org/other/weak_Collatz_conjecture_43_4.txt (unverified)
|
|
Line 89: Line 203:
Not independently verified, and probably easy to further optimise.
Not independently verified, and probably easy to further optimise.
|-
|-
| Bigfoot - compiled|| [[BB(7)]]|| <code>0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB</code>|| [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-2140887228 Bigfoot Comment] || June 2024 || <code>@Iijil1</code>|| Compilation of Bigfoot into 2 symbols, there was a previous compilation [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-1774200442 with 8 states]
| Bigfoot - compiled|| [[BB(7)]]||style="width:30%;word-break:break-word"| <code>0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB</code>|| [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-2140887228 Bigfoot Comment] || June 2024 || <code>@Iijil1</code>|| Compilation of Bigfoot into 2 symbols, there was a previous compilation [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-1774200442 with 8 states]
|-
|-
| Hydra - compiled
| Hydra - compiled
|BB(9)
|BB(9)
|<pre>
|style="width:30%;word-break:break-word"|<pre>
0RB0LD_1LC0LI_1LD1LB_0LE0RG_1RF0RH_1RA---_0RD0LB_0RA---_0RF1RZ
0RB0LD_1LC0LI_1LD1LB_0LE0RG_1RF0RH_1RA---_0RD0LB_0RA---_0RF1RZ
</pre>[[File:Hydra_9_states.txt]]
</pre>[[File:Hydra_9_states.txt]]
Line 99: Line 213:
|June 2024
|June 2024
|<code>@Iijil1</code>
|<code>@Iijil1</code>
|Compilation of Hydra into 2 symbols, all[https://discord.com/channels/960643023006490684/1084047886494470185/1253193750486974464 confirmed by Shawn Ligocki]. <code>@Iijil1</code> provided 24 TMs which all emulate the same behavior.
|Compilation of Hydra into 2 symbols, all [https://discord.com/channels/960643023006490684/1084047886494470185/1253193750486974464 confirmed by Shawn Ligocki]. <code>@Iijil1</code> provided 24 TMs which all emulate the same behavior.
<small>[https://discord.com/channels/960643023006490684/1084047886494470185/1247560072427474955 Previous compilation had 10 states], by Daniel Yuan, also [https://discord.com/channels/960643023006490684/1084047886494470185/1247579473042346136 confirmed by Shawn Ligocki].</small>  
<small>[https://discord.com/channels/960643023006490684/1084047886494470185/1247560072427474955 Previous compilation had 10 states], by Daniel Yuan, also [https://discord.com/channels/960643023006490684/1084047886494470185/1247579473042346136 confirmed by Shawn Ligocki].</small>  
|}
|}

Latest revision as of 02:32, 21 August 2025

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 domain Machine Date Discoverer Note
Bigfoot BB(3,3) 1RB2RA1LC_2LC1RB2RB_---2LA1LA (bbch) Nov 2023 Shawn Ligocki
Hydra BB(2,5) 1RB3RB---3LA1RA_2LA3RA4LB0LB0LA (bbch) May 2024 Daniel Yuan
Bonus cryptid BB(2,5) 1RB3RB---3LA1RA_2LA3RA4LB0LB1LB (bbch) May 2024 Daniel Yuan Probviously non-halting.
Antihydra BB(6) 1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA (bbch) June 2024 @mxdys, shown to be a Cryptid by @racheline. Same as Hydra but starting iteration from 8 instead of 3 and with termination condition O > 2E instead of E > 2O, hence the name Antihydra.
Lucy's Moonlight BB(6) 1RB0RD_0RC1RE_1RD0LA_1LE1LC_1RF0LD_---0RA (bbch) Mar 2025 Racheline Probviously halting.
BB(6) 1RB1RC_1LC1LE_1RA1RD_0RF0RE_1LA0LB_---1RA (bbch) Jul 2024 mxdys Variant of Hydra and Antihydra. Probviously non-halting.
BB(6) 1RB1LD_1RC1RE_0LA1LB_0LD1LC_1RF0RA_---0RC (bbch) Aug 2024 mxdys Similar random walk mechanism to Hydra, Antihydra. Probviously non-halting.
BB(6) 1RB0LD_1RC1RF_1LA0RA_0LA0LE_1LD1LA_0RB--- (bbch) Sep 2024 Daniel Yuan Similar random walk mechanism to Hydra, Antihydra. Probviously non-halting.
BB(6) 1RB0LB_1LC0RE_1LA1LD_0LC---_0RB0RF_1RE1RB (bbch) Nov 2024 Racheline Similar random walk mechanism to Hydra, Antihydra. Probviously non-halting.
BB(6) 1RB1LA_1LC0RE_1LF1LD_0RB0LA_1RC1RE_---0LD (bbch) Jan 2025 mxdys Probviously non-halting.
BB(6) 1RB1RA_0RC1RC_1LD0LF_0LE1LE_1RA0LB_---0LC (bbch) Jul 2024 mxdys Has near-identical behavior to 16 related BB(6) holdouts. Probviously halting.
BB(6) 1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF (bbch) Jul 2024 Racheline Probviously halting.
BB(6) 1RB0RE_1LC1LD_0RA0LD_1LB0LA_1RF1RA_---1LB (bbch) Jul 2024 Racheline Probviously halting.
BB(6) 1RB0LC_0LC0RF_1RD1LC_0RA1LE_---0LD_1LF1LA (bbch) Jul 2024 Racheline Probviously halting.
BB(6) 1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE (bbch) Nov 2024 Racheline Probviously halting.
BB(6) 1RB---_0RC0RE_1RD1RF_1LE0LB_1RC0LD_1RC1RA (bbch) Nov 2024 Racheline Probviously halting.
BB(6) 1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE (bbch) Jul 2025 mxdys Probviously halting.
BB(6) 1RB1LE_0LC0LB_1RD1LC_1RD1RA_1RF0LA_---1RE (bbch) Jul 2024 Racheline Probviously decidable. Estimated to have a 3/5 chance of 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.

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 domain Machine Announcement Date Discoverer Note
ZF BB(745) O'Rear's machine: https://github.com/sorear/metamath-turing-machines/blob/master/zf2.nql

Riebel's analysis: https://www.ingo-blechschmidt.eu/assets/bachelor-thesis-undecidability-bb748.pdf

2016, 2023 O’Rear and Riebel The machine halts if and only if Zermelo–Fraenkel set theory is inconsistent.
RH BB(744) https://github.com/sorear/metamath-turing-machines/blob/master/riemann-matiyasevich-aaronson.nql 2016 Matiyasevich and O’Rear The machine halts if and only if Riemann Hypothesis is false.
Goldbach BB(25) https://gist.github.com/anonymous/a64213f391339236c2fe31f8749a0df6
Machine code:
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
 2016 anonymous The machine halts if and only if Golbach's conjecture is false. Its behavior has been verified in Lean.[1]
Erdős BB(5,4) and BB(15)

https://docs.bbchallenge.org/other/powers_of_two_5_4.txt

Machine code:
1RB3RA2RA1RB_0LC2RB1RA3RB_0LD1LC2LE3LC_3RE2RE---1RE_0RB1LE2LE3LE

https://docs.bbchallenge.org/other/powers_of_two_15_2.txt

Machine code:
1RB1RO_0RC0RC_0RD1RJ_0LE1RC_0LF1LK_0LG1LE_0LH1LF_1RI0LL_0RB1LK_1RC0RA_0LI1LN_1RM---_0RI0RO_0LK1LK_1LM1RA
 arxiv preprint Jul 2021 Tristan Stérin (@cosmo) and Damien Woods The machine halts if and only if the following conjecture by Erdős is false: "For all n > 8, there is at least one 2 in the base-3 representation of 2^n"
Weak Collatz BB(124) and BB(43,4) https://docs.bbchallenge.org/other/weak_Collatz_conjecture_124_2.txt (unverified)

https://docs.bbchallenge.org/other/weak_Collatz_conjecture_43_4.txt (unverified)

Jul 2021 Tristan Stérin The machine halts if and only if the "weak Collatz conjecture" is false. The weak Collatz conjecture states that the iterated Collatz map (3x+1) has only one cycle on the positive integers.

Not independently verified, and probably easy to further optimise.

Bigfoot - compiled BB(7) 0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB Bigfoot Comment June 2024 @Iijil1 Compilation of Bigfoot into 2 symbols, there was a previous compilation with 8 states
Hydra - compiled BB(9) 
0RB0LD_1LC0LI_1LD1LB_0LE0RG_1RF0RH_1RA---_0RD0LB_0RA---_0RF1RZ
File:Hydra 9 states.txt 		Discord message June 2024 @Iijil1 Compilation of Hydra into 2 symbols, all confirmed by Shawn Ligocki. @Iijil1 provided 24 TMs which all emulate the same behavior.

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=3272"