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".

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".

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.