1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA

This machine was the first identified BB(6) Collatz-like Cryptid, and is closely related to Hydra.

It simulates the Collatz-like iteration

$${\begin{array}{l}A(2a,&b)&\to &A(3a,&b+2)\\A(2a+1,&b)&\to &A(3a+1,&b-1)&{\text{if}}&b>0\\A(2a+1,&0)&\to &{\text{HALT}}\end{array}}$$

starting from

A(8, 0)

,

using configurations of the form

A(a+4, b) = ^ 1^b 0 1^a E> $

It was discovered by mxdys on 28 Jun 2024 and shared on Discord [1].

Compared to the Hydra iteration, this one starts at (8, 0) rather than (3, 0), and the roles of odd and even

a

are exchanged (in terms of which increases

b

by two, and which decrements

b

or halts).

Obstacles to proving the long-run behavior are equally serious.

Like the Hydra iteration, this one is biased toward increasing the value of

b

(assuming equal chances of adding +2 or -1). There is no halt in the first ten million iterations, by which point

b

has reached 498503.