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 one million iterations, by which point b has reached 498503.