Bigfoot

Unsolved problem:

Does Bigfoot run forever?

1RB2RA1LC_2LC1RB2RB_---2LA1LA (bbch)

Bigfoot is a BB(3,3) Cryptid. It simulates the Collatz-like function

$${\begin{array}{l}A(a,&6k,&c)&\to &A(a,&8k+c-1,&2)&{\text{if}}&8k+c\geq 1\\A(a,&6k+1,&c)&\to &A(a+1,&8k+c-1,&3)&{\text{if}}&8k+c\geq 1\\A(a,&6k+2,&c)&\to &A(a-1,&8k+c+3,&2)&{\text{if}}&a\geq 1\\A(a,&6k+3,&c)&\to &A(a,&8k+c+1,&5)\\A(a,&6k+4,&c)&\to &A(a+1,&8k+c+3,&2)\\A(a,&6k+5,&c)&\to &A(a,&8k+c+5,&3)\\\end{array}}$$

$$A(0,6k+2,c)\to {\text{Halt}}(16k+2c+7)$$

starting from $A(2,1,2)$.

It was discovered by Shawn Ligocki on 14 Oct 2023 and shared in the blog post BB(3, 3) is Hard.

In May 2024, Iijil shared a 7-state, 2-symbol machine with the same behavior as Bigfoot.