Bigfoot

Unsolved problem:

Does Bigfoot run forever?

1RB2RA1LC_2LC1RB2RB_---2LA1LA (bbch)

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

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

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

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.