1RB---_0RC0RD_1LD1RB_0LE0LC_1RA0LF_1LD1LE

1RB---_0RC0RD_1LD1RB_0LE0LC_1RA0LF_1LD1LE (bbch) appears to be a chaotic probviously halting BB(6) TM, but with no estimate for halting time. It is still under analysis as of 24 Apr 2026.

Analysis by Shawn Ligocki

https://discord.com/channels/960643023006490684/1239205785913790465/1497001816741646407

1RB---_0RC0RD_1LD1RB_0LE0LC_1RA0LF_1LD1LE

Let A(a,b,c) = 0^inf 1^a 10^b C> 1^c 0^inf

A(a+1,b,c+3) --> A(a,b+2,c)

A(a,b,0) --> A(2b+1,1,a+1)
A(a,b,1) --> A(2b+3,1,a+1)
A(a,b,2) --> A(2b+5,1,a+1)

A(0,b,c+5) --> A(2b+4,2,c)
A(0,b,4) --> Halt
A(0,b,3) --> Halt

Start: A(0,1,0)

Simulated out to 100B "resets" (rule count ignoring the first rule):

  1_000_000_000  A(  1_449_166_375,  1,   3_050_820_388)
100_000_000_000  A(150_379_323_247,  1, 299_620_772_649)

Probabilistic Model

Distribution of r values over the first 5B steps (1000 buckets).

Map governing update of r stat in the limit. It is a Skewed or Asymmetric Tent Map.

Consider $r=\frac{a}{a+c}$. This value seems empirically to be be extremely uniform on the range [0,1]. And for large values of a,c there is a clear reason why: The update function is a Skewed Tent Map, a map which is known to have long-run time average distribution completely uniform.