View source for 1RB1LD 1RC1RB 1LC1LA 0RC0RD

{{machine|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}
{{TM|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}

[[Blanking Beaver]] BLB(4,2) champion which creates a blank tape after 32,779,477 steps. It was discovered and reported by Nick Drozd in 2021.<ref>Nick Drozd. [https://nickdrozd.github.io/2021/07/11/self-cleaning-turing-machine.html A New Record in Self-Cleaning Turing Machines]. 2021.</ref>

== Analysis by [[User:sligocki|Shawn Ligocki]] ==
Let <math display="block">D(a, b) = 0^\infty \; 1^a \; 0^b \; \textrm{D>} \; 0^\infty</math>then:<math display="block">\begin{array}{lc}
  D(a+3, & b) & \to & D(a, b+5) \\
  D(0, & b) & = & \textrm{Blank} \\
  D(1, & b) & \to & D(b+2, 4) \\
  D(2, & b) & \to & D(b+3, 4) \\
\end{array}</math>let <math>D(a) = D(a, 4)</math>, then we can simplify to:

<math display="block">\begin{array}{lc}
  D(3k  ) & \to & \textrm{Blank} \\
  D(3k+1) & \to & D(5k+6) \\
  D(3k+2) & \to & D(5k+7) \\
\end{array}</math>Starting from <math>D(2)</math> (at step 19) we get the trajectory:

<math display="block">\begin{array}{l}
D(2) 
    & \to & D(7) & \to & D(16) & \to & D(31) & \to & D(56) & \to & D(97) \\
    & \to & D(166) & \to & D(281) & \to & D(472) & \to & D(791) & \to & D(1322) \\
    & \to & D(2207) & \to & D(3682) & \to & D(6141) & \to & \textrm{Blank} \\
\end{array} </math>which has the remarkable luck of applying this [[Collatz-like]] map 14 times before reaching the blanking config (expected # of applications before halting is 3).

The map and trajectory are equivalent to that of the [[BB(5) champion]]. For all <math>k</math>, let <math>f(k)</math> be the number such that <math>D(k)\to D(f(k))</math>, or <math>\text{HALT}</math> if <math>D(k)\to\textrm{Blank}</math>, and let <math>g</math> be the map simulated by the BB(5) champion. Then:

<math display="block">\begin{array}{lc}
  g(2(3k)+2) & = & g(6k+2) & = & \text{HALT} & = & f(3k) \\
  g(2(3k+1)+2) & = & g(6k+4) & = & 10k+14 & = & 2f(3k+1)+2 \\
  g(2(3k+2)+2) & = & g(6k+6) & = & 10k+16 & = & 2f(3k+2)+2 \\
\end{array}</math>

So the size of this machine's BLB output is tied to the size of the BB(5) champion's output.

== References ==