1RB1RA 0LC1LE 1LD1LC 1LA0LB 1LF1RE ---0RA: Difference between revisions

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{{machine|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA}}
{{machine|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA}}
This machine was the first identified [[BB(6)]] Collatz-like [[Cryptid]], and is closely related to [[Hydra]].


This machine was the first identified 6-state Collatz-like [[Cryptid]] and it is closely related to [[Hydra]].
It simulates the Collatz-like iteration


On June 28th 2024 on bbchallenge discord server:
<math display="block">\begin{array}{l}
* mxdys identifies the machine as a potential [[Cryptid]]:
  A(2a,  & b) & \to & A(3a,  & b+2) \\
<pre>
  A(2a+1, & b) & \to & A(3a+1, & b-1) & \text{if} & b>0 \\
1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA
  A(2a+1, & 0) & \to & \text{HALT}
(0^inf 1^4 0 1^1 0 1^19) A> (1^0 0 0^inf)
\end{array}</math>
(0^inf 1^6 0 1^2 0 1^31) A> (1^0 0 0^inf)
<br>
(0^inf 1^5 0 1^1 0 1^52) A> (1^0 0 0^inf)
starting from <pre>A(8, 0)</pre>,
(0^inf 1^7 0 1^1 0 1^82) A> (1^0 0 0^inf)
<br>
(0^inf 1^9 0 1^1 0 1^127) A> (1^0 0 0^inf)
using configurations of the form <pre>A(a+4, b) = ^ 1^b 0 1^a E> $</pre>
(0^inf 1^11 0 1^2 0 1^193) A> (1^0 0 0^inf)
(0^inf 1^10 0 1^1 0 1^295) A> (1^0 0 0^inf)
(0^inf 1^12 0 1^2 0 1^445) A> (1^0 0 0^inf)
(0^inf 1^11 0 1^1 0 1^673) A> (1^0 0 0^inf)
(0^inf 1^13 0 1^2 0 1^1012) A> (1^0 0 0^inf)
(0^inf 1^12 0 1^2 0 1^1522) A> (1^0 0 0^inf)
(0^inf 1^11 0 1^2 0 1^2287) A> (1^0 0 0^inf)
(0^inf 1^10 0 1^1 0 1^3436) A> (1^0 0 0^inf)
(0^inf 1^12 0 1^1 0 1^5158) A> (1^0 0 0^inf)
(0^inf 1^14 0 1^1 0 1^7741) A> (1^0 0 0^inf)
(0^inf 1^16 0 1^2 0 1^11614) A> (1^0 0 0^inf)
(0^inf 1^15 0 1^2 0 1^17425) A> (1^0 0 0^inf)
(0^inf 1^14 0 1^1 0 1^26143) A> (1^0 0 0^inf)
(0^inf 1^16 0 1^2 0 1^39217) A> (1^0 0 0^inf)
(0^inf 1^15 0 1^1 0 1^58831) A> (1^0 0 0^inf)
(0^inf 1^17 0 1^2 0 1^88249) A> (1^0 0 0^inf)
(0^inf 1^16 0 1^1 0 1^132379) A> (1^0 0 0^inf)
(0^inf 1^18 0 1^2 0 1^198571) A> (1^0 0 0^inf)
(0^inf 1^17 0 1^1 0 1^297862) A> (1^0 0 0^inf)
(0^inf 1^19 0 1^1 0 1^446797) A> (1^0 0 0^inf)
(0^inf 1^21 0 1^2 0 1^670198) A> (1^0 0 0^inf)
This TM looks like a random work like hydra
</pre>


* Then Yto analyses the machine and confirms that the machine is running the [[Hydra]]'s Collatz-like iterated map:  
It was discovered by mxdys on 28 Jun 2024 and shared on Discord [https://discord.com/channels/960643023006490684/1026577255754903572/1256223215206924318].
<pre>
f(2n) = 3n
f(2n+1) = 3n+1
</pre>


But iterated from 8 rather than 3 in the case of [[Hydra]] and also, the halting condition is the opposite: this machine halts iff there comes a point where O > 2E with O the number of odd iterates and E the number of even iterates.
Compared to the [[Hydra]] iteration, this one starts at (8, 0) rather than (3, 0), and the roles of odd and even <pre>a</pre> are exchanged (in terms of which increases <pre>b</pre> by two, and which decrements <pre>b</pre> or halts).
 
Obstacles to proving the long-run behavior are equally serious.
* An alternative ruleset for this TM is shown below:
Like the [[Hydra]] iteration, this one is biased toward increasing the value of <pre>b</pre> (assuming equal chances of adding +2 or -1). There is no halt in the first ten million iterations, by which point <pre>b</pre> has reached 498503.
<pre>
A(a+4, b) = 0^inf 1^b 0 1^a E> 0^inf
 
A(2a, b) -> A(3a, b+2)
A(2a+1, b) -> A(3a+1, b-1), and halt if b=0
 
Start from A(8, 0)
</pre>
 
== Review of the result ==
Pending

Revision as of 19:34, 28 June 2024

This machine was the first identified BB(6) Collatz-like Cryptid, and is closely related to Hydra.

It simulates the Collatz-like iteration


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 ten million iterations, by which point 

b

has reached 498503.

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