User:Azerty/Champions Zoology: Difference between revisions

Revision as of 09:08, 30 December 2025

This is a zoology of champions and what they compute.

Classification	Examples	Scale
Chaotic	`1RB1LB_1LA---` (bbch) BB(2,2) `1RB---_1LB0RC_1LC1LA` (bbch) BB(3,2) `1RB1LB_1LA0LC_---1LD_1RD0RA` (bbch) BB(4,2)	$O (n^{2})$
Multiplier	`1RB2LB---_2LA2RB1LB` (bbch) BB(2,3) `1RB1LB_1LA1LC_1RC0LC` (bbch) BBt(3,2)	$O (n^{2})$
Piecewise Affine Function	`1PB1PA1TA_2TB2PB2PC_---2PA1TC` TT(3,3)	$O (n^{3})$
Counter	`1RB------_0RC0RB1LC_1LB2RC0LB` (bbch) BBt(3,3,2) `1RB------_1RC------_0RD0RC1LD_1LC2RD0LC` (bbch) BBti(8)	$O (2^{n})$
Collatz-like	`1RB1RA_1RC1RE_1LD---_1LA1LD_---0RB` (bbch) BBwsms(5,2)	$O (2^{n})$

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 {| class="wikitable"
 !Classification
-!Description
 !Examples
 !Scale
 |-
 |Chaotic
-|Have a chaotic behavior and repeating patterns that go back and forth.
 |
 * {{TM|1RB1LB_1LA---|halt}} BB(2,2)
@@ Line 15: / Line 13: @@
 |-
 |Multiplier
-|Create a number then multiply it.
 |
 * {{TM|1RB2LB---_2LA2RB1LB|halt}} BB(2,3)
@@ Line 22: / Line 19: @@
 |-
 |[[Piecewise Affine Function]]
-|Iterate a function built by gluing together straight-line formulas, each one used on a different part of the input.
 |
 * <code>1PB1PA1TA_2TB2PB2PC_---2PA1TC</code> TT(3,3)
@@ Line 28: / Line 24: @@
 |-
 |Counter
-|Count in base ≥ 2 until the number reaches a certain length.
 |
 * {{TM|1RB------_0RC0RB1LC_1LB2RC0LB|halt}} BBt(3,3,2)
@@ Line 35: / Line 30: @@
 |-
 |[[Collatz-like]]
-|Iterate a function that return a larger number depending of the input modulo.
 |
 * {{TM|1RB1RA_1RC1RE_1LD---_1LA1LD_---0RB|halt}} BBwsms(5,2)
 |<math>O(2^n)</math>
 |}