User:Azerty/Champions Zoology: Difference between revisions

Latest revision as of 14:41, 5 January 2026

This is a zoology of champions and what they compute.

Classification	Examples	Scale
Trivial		$O (n)$
Multiplier	`1RB2LB---_2LA2RB1LB` (bbch) BB(2,3) `1RB1LB_1LA1LC_1RC0LC` (bbch) BLB(3,2)	$O (n^{2})$
Piecewise Affine Function	`1PB1PA1TA_2TB2PB2PC_---2PA1TC` TT(3,3)	$O (2^{n})$
Chaotic	`1RB1LB_1LA---` (bbch) BB(2,2) `1RB---_1LB0RC_1LC1LA` (bbch) BB(3,2) `1RB1LB_1LA0LC_---1LD_1RD0RA` (bbch) BB(4,2)	$O (2^{n})$
Exponentiater	`1RB------_1RC------_0RD0RC1LD_1LC2RD0LC` (bbch) BBti(8)	$O (2^{n})$
Collatz-like	`1RB2LA1RA1RA_1LB1LA3RB---` (bbch) BB(2,4) `1RB1LC_1RC1RB_1RD0LE_1LA1LD_---0LA` (bbch) BB(5,2) `0RB2LA1RA_1LA2RB1RC_---1LB1LC` (bbch) BB(3,3)	$O (2^{n})$

@@ Line 2: / Line 2: @@
 {| class="wikitable"
 !Classification
-!Description
 !Examples
 !Scale
+|-
+|Trivial
+|
+|<math>O(n)</math>
+|-
+|Multiplier
+|
+* {{TM|1RB2LB---_2LA2RB1LB|halt}} BB(2,3)
+* {{TM|1RB1LB_1LA1LC_1RC0LC|halt}} BLB(3,2)
+|<math>O(n^2)</math>
+|-
+|[[Piecewise Affine Function]]
+|
+* <code>1PB1PA1TA_2TB2PB2PC_---2PA1TC</code> TT(3,3)
+|<math>O(2^n)</math>
 |-
 |Chaotic
-|Have a chaotic behavior and repeating patterns that go back and forth.
 |
 * {{TM|1RB1LB_1LA---|halt}} BB(2,2)
 * {{TM|1RB---_1LB0RC_1LC1LA|halt}} BB(3,2)
 * {{TM|1RB1LB_1LA0LC_---1LD_1RD0RA|halt}} BB(4,2)
-|<math>O(n^2)</math>
+|<math>O(2^n)</math>
 |-
-|Countdown
+|Exponentiater
-|Compute a number then "count down" (usually while bouncing) until reaching 0.
 |
-* {{TM|1RB2LB---_2LA2RB1LB|halt}} BB(2,3)
+* {{TM|1RB------_1RC------_0RD0RC1LD_1LC2RD0LC|halt}} BBti(8)
-* {{TM|1RB1LB_1LA1LC_1RC0LC|halt}} BBt(3,2)
+|<math>O(2^n)</math>
-|<math>O(n^2)</math>
 |-
-|Exponential countdown
+|[[Collatz-like]]
-|Count a number in base > 2 until reaching a certain length.
 |
-* {{TM|1RB------_0RC0RB1LC_1LB2RC0LB|halt}} BBt(3,3,2)
+* {{TM|1RB2LA1RA1RA_1LB1LA3RB---|halt}} BB(2,4)
-* {{TM|1RB------_1RC------_0RD0RC1LD_1LC2RD0LC|halt}} BBti(8)
+* {{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_---0LA|halt}} BB(5,2)
+* {{TM|0RB2LA1RA_1LA2RB1RC_---1LB1LC|halt}} BB(3,3)
 |<math>O(2^n)</math>
 |}