User:Azerty/Champions Zoology: Difference between revisions

Revision as of 21:06, 28 December 2025

This is a zoology of champions and what they compute.

Classification	Description	Examples	Scale
Chaotic	Have a chaotic behavior and repeating patterns that go back and forth.	`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	Create a number then multiply it.	`1RB2LB---_2LA2RB1LB` (bbch) BB(2,3) `1RB1LB_1LA1LC_1RC0LC` (bbch) BBt(3,2)	$O (n^{2})$
Piecewise Affine Function	Iterate a function where each case depend of the region.	`1PB1PA1TA_2TB2PB2PC_---2PA1TC` TT(3,3)	$O (n^{3})$
Counter	Count in base ≥ 2 until the number reaches a certain length.	`1RB------_0RC0RB1LC_1LB2RC0LB` (bbch) BBt(3,3,2) `1RB------_1RC------_0RD0RC1LD_1LC2RD0LC` (bbch) BBti(8)	$O (2^{n})$

@@ Line 14: / Line 14: @@
 |<math>O(n^2)</math>
 |-
-|Countdown
+|Multiplier
-|Compute a number then "count down" (usually while bouncing) until reaching 0.
+|Create a number then multiply it.
 |
 * {{TM|1RB2LB---_2LA2RB1LB|halt}} BB(2,3)
@@ Line 21: / Line 21: @@
 |<math>O(n^2)</math>
 |-
-|Exponential countdown
+|[[Piecewise Affine Function]]
-|Count a number in base > 2 until reaching a certain length.
+|Iterate a function where each case depend of the region.
+|
+* <code>1PB1PA1TA_2TB2PB2PC_---2PA1TC</code> TT(3,3)
+|<math>O(n^3)</math>
+|-
+|Counter
+|Count in base ≥ 2 until the number reaches a certain length.
 |
 * {{TM|1RB------_0RC0RB1LC_1LB2RC0LB|halt}} BBt(3,3,2)