Champions: Difference between revisions

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Busy Beaver '''Champions''' are the current record holding [[Turing machine|Turing machines]] who maximize a [[Busy Beaver function]]. In this article we focus specifically on the longest running TMs. Some have been proven to be the longest running of all (and so are the ultimate champion) while others are only current champions and may be usurped in the future. For smaller domains, Pascal Michel's website is the canonical source for [https://bbchallenge.org/~pascal.michel/bbc Busy Beaver champions] and the [https://bbchallenge.org/~pascal.michel/ha History of Previous Champions].
Busy Beaver '''Champions''' are the current record holding [[Turing machine|Turing machines]] which maximize a [[Busy Beaver function]]. In this article we focus specifically on the longest running TMs. Some have been proven to be the longest running of all (and so are the ultimate champion) while others are only current champions and may be usurped in the future. For smaller domains, Pascal Michel's website is the canonical source for [https://bbchallenge.org/~pascal.michel/bbc Busy Beaver champions] and the [https://bbchallenge.org/~pascal.michel/ha History of Previous Champions]. 1-state domains are omitted as [[BB(1,m)]] = 1 for m > 1.
 
== Trivial Champions ==
[[BB(n,1)]] = n
 
[[BB(1,m)]] = 1


== 2-Symbol TMs ==
== 2-Symbol TMs ==
Rows are blank if no champion has been found which surpasses a smaller size problem. Take also note that the <math> f_{x}(n) </math> used in the lowerbounds represent the [[Fast-Growing Hierarchy]]. Note that most champions above 6 states are self-reported and have not been independently verified.
Rows are blank if no champion has been found which surpasses a smaller size problem. Also take note that the <math>f_{x}(n)</math> used in the lower bounds represent the [[Fast-Growing Hierarchy]] while <math>\uparrow</math> represents [[wikipedia:Knuth's_up-arrow_notation|Knuth's up-arrow notation]]. Note that most champions above 6 states are self-reported and have not been independently verified.


{| class="wikitable"
{| class="wikitable"
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|-
|-
|[[BB(2)]]
|[[BB(2)]]
|<math> 6 </math>
|<math>6</math>
|{{TM|1RB1LB_1LA1RZ|halt}} {{TM|1RB0LB_1LA1RZ|halt}} {{TM|1RB1RZ_1LB1LA|halt}} {{TM|1RB1RZ_0LB1LA|halt}} {{TM|0RB1RZ_1LA1RB|halt}}
|{{TM|1RB1LB_1LA1RZ|halt}} {{TM|1RB0LB_1LA1RZ|halt}} {{TM|1RB1RZ_1LB1LA|halt}} {{TM|1RB1RZ_0LB1LA|halt}} {{TM|0RB1RZ_1LA1RB|halt}}
|Tibor Radó
|[[Tibor Radó]]
|Direct Simulation
|Direct Simulation
|-
|-
|[[BB(3)]]
|[[BB(3)]]
|<math> 21 </math>
|<math>21</math>
|{{TM|1RB1RZ_1LB0RC_1LC1LA|halt}}
|{{TM|1RB1RZ_1LB0RC_1LC1LA|halt}}
|Proven by Shen Lin
|Proven by [[Shen Lin]]
|Direct Simulation
|Direct Simulation
|-
|-
|[[BB(4)]]
|[[BB(4)]]
|<math> 107 </math>
|<math>107</math>
|{{TM|1RB1LB_1LA0LC_1RZ1LD_1RD0RA|halt}}
|{{TM|1RB1LB_1LA0LC_1RZ1LD_1RD0RA|halt}}
|Allen Brady
|Allen Brady
Line 31: Line 36:
|-
|-
|[[BB(5)]]
|[[BB(5)]]
|<math> 47\,176\,870 </math>
|<math>47\,176\,870</math>
|{{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA|halt}}
|{{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA|halt}}
|Heiner Marxen & Jürgen Buntrock in 1989
|Heiner Marxen & Jürgen Buntrock in 1989
Line 37: Line 42:
|-
|-
|[[BB(6)]]
|[[BB(6)]]
|<math> > 10 \uparrow\uparrow 15 </math>
|<math>> 2\uparrow\uparrow\uparrow 5</math>
|{{TM|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE|halt}}
|{{TM|1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE|halt}}
|Pavel Kropitz in 2022
|mxdys in 2025
|[https://www.sligocki.com/2022/06/21/bb-6-2-t15.html Analysis by Shawn Ligocki]
|See mxdys's analysis on the TM page
|-
|-
|[[BB(7)]]
|[[BB(7)]]
Line 48: Line 53:
|Analyzed by Shawn Ligocki (see TM page)
|Analyzed by Shawn Ligocki (see TM page)
|-
|-
|BB(8)
|[[BB(8)]]
|
|
|
|
Line 55: Line 60:
|-
|-
|BB(9)
|BB(9)
|<math> > f_\omega(f_9(2)) </math>
|<math>> f_\omega(f_9(2))</math>
|{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH|halt}}
|{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH|halt}}
|Jacobzheng in 2024
|Jacobzheng in 2024
Line 61: Line 66:
|-
|-
|BB(10)
|BB(10)
|<math> > f_\omega^2(25) </math>
|<math>> f_\omega^2(25)</math>
|{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ|halt}}
|{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ|halt}}
|Racheline in 2024
|Racheline in 2024
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|-
|-
|BB(11)
|BB(11)
|<math> > f_\omega^2(2 \uparrow\uparrow 12) > f_\omega^2(f_3(9)) </math>
|<math>> f_\omega^2(2 \uparrow\uparrow 12) > f_\omega^2(f_3(9))</math>
|{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE|halt}}
|{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE|halt}}
|Racheline in 2024
|Racheline in 2024
Line 73: Line 78:
|-
|-
|BB(12)
|BB(12)
|<math> > f_\omega^4(2 \uparrow\uparrow\uparrow 4-3) > f_\omega^4(f_4(2)) </math>
|<math>> f_\omega^4(2 \uparrow\uparrow\uparrow 4-3) > f_\omega^4(f_4(2))</math>
|{{TM|0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL|halt}}
|{{TM|0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL|halt}}
|Racheline in 2024
|Racheline in 2024
Line 85: Line 90:
|-
|-
|BB(14)
|BB(14)
|<math> > f_{\omega + 1}(65\,536) > g_{64} </math>
|<math>> f_{\omega + 1}(65\,536) > g_{64}</math>
|{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ---|halt}}
|{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ---|halt}}
|[https://discord.com/channels/960643023006490684/960643023530762341/1274366178529120287 Racheline in 2024]
|[https://discord.com/channels/960643023006490684/960643023530762341/1274366178529120287 Racheline in 2024]
Line 91: Line 96:
|-
|-
|BB(15)
|BB(15)
|
|<math>> f_{\omega + 1}(f_\omega(10^{57}))</math>
|
|{{TM|0RH1LD_1RI0RC_1RB1LD_0LD1LE_1LF1RA_1RG0LE_1RB1RG_1RD1RA_0LN0RJ_1RZ0LK_0LK1LL_1RG1LM_0LL0LL_1LO1LN_0LG1LN|halt}}
|
|Jacobzheng in 2025
|
|
|-
|-
|BB(16)
|BB(16)
|<math> > f_{\omega + 1}(2 \uparrow\uparrow\uparrow\uparrow 2 \uparrow\uparrow\uparrow\uparrow 9) </math>
|<math>> f_{\omega + 1}^2(10^{10^{57}})</math>
|[[User:Jacobzheng/BB(16)]]
|Jacobzheng in 2025
|
|
|Daniel Nagaj in 2021
|[https://www.sligocki.com/2022/07/11/bb-16-graham.html Analysis by Shawn Ligocki]
|-
|-
|BB(17)
|BB(17)
|<math> > f_{\omega + 1}(f_\omega(60)) </math>
|
|[[User:Jacobzheng/BB(17)]]
|
|Jacobzheng in 2024
|
|
|
|-
|-
|BB(18)
|BB(18)
|<math> > f_{\omega + 1}(f_\omega^2(60)) </math>
|<math>> f_{\omega + 2}(f_{\omega + 1}^3(f_{\omega}^2(60)))</math>
|[[User:Jacobzheng/BB(18)]]
|[[User:Jacobzheng/BB(18)]]
|Jacobzheng in 2024
|Jacobzheng in 2025
|
|
|-
|-
|BB(19)
|BB(19)
|<math> > f_{\omega + 1}^3(f_\omega(60)) </math>
|
|[[User:Jacobzheng/BB(19)]]
|
|Jacobzheng in 2024
|
|
|
|-
|-
|BB(20)
|BB(20)
|<math> > f_{\omega + 2}^2(21) </math>
|<math>> f_{\omega + 2}^2(21)</math>
|
|
|[https://discord.com/channels/960643023006490684/1026577255754903572/1274414683331366924 Racheline in 2024]
|[https://discord.com/channels/960643023006490684/1026577255754903572/1274414683331366924 Racheline in 2024]
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|-
|-
|BB(21)
|BB(21)
|<math> > f_{\omega^2}^2(4 \uparrow\uparrow 341) </math>
|<math>> f_{\omega^2}^2(4 \uparrow\uparrow 341)</math>
|
|
|[https://discord.com/channels/960643023006490684/1026577255754903572/1274471360206344213 Racheline in 2024]
|[https://discord.com/channels/960643023006490684/1026577255754903572/1274471360206344213 Racheline in 2024]
Line 133: Line 138:
|-
|-
|BB(40)
|BB(40)
|<math> > f_{\omega^\omega}(75\,500) </math>
|<math>> f_{\omega^\omega}(75\,500)</math>
|[[User:Jacobzheng/BB(40)]]
|[[User:Jacobzheng/BB(40)]]
|Jacobzheng in 2024
|Jacobzheng in 2024
Line 139: Line 144:
|-
|-
|BB(41)
|BB(41)
|<math> > f_{\omega^\omega}^4(32) </math>
|<math>> f_{\omega^\omega}^4(32)</math>
|[[User:Jacobzheng/BB(41)]]
|[[User:Jacobzheng/BB(41)]]
|Jacobzheng in 2024
|Jacobzheng in 2024
Line 145: Line 150:
|-
|-
|BB(51)
|BB(51)
|<math> > f_{\varepsilon_0 + 1}(8) </math>
|<math>> f_{\varepsilon_0 + 1}(8)</math>
|
|
|[https://discord.com/channels/960643023006490684/1026577255754903572/1276881449685094495 Racheline in 2024]
|[https://discord.com/channels/960643023006490684/1026577255754903572/1276881449685094495 Racheline in 2024]
Line 162: Line 167:
|-
|-
|[[BB(2,3)]]
|[[BB(2,3)]]
|<math> 38 </math>
|<math>38</math>
|{{TM|1RB2LB1RZ_2LA2RB1LB|halt}}
|{{TM|1RB2LB1RZ_2LA2RB1LB|halt}}
|
|Allen Brady in 1988
|
|Direct Simulation
|-
|-
|[[BB(3,3)]]
|[[BB(3,3)]]
|<math> > 10^{17} </math>
|<math>> 10^{17}</math>
|{{TM|0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC|halt}}
|{{TM|0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC|halt}}
|
|Terry & Shawn Ligocki in 2007
|
|[https://bbchallenge.org/~pascal.michel/beh#tm33h Analysis by Pascal Michel]
|-
|-
|[[BB(4,3)]]
|[[BB(4,3)]]
|<math> > 2 \uparrow\uparrow\uparrow 2^{2^{32}}</math>
|<math>> 10 \uparrow^{4} 4</math>
|{{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}}
|{{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD|halt}}
|
|Pavel Kropitz in 2024
|
|
|}
|}
Line 189: Line 194:
!Verification
!Verification
|-
|-
|BB(2,4)
|[[BB(2,4)]]
|<math> 3\,932\,964 </math>
|<math>3\,932\,964</math>
|{{TM|1RB2LA1RA1RA_1LB1LA3RB1RZ|halt}}
|{{TM|1RB2LA1RA1RA_1LB1LA3RB1RZ|halt}}
|Shawn & Terry Ligocki in 2005
|Terry & Shawn Ligocki in 2005
|Pascal Michel, Heiner Marxen, Allen Brady
|Pascal Michel, Heiner Marxen, Allen Brady
|-
|-
|BB(3,4)
|[[BB(3,4)]]
|<math> > 2 \uparrow^{15} 5 </math>
|<math>> 2 \uparrow^{15} 5</math>
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|
|Pavel Kropitz in 2024
|
|[https://www.sligocki.com/2024/05/22/bb-3-4-a14.html Analysis by Shawn Ligocki]
|}
|}


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!Verification
!Verification
|-
|-
|BB(2,5)
|[[BB(2,5)]]
|<math> > 10^{10^{10^{3\,314\,360}}} </math>
|<math>> 10^{10^{10^{3\,314\,360}}}</math>
|{{TM|1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ|halt}}
|{{TM|1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ|halt}}
|
|Daniel Yuan in 2024
|
|[https://discord.com/channels/960643023006490684/1259770421046411285/1379877629288644722 mxdys in Rocq]
|-
|-
|BB(3,5)
|[[BB(3,5)]]
|<math> > f_\omega(2 \uparrow^{15} 5) > f_\omega^2(15) </math>
|<math>> f_\omega(2 \uparrow^{15} 5) > f_\omega^2(15)</math>
|{{TM|1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC|halt}}
|{{TM|1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC|halt}}
|
|Racheline in 2024
|
|
|}
|}
Line 231: Line 236:
!Verification
!Verification
|-
|-
|BB(2,6)
|[[BB(2,6)]]
|<math> > 10 \uparrow\uparrow 10 \uparrow\uparrow 10^{10^{115}} </math>
|<math>> 10 \uparrow\uparrow 10 \uparrow\uparrow 10^{10^{115}}</math>
|{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}}
|{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}}
|Pavel Kropitz in 2023
|[https://www.sligocki.com/2023/05/20/bb-2-6-p3.html Analysis by Shawn Ligocki]
|}
== Zoology ==
{| class="wikitable"
|+
!Classification
!Description
!Examples
!Scale
|-
|Trivial
|The simplest champions that can exist. They mostly appear in some BB-adjacent functions like [[Fractran|BBf]].
|
|
|<math>O(n)</math>
|-
|Chaotic
|Have a chaotic behavior with often repeating patterns that go back and forth.
|
|
* {{TM|1RB1LB_1LA---|halt}}
* {{TM|1RB---_1LB0RC_1LC1LA|halt}}
* {{TM|1RB1LB_1LA0LC_---1LD_1RD0RA|halt}}
|<math>O(n^2)</math>
|-
|Countdown
|Compute a number then "count down" (usually while bouncing) until reaching 0. They are common in some BB-adjacent functions like [[Fractran|BBf]].
|
* {{TM|1RB2LB---_2LA2RB1LB|halt}}
|<math>O(n^2)</math>
|-
|Collatz-like
|Compute a Collatz-like function. Repeatedly multiply and add a number depending of its modulo until reaching a number with a certain modulo.
|
* {{TM|1RB2LA1RA1RA_1LB1LA3RB---|halt}}
* {{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_---0LA|halt}}
|<math>O(2^n)</math>
|}
|}
== References ==
<references />

Latest revision as of 18:11, 24 December 2025

Busy Beaver Champions are the current record holding Turing machines which maximize a Busy Beaver function. In this article we focus specifically on the longest running TMs. Some have been proven to be the longest running of all (and so are the ultimate champion) while others are only current champions and may be usurped in the future. For smaller domains, Pascal Michel's website is the canonical source for Busy Beaver champions and the History of Previous Champions. 1-state domains are omitted as BB(1,m) = 1 for m > 1.

Trivial Champions

BB(n,1) = n

BB(1,m) = 1

2-Symbol TMs

Rows are blank if no champion has been found which surpasses a smaller size problem. Also take note that the fx(n) used in the lower bounds represent the Fast-Growing Hierarchy while ↑ represents Knuth's up-arrow notation. Note that most champions above 6 states are self-reported and have not been independently verified.

Runtime Champions Discovered By Verification
BB(2) 6 1RB1LB_1LA1RZ (bbch) 1RB0LB_1LA1RZ (bbch) 1RB1RZ_1LB1LA (bbch) 1RB1RZ_0LB1LA (bbch) 0RB1RZ_1LA1RB (bbch) Tibor Radó Direct Simulation
BB(3) 21 1RB1RZ_1LB0RC_1LC1LA (bbch) Proven by Shen Lin Direct Simulation
BB(4) 107 1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch) Allen Brady Direct Simulation
BB(5) 47176870 1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch) Heiner Marxen & Jürgen Buntrock in 1989 Direct Simulation
BB(6) >2↑↑↑5 1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch) mxdys in 2025 See mxdys's analysis on the TM page
BB(7) >2↑112↑113 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) Pavel Kropitz in 2025 Analyzed by Shawn Ligocki (see TM page)
BB(8)
BB(9) >fω(f9(2)) 1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH (bbch) Jacobzheng in 2024
BB(10) >fω2(25) 1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ (bbch) Racheline in 2024
BB(11) >fω2(2↑↑12)>fω2(f3(9)) 1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE (bbch) Racheline in 2024
BB(12) >fω4(2↑↑↑4−3)>fω4(f4(2)) 0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL (bbch) Racheline in 2024
BB(13)
BB(14) >fω+1(65536)>g64 1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ--- (bbch) Racheline in 2024
BB(15) >fω+1(fω(1057)) 0RH1LD_1RI0RC_1RB1LD_0LD1LE_1LF1RA_1RG0LE_1RB1RG_1RD1RA_0LN0RJ_1RZ0LK_0LK1LL_1RG1LM_0LL0LL_1LO1LN_0LG1LN (bbch) Jacobzheng in 2025
BB(16) >fω+12(101057) User:Jacobzheng/BB(16) Jacobzheng in 2025
BB(17)
BB(18) >fω+2(fω+13(fω2(60))) User:Jacobzheng/BB(18) Jacobzheng in 2025
BB(19)
BB(20) >fω+22(21) Racheline in 2024
BB(21) >fω22(4↑↑341) Racheline in 2024
BB(40) >fωω(75500) User:Jacobzheng/BB(40) Jacobzheng in 2024
BB(41) >fωω4(32) User:Jacobzheng/BB(41) Jacobzheng in 2024
BB(51) >fε0+1(8) Racheline in 2024

3-Symbol TMs

Runtime Champions Discovered By Verification
BB(2,3) 38 1RB2LB1RZ_2LA2RB1LB (bbch) Allen Brady in 1988 Direct Simulation
BB(3,3) >1017 0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch) Terry & Shawn Ligocki in 2007 Analysis by Pascal Michel
BB(4,3) >10↑44 1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD (bbch) Pavel Kropitz in 2024

4-Symbol TMs

Runtime Champions Discovered By Verification
BB(2,4) 3932964 1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch) Terry & Shawn Ligocki in 2005 Pascal Michel, Heiner Marxen, Allen Brady
BB(3,4) >2↑155 1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC (bbch) Pavel Kropitz in 2024 Analysis by Shawn Ligocki

5-Symbol TMs

Runtime Champions Discovered By Verification
BB(2,5) >1010103314360 1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch) Daniel Yuan in 2024 mxdys in Rocq
BB(3,5) >fω(2↑155)>fω2(15) 1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC (bbch) Racheline in 2024

6-Symbol TMs

Runtime Champions Discovered By Verification
BB(2,6) >10↑↑10↑↑1010115 1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch) Pavel Kropitz in 2023 Analysis by Shawn Ligocki

Zoology

Classification Description Examples Scale
Trivial The simplest champions that can exist. They mostly appear in some BB-adjacent functions like BBf. O(n)
Chaotic Have a chaotic behavior with often repeating patterns that go back and forth.
  • 1RB1LB_1LA--- (bbch)
  • 1RB---_1LB0RC_1LC1LA (bbch)
  • 1RB1LB_1LA0LC_---1LD_1RD0RA (bbch)
 O(n2)
Countdown Compute a number then "count down" (usually while bouncing) until reaching 0. They are common in some BB-adjacent functions like BBf.
  • 1RB2LB---_2LA2RB1LB (bbch)
 O(n2)
Collatz-like Compute a Collatz-like function. Repeatedly multiply and add a number depending of its modulo until reaching a number with a certain modulo. O(2n)
Retrieved from "https://wiki.bbchallenge.org/w/index.php?title=Champions&oldid=5760"