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19 October 2025

  • 14:1214:12, 19 October 2025 1RB2LB0LB 2LC2LA0LA 2RD1LC1RZ 1RA2LD1RD (hist | edit) [4,159 bytes] Polygon (talk | contribs) (Created page with "{{machine|1RB2LB0LB_2LC2LA0LA_2RD1LC1RZ_1RA2LD1RD}} {{TM|1RB2LB0LB_2LC2LA0LA_2RD1LC1RZ_1RA2LD1RD|halt}} is a pentational halting BB(4,3) TM. It was discovered in May 2024 by Pavel Kropitz as one of seven long running TMs and achieves a score of over <math>3 \uparrow\uparrow\uparrow 88574</math>. Polygon analysed the TM by hand in October 2025, providing its score. Pavel listed the halting tape as: <pre> 1 Z> 1^(162*3^((3*<(243*3^(6) - 5)/2; (<(54*3^((3b + 11)/2) - 2...")

12 October 2025

6 October 2025

5 October 2025

30 September 2025

  • 20:3720:37, 30 September 2025 Linear-Inequality Affine Transformation Automata (hist | edit) [3,222 bytes] Sligocki (talk | contribs) (Created page with "'''Linear-Inequality Affine Transformation Automata (LIATA)''' are a model for computation based upon applying affine transformations to vectors based on cases defined by linear inequalities. They are a generalization of the rules for BMO1 and were proven to be Turing complete. == Example == An example of a LIATA are the rules for BMO1:<math display="block">f(a,b) = \begin{cases} (a-b, 4b+2) & \text{if } a > b \\ (2a+1, b-a) & \text{if } a < b \\ \end{cases}</ma...") Tag: Visual edit
  • 17:1117:11, 30 September 2025 Bug Game (hist | edit) [6,391 bytes] Sligocki (talk | contribs) (Created page with "The '''Bug Game''' is an optimization game in which players design a 2d ''maze'' that a ''bug'' will be slowest to solve. The bug follows a relatively simple algorithm which preferentially visits locations less visited which is guaranteed to always eventually find a way to the destination (if such a path exists), but by exploiting the details of the tie-breaking logic, some mazes can trap the bug for a long time. You can play online at https://buglab.ru/ == History == T...")

29 September 2025

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20 September 2025

11 September 2025

1 September 2025

31 August 2025

30 August 2025

27 August 2025

25 August 2025

24 August 2025

23 August 2025

  • 18:2118:21, 23 August 2025 BB(1,m) (hist | edit) [694 bytes] Buffalo Buffalo 1 (talk | contribs) (Created page with "{| class="wikitable" |+ Small busy beaver values<ref>P. Michel, "[https://bbchallenge.org/~pascal.michel/ha.html Historical survey of Busy Beavers]".</ref> ! !!1-state |- ! 2-symbol | BB(1) = 1 (Halt) |}") originally created as "BB(1)"

19 August 2025

  • 20:3520:35, 19 August 2025 Universal Turing Machine (hist | edit) [1,684 bytes] Sligocki (talk | contribs) (Created page with "A '''Universal Turing Machine''' (UTM) is a Turing Machine which can simulate any other TM (encoded onto input tape). The precise definition requires defining the encoding function to map simulated TMs and TM inputs into UTM initial tapes. Since a UTM can simulate any TM, the halting problem for any UTM is not computable. There is a common misconception that the Busy Beaver Functions will become uncomputable once we reach a domain with a UTM (since the general h...") Tag: Visual edit

8 August 2025

  • 18:0818:08, 8 August 2025 1RB0RD 0LC1RA 0RA1LB 1RE1LB 1LF1LB ---1LE (hist | edit) [1,365 bytes] Sligocki (talk | contribs) (Created page with "{{machine|1RB0RD_0LC1RA_0RA1LB_1RE1LB_1LF1LB_---1LE}} {{TM|1RB0RD_0LC1RA_0RA1LB_1RE1LB_1LF1LB_---1LE}} is a non-halting BB(6) TM discovered by mxdys on 14 Sep 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1284419946759323700 Discord]) and proven non-halting the next day ([https://discord.com/channels/960643023006490684/1239205785913790465/1284838151348551795 Discord]). It follows rules similar to {{TM|1RB1RE_1LC0RA_0RD1LB_---1RC_1LF1RE_0...")

6 August 2025

  • 18:4318:43, 6 August 2025 Tₘ function (hist | edit) [991 bytes] Qwerpiw (talk | contribs) (Created page with "Let M be a non-deterministic Turing machine which recognizes a language L, that is, for every input word u there is an accepting computation with input u if and only if u ∈ L. Let us assume that M terminates on every input. The simplest thing to assume is that if u ∈ L, the TM eventually gives "yes" and if u ∉ L, it gives "no". The smallest time (number of steps) of such a computation is denoted by T<sub>M</sub>(u) . For every n >= 1 we define T<sub>M</sub>(...") Tag: Visual edit: Switched originally created as "T M function"

5 August 2025

2 August 2025

31 July 2025

  • 21:4321:43, 31 July 2025 Doodle function (hist | edit) [1,226 bytes] Qwerpiw (talk | contribs) (Created page with "The '''doodle function''' is a function made by Lawrence Hollom. It is a two-argument function.<ref>https://web.archive.org/web/20230901195926/https://sites.google.com/a/hollom.com/extremely-big-numbers/home/doodle-function</ref> == Definition == The function revolves around a specific type of one-dimensional cellular automaton, in which state of a cell is determined by its own state and state of the cell to its right at previous generation (Hollom's original explanatio...") Tag: Visual edit: Switched

30 July 2025

  • 15:5915:59, 30 July 2025 1RB0LD 1RC1RA 1LD0RB 1LE1LA 1RF0RC ---1RE (hist | edit) [1,807 bytes] Sligocki (talk | contribs) (Created page with "{{machine|1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE}} {{TM|1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE}} is a probviously halting BB(6) Cryptid analzyed by mxdys on 30 July 2025. == Analysis by mxdys == [https://discord.com/channels/960643023006490684/1239205785913790465/1400141896944320602] <pre> 1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE (a,b,c) := 0^inf 1^a 0 01^b 0 11^c+1 B> 0^inf (a,2+b,c) --> (a,b,3+c) (a+1,0,c) --> (a,c,2) (a+1,1,c) --> (a,c,6) (0,0,c...")

27 July 2025

  • 03:1703:17, 27 July 2025 1RB1LA------ 1RC3LB1RB--- 2LA2LC---0LC (hist | edit) [1,090 bytes] Sligocki (talk | contribs) (Created page with "{{machine|1RB1LA------_1RC3LB1RB---_2LA2LC---0LC}} {{TM|1RB1LA------_1RC3LB1RB---_2LA2LC---0LC}} is the current BBi(8) champion. It runs for over <math>10^{1565}</math> steps and has a sigma score of exactly <math>\frac{3^{1642} - 11}{2}</math>. It was discovered by Nick Drozd on 26 July 2025 ([https://discord.com/channels/960643023006490684/1084047886494470185/1398753236835635252 Discord link]). == Analysis by Shawn Ligocki == <pre> A(a, b, c) = <A 2^a 0 3^b 1^...")

22 July 2025

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