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- 20:15, 29 September 2025 TMBR: October 2025 (hist | edit) [449 bytes] Sligocki (talk | contribs) (Move Katelyn's blog post to next TMBR) Tag: Visual edit
- 18:42, 23 September 2025 1RB3RB5RA1LB5LA2LB 2LA2RA4RB1RZ3LB2LA (hist | edit) [5,044 bytes] Polygon (talk | contribs) (Created page for BB(2,6) champion)
- 07:29, 20 September 2025 Maximum Space Function (hist | edit) [1,081 bytes] Azerty (talk | contribs) (Added Maximum Space Function page) Tag: Visual edit
- 07:29, 11 September 2025 BB(3,4) (hist | edit) [5,916 bytes] Azerty (talk | contribs) (I added the BB(3,4) page.) Tag: Visual edit
- 02:38, 1 September 2025 TMBR: September 2025 (hist | edit) [7,370 bytes] Qwerpiw (talk | contribs) (Created page with "{{stub}} This Month in Beaver Research for August 2025") Tag: Visual edit: Switched
- 12:33, 31 August 2025 Irregular Turing Machine (hist | edit) [219 bytes] Polygon (talk | contribs) (Created page for irregular TMs)
- 15:33, 30 August 2025 BB(n,1) (hist | edit) [644 bytes] Polygon (talk | contribs) (Created page for 1-symbol TMs)
- 19:50, 27 August 2025 Blanking Busy Beaver Function (hist | edit) [1,968 bytes] Polygon (talk | contribs) (Created page for the Blanking Busy Beaver Function)
- 16:52, 27 August 2025 1RB1LA 1RC0RC 1LA1RD 1LE1RD ---1LF 1LE0LA (hist | edit) [565 bytes] Polygon (talk | contribs) (Created page for codata migration)
- 16:23, 27 August 2025 1RB1RE 1LC1RB 0RA0LD 1LB1LD ---0RA (hist | edit) [1,686 bytes] Polygon (talk | contribs) (Created article for Finned 3 (migration from codata))
- 11:42, 25 August 2025 BB(2,6) (hist | edit) [7,177 bytes] ADucharme (talk | contribs) (create 2x6 page) Tag: Visual edit
- 18:09, 24 August 2025 Surprise in a Box (hist | edit) [332 bytes] Sligocki (talk | contribs) (Created page with "{{machine|1RB2LB1LC_1LA2RB1RB_1RZ2LA0LC}} {{TM|1RB2LB1LC_1LA2RB1RB_1RZ2LA0LC}}, named '''Surprise in a Box''' by Allen Brady, is a halting BB(3,3) TM which runs surprisingly long on a surprisingly small segment of the tape. It halts after 2,315,619 steps, but only touches 51 cells on the tape. Category:Stub") Tag: Visual edit: Switched
- 18:21, 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)"
- 20:35, 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
- 18:08, 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...")
- 18:43, 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"
- 14:33, 5 August 2025 1RB--- 0RC1RD 1LA0LA 1LE0RB 1LF1LE 1LC0LD (hist | edit) [904 bytes] N1vi (talk | contribs) (Created page with "{{machine|1RB---_0RC1RD_1LA0LA_1LE0RB_1LF1LE_1LC0LD}} 1D — CA, rule 30 or rule 110")
- 14:06, 5 August 2025 1RB1LE 1LC0RA 0RF0LD 1LE1LA 1RC0LB ---1RC (hist | edit) [2,313 bytes] N1vi (talk | contribs) (Created page with "thumb It is really interesting. I high likely doubt it halts, but it creates pseudo random spaces at the right. I ran it for ~860 million steps and the result is shown at the image. Though it might be a fractal.") Tag: Visual edit
- 16:01, 2 August 2025 TMBR: August 2025 (hist | edit) [9,138 bytes] Qwerpiw (talk | contribs) (Created page with "{{Stub}} this month in busy beaver for 2025 August") Tag: Visual edit
- 21:43, 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
- 15:59, 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...")
- 03:17, 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^...")
- 18:34, 22 July 2025 Meet-in-the-Middle Weighted Finite Automata Reduction (MITMWFAR) (hist | edit) [408 bytes] Sligocki (talk | contribs) (Created page with "'''Meet-in-the-Middle Weighted Finite Automata Reduction''' ('''MITMWFAR''') is a Turing machine decider. It is a variation of Finite Automata Reduction (FAR) based upon Weighted Finite Automata. This allows it to decide irregular TMs which cannot be decided by FAR or any other regular decider. See: https://github.com/Iijil1/MITMWFAR/tree/main Category:Deciders Category:Stub") Tag: Visual edit
- 21:47, 16 July 2025 Instruction-Limited Busy Beaver (hist | edit) [23,359 bytes] Sligocki (talk | contribs) (Created page with "An '''n-instruction Turing machine''' is a Turing machine with an arbitrary number of states and symbols, but limited to only ''n'' defined transitions/instructions in its transition table (all others are undefined). The '''Limited Instruction Busy Beaver''' (BBi(n)) problem is the Busy Beaver problem limited to n-instruction TMs. So BBi(n) is the longest runtime for all halting n-instruction TMs when started on a blank tape. A TM is considered to halt as soon as it...") originally created as "Limited Instruction Busy Beaver"
- 21:00, 16 July 2025 Terminating Turmite (hist | edit) [987 bytes] Sligocki (talk | contribs) (Created page with "A '''Terminating Turmite''' or '''Relative Movement Turing Machine''' is a Turing machine which uses relative directions instead of absolute ones. So instead of moving (L)eft or (R)ight, it (P)roceeds forward (for one step in the same direction as last move or (T)urns-around (move one direction in the opposite direction). TT(n,k) is the maximum steps of all halting n-state, k-symbol Terminating Turmites when started on a blank tape. It was coined by @creeperman7002 w...")
- 20:41, 16 July 2025 1RB2LA2LC--- 1LA2RB2RD--- 3RB1LC1RD0LA 3LA1RD1LC0RB (hist | edit) [854 bytes] Sligocki (talk | contribs) (Created page with "{{machine|1RB2LA2LC---_1LA2RB2RD---_3RB1LC1RD0LA_3LA1RD1LC0RB}} {{TM|1RB2LA2LC---_1LA2RB2RD---_3RB1LC1RD0LA_3LA1RD1LC0RB}} is a non-halting TT(2,4) TM that is "pretending to be" a probviously halting Cryptid. Rules by Shawn Ligocki: <pre> C(a, b, c) = 0^inf 3 2^a <C 1^b 2^c 3 0^inf = 0^inf 3 2^c 1^b D> 2^a 3 0^inf C(a+1, b, c) -> C(c, b+1, a) C(0, b, c+3) -> C(c, 0, b+6) C(0, b, 2) -> Halt(b+7) C(0, b, 1) -> C(b+5, 0, 2) C(0, b, 0) -> C(b+2, 0, 5) Start: C(1, 0, 2) @...")
- 21:32, 15 July 2025 TMBR: July 2025 (hist | edit) [5,332 bytes] Sligocki (talk | contribs) (Created page with "Category:This Month in Busy Beaver This Month in Busy Beaver for July 2025. == Champions == * (Late June) mxdys found a pair of new BB(6) champions pushing it into the pentational values: {{TM| 1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE}} (scoring over 2↑↑2↑↑2↑↑10) and {{TM|1RB1LC_1LA1RE_0RD0LA_1RZ1LB_1LD0RF_0RD1RB}} (scoring over 10↑↑11010000). * mxdys confirms dyuan's BB(2,5) champion {{TM|1RB3LA4RB0R...") originally created as "TMiBB: July 2025"
- 02:59, 13 July 2025 Reversible Turing Machine (hist | edit) [3,668 bytes] Sligocki (talk | contribs) (Created page with "A '''Reversible Turing Machine''' is a Turing machine for which the computation can always be run backwards from any step back to the original configuration. This property (called logical reversibility) has theoretical implications for the limits of computation. Specifically, non-reversible computation cannot scale beyond some limit due to the inherent entropy cost whereas reversible computations may be able to. == Definition == There does not seem to be a completel...") Tag: Visual edit: Switched
- 16:43, 9 July 2025 Maximum Consecutive Ones Function (hist | edit) [2,967 bytes] Sligocki (talk | contribs) (Created page with "The '''Maximum Consecutive Ones''' function (named <math>num(n)</math> by Ben-Amram) is a Busy Beaver function which measures the maximum number of consecutive 1s left on the tape at halt across all n-state 2-symbol Turing machines which leave all their 1s consecutively. Unlike <math>\Sigma(n)</math>, this allows some amount of order over the "API" of these TMs, so that their output can be used as inputs to another TM in some deterministic fashion. Note however,...") Tag: Visual edit: Switched
