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5 November 2025

28 October 2025

  • 18:0918:09, 28 October 2025 Generalized Collatz Function (hist | edit) [2,706 bytes] Sligocki (talk | contribs) (Created page with "A '''Generalized Collatz Function (GCF)''' is a function which naturally generalizes the classic Collatz function defined by Conway in his 1972 paper "Unpredictable iterations".<ref name=":0">John. H. Conway. 1972. [https://gwern.net/doc/cs/computable/1972-conway.pdf Unpredictable iterations]. In Proc. 1972 Number Theory Conf., Univ. Colorado, Boulder, pages 49–52.</ref> They are functions defined piecewise based upon the remainder of the input (modulo some value) wher...") Tag: Visual edit

26 October 2025

24 October 2025

22 October 2025

  • 18:0118:01, 22 October 2025 1RB1RF 0LC1RC 1RD1LC 1RZ0RE 1RA1LF 1RA0LE (hist | edit) [3,560 bytes] Sligocki (talk | contribs) (Created page with "{{machine|1RB1RF_0LC1RC_1RD1LC_---0RE_1RA1LF_1RA0LE}} {{TM|1RB1RF_0LC1RC_1RD1LC_---0RE_1RA1LF_1RA0LE}} == Analysis by Shawn Ligocki == https://discord.com/channels/960643023006490684/1239205785913790465/1430590536825442384 <pre> 1RB1RF_0LC1RC_1RD1LC_---0RE_1RA1LF_1RA0LE A> 10 -> 11 A> 0 1^n A> 00 -> 11 A> 1^n 0 for n >= 1 0 1^2k+3 A> 11 -> 1^4 0 1^2k+1 A> 0 1 A> 1^2 0 -> 1^5 Z> (Halt) 0 1 A> 1^3 0 -> 1^4 0 1 A> 0 1 A> 1^4 -> 1^5 A> 1 0 1^2k A> 11 -> 1^2k+3 A> A(...") originally created as "1RB1RF 0LC1RC 1RD1LC ---0RE 1RA1LF 1RA0LE"

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 Piecewise Affine Function (hist | edit) [6,277 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 originally created as "Linear-Inequality Affine Transformation Automata"
  • 17:1117:11, 30 September 2025 Bug Game (hist | edit) [6,416 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

23 September 2025

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
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