Ponder This Challenge - May 2020 - Conway's Game of Life

On Saturday, April 11, 2020, the mathematical genius John Horton Conway passed away.
This month's challenge is dedicated, with deep love, to his memory.

Conway researched many topics in mathematics. One of his most famous inventions is the Game of Life.
In the standard game, each cell has eight neighbors; in our version, each cell has only four neighbors (only those cells with adjacent edges).
The standard rules can be formulated as 000100000;001100000 (if the cell is empty, it is born if it has exactly three live neighbors; if the cell is alive, it stays alive if it has two or three live neighbors).

In our version of the game, the rules 01100;00010 mean that a cell is born if it has one or two neighbors, and stays alive if it has three. If we start with a single cell in the middle of an 11x11 torus board, then after 15 generations, you will have an alternating chess-like pattern, and after 16 steps, just the four corners.
Your task, this month, is to find rules for our version of the game and an initial input on an 11x11 torus board that will lead, after at least 100,000 generations, to a 72-long cycle.

Solution

• Click here to view the solution

  Our solution was a heart ("with love"):

  ...........
  ...........
  ...........
  ...........
  ..*.*......
  .*.*.*.....
  .*...*.....
  .*...*.....
  ..*.*......
  ...*.......
  ...........
  

  which gives, after 192,642 generations with the rules 01100;00010, a cycle of 72.

  Florian Fischer sent us another solution with the rules 01100;00100:

  In Florian's solution, you can see the Tree of Wisdom representing John Conway's immense knowledge, an aura showing his influence on us, a star at the zenith symbolizes his guidance and, at the corners, four little ornamental angels in the shape of gliders remind of his Game of Life.

  It runs for 6,792,329 generations before entering the 72-length cycle.

  Bertram Felgenhauer sent us the longest tail (10,069,808,235 generations): rule=01100;00010

  ..*.*****.*
  ..*..******
  .***..*...*
  ****.*.****
  ***......**
  *.......*..
  ....**.***.
  .*.....*...
  *..*...**..
  .*.*...*.*.
  **..*...**.
  

  He also sent us a "PONDER" solution: same rules, after 1,114,393,074 generations:

  **...*...*.
  *.*.*.*.*.*
  **..*.*.*.*
  *...*.*.*.*
  *....*..*.*
  ...........
  **..***.**.
  *.*.*...*.*
  *.*.***.**.
  *.*.*...*.*
  **..***.*.*
  

  Thanks also to Nyles Heise for sending us the interesting reference to A. K. Dewdney's WireWorld.

Solvers

• Bert Dobbelaere (28/04/2020 11:23 PM IDT)
• Richard Gosiorovsky (29/04/2020 10:47 AM IDT)
• Kevin Bauer (30/04/2020 02:38 AM IDT)
• Arthur Vause (30/04/2020 04:16 PM IDT)
• Ariel Landau (30/04/2020 11:31 PM IDT)
• Deron Stewart (30/04/2020 11:31 PM IDT)
• Guillermo Wildschut (01/05/2020 01:37 PM IDT)
• Florian Fischer (02/05/2020 02:11 AM IDT)
• Victor Chang (02/05/2020 09:47 AM IDT)
• Li Li (03/05/2020 12:56 AM IDT)
• Latchezar Christov (03/05/2020 07:56 AM IDT)
• Andreas Puccio (03/05/2020 12:34 PM IDT)
• Clive Tong (03/05/2020 04:28 PM IDT)
• Graham Hemsley (03/05/2020 05:16 PM IDT)
• Walter Sebastian Gisler (03/05/2020 05:49 PM IDT)
• Dieter Beckerle (03/05/2020 05:49 PM IDT)
• Alper Halbutogullari (04/05/2020 11:37 AM IDT)
• Thomas Egense (04/05/2020 10:58 PM IDT)
• Nyles Heise (05/05/2020 08:47 AM IDT)
• Khaled Fayed (07/05/2020 05:33 AM IDT)
• Lorenz Reichel (08/05/2020 11:40 PM IDT)
• Bertram Felgenhauer (09/05/2020 10:31 PM IDT)
• Eden Saig (11/05/2020 02:13 AM IDT)
• Daniel Bitin (11/05/2020 01:53 PM IDT)
• David Greer (14/05/2020 04:26 PM IDT)
• Kang Jin Cho (15/05/2020 07:40 PM IDT)
• Haye Chan (16/05/2020 04:23 PM IDT)
• Daniel Chong Jyh Tar (16/05/2020 06:27 PM IDT)
• Mathieu Roget (16/05/2020 08:39 PM IDT)
• Vladimir Volevich (17/05/2020 06:23 PM IDT)
• Charles Joscelyne (20/05/2020 03:18 AM IDT)
• Reda Kebbaj (22/05/2020 01:29 AM IDT)
• Yongxing Jim Wang (22/05/2020 07:41 PM IDT)
• Motty Porat (23/05/2020 02:06 AM IDT)
• Todd Will (23/05/2020 06:16 PM IDT)
• Joerg Schepers (23/05/2020 10:26 PM IDT)
• Erik Wünstel (28/05/2020 10:16 PM IDT)
• Gary M. Gerken (30/05/2020 01:01 PM IDT)
• Erik Wünstel (28/05/2020 10:16 PM IDT)
• Gary M. Gerken (30/05/2020 01:01 PM IDT)
• Willem Hendriks (30/05/2020 10:46 PM IDT)
• Radu-Alexandru Todor (31/05/2020 06:59 PM IDT)
• Andreas Stiller (31/05/2020 10:36 PM IDT)