IBM Ponder This #265 · May 2020

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

Best opened after a real attempt

To be added.