![]() This proves once and for all that the Game of Life is indeed omniperiodic. “The search has finally ended, with the discovery of oscillators having the final two periods,” they say. Now Mitchell and co announce the work is done. The final piece of Life's omniperiodic puzzle (source: /abs/2312.02799) In this century, computer scientists found all these oscillators, except two: 19 and 41. “At the turn of the millennium, only twelve periods remained to be found: 19, 23, 27, 31, 34, 37, 38, 39, 41, 43, 51 and 53,” they say. “Periods in the “missing middle”, 15 < p < 43, particularly those that are prime, proved more difficult to find,” say Mitchell Riley, at New York University in Aby Dhabi and colleagues.īut as work continued, researchers began to fill the gaps. The first few were relatively easy to find. Given the proof above, this boils down to the problem of finding oscillating patterns that repeat for every period from 1 to 42. Is it possible to make patterns that repeat over all possible periods? In other words, is the Game of Life omniperiodic? By increasing its size, mathematicians can make patterns repeat over any number of time steps. The smallest possible loop can be traversed in 43 steps. Mathematicians proved this by sending patterned signals along tracks that form loops. ![]() Then in the 1990s, it became clear it was possible to produce patterns with any periodicity greater than or equal to 43 time steps. Others repeat every two steps or three or four or five steps. It has long been clear that some patterns do not change over time, in other words they have a periodicity of one time step. One of these relates to the periodicity of the patterns in this universe. Indeed, nobody is quite sure where the limits lie for the Game of Life and computer scientists are still wrestling with numerous unsolved problems.
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