Fans have been talking about Game of life bent, a mathematical modeling game, and found the answer to a question that has perplexed mathematicians and hobbyists for decades.
After more than fifty years, a mystery about the patterns repeated in… Game of life, a two-dimensional math game, finally solved. The discovery of the final two pieces of the puzzle was the deciding factor.
Life and death
Mathematician John Conway invented the Game of life in 1970. The game begins with a two-dimensional grid of cells. Color a random number of cells. This is the starting position. We call the colored cells “living” and the empty cells “dead”. Then the cells change with each new step (or “generation”) according to a set of simple rules. Any cell that touches fewer than two living cells dies. So is any cell surrounded by more than three living cells. If a cell has two or three living neighbors, it remains alive. A dead cell comes to life (again) when it has exactly three living cells around it.
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These rules ensure that at each step a new pattern appears, of seemingly infinite complexity. Three types of shapes can emerge: stationary patterns that no longer change, “oscillators” that form a repetitive but stationary pattern, and so-called “spaceships,” which repeat but also move across the grid.
Every period
One of the outstanding questions in the research on Game of lifeis whether oscillators exist for every possible period: oscillators that repeat every two steps, every three steps, four steps, five steps, and so on ad infinitum.
Mathematician David Buckingham invented a technique that allows you to create oscillators with any possible period greater than 57. This seemed to indicate that the answer is yes to this question. On the other hand, there were a number of small numbers for which no oscillators were known.
Now a team of hobbyists has filled in those final gaps. One article describes oscillators with periods 19 and 41. These were the last missing forms.
After 19 steps this pattern starts again.
One of the team members, Mitchell Riley, works as a quantum scientist at New York University in Abu Dhabi. He also likes to tinker in his free time Game of life-problems. He says there are many methods to invent new oscillators, but there is no way yet to make them with specific periods. This means that research in this area is a matter of guesswork. “It’s like playing darts: we’ve never hit 19 and 41 before,” he says.
Annoying and catalysts
Riley worked with well-known forms consisting of two parts, the so-called annoying and catalysts. Game of lifefans have coined these terms for forms that do not change – catalysts – which contain within them a changing form – the annoying. The shape inside responds to the outside, but does not change it. Together they form an oscillator with a certain period. Riley wrote a computer program to identify useful catalysts.
You have to be lucky for everything to fall into place, he says. “The change in the center must not destroy the external thing, and the center must return to its original state at the right time.”
Riley says there are no known applications for this research yet. His attraction to the problem was “pure curiosity.”
Not finished yet
Computer scientist Susan Stepney of the University of York in the UK says the work shows some “extremely clever and creative techniques”. She also says that this is certainly not the last work to be made based on Conway’s creation.
‘I don’t think the work on Game of life it will never be finished,” Stepney says. “He’s so simple to describe, yet so complex in his behavior, that he continues to fascinate many people.”
2023-12-30 07:06:08
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