The Game of Life is a cellular automaton invented by the British mathematician John Horton Conway in 1970 and has been proven Turing completeness. It first appeared in Martin Gordonner\’s \”Mathematics Game\” column in Scientific American in October 1970. The principle is very simple, that is, there are several cells living on a two-dimensional plane, and their survival at the next moment depends on the existence of cells in the surrounding 8 grids. The specific rules are as follows:
If there are 2 cells in the surrounding 8 cells, the cell remains in its original state.
If there are 3 cells in the surrounding 8 grids, cells appear in this grid (or remain in the state of cells)
If the number of cells in the surrounding 8 grids is less than or equal to 1 or greater than or equal to 4, the cells in this grid will become blanks (or remain blanks) because they are lonely or overcrowded
1. Historical overview
The earliest discovery was at the end of 1969, when Conway and graduate students initially explored B3/S23, they discovered the R-pentomino five-segment domino, and the resulting glider glider.
In the 1970s, it was dominated by common spacecraft and oscillating bodies. These include the queen bee shuttle honeycomb and the Gosper glider gun modeled on it. Of course there are large, medium and small spacecraft with a speed of 2/c.
In the 1980s, oscillating bodies with higher periods were discovered, such as Achim\’s p4 objects Mold and Jam. There are also c/3 and c/4 spacecraft.
1991 was a new starting point, thanks to the \”lifesrc\” search program written by David Bell, new speeds such as 2c/5 and c/12 also had corresponding spacecraft.
The 1990s was also an era of great prosperity in search programs. For details, please refer to David Eppstein\’s paper \”Searching for Spaceships\”
2. Field classification
(1) Pure theoretical research. For example, Father Conway’s two proofs prove that the B3/S23 rule is Turing complete, and the other proves that there are “self-replicating” objects in the game of life world. There is also a study on how many still life bodies can exist in a certain number of cells (A019473 sequence).
(2) Natural graphics search. Search for graphics of new stationary bodies, oscillating bodies, space ships, etc. At present, the main focus is on new cycles that have not been discovered, and new speeds where no spacecraft exists. For example, from period 2 to period 60, almost all periods have an oscillating body, but a period 19 (p19) is missing. There is also the new speed of the spacecraft. No corresponding spacecraft has been found for speeds such as 4c/9.
(3) Large-scale pattern construction. Mainly refers to the application of discovered natural objects and natural laws discovered in theoretical research to artificially transform and construct various types of interesting patterns. For example, various guns, planters, and gliders are combined. For example, the prime number machine can generate the corresponding prime number sequence of the glider. One of the most complicated projects is the MetaPixel, which can construct a set of grids in the living world to run the living world.