12/3/2023 0 Comments Conway game of life question![]() Of course, he also gave us the Game of Life. ![]() Together with a colleague invented the paper-and-pencil game Sprouts. Conway enjoyed playing games–such as backgammon–and magic tricks. Spanning into the areas of knot theory, number theory, finite groups, combinatorial game theory, and coding theory. His contributions to the field are numerous. He was a Fellow of the Royal Society and won numerous awards in mathematics. He later became Chair of Mathematics at Princeton University in New Jersey. in mathematics from the University of Cambridge, where he also was a lecturer. Born in Liverpool, England, Conway obtained his Ph.D. Last April, John Conway died of COVID-19 in New Brunswick, New Jersey, at the age of 82. The ConwayLife website contains more resources and a free program to explore the Game of Life.ĭr. """ Start Game of Life with a 10x10 grid, and run it for 20 periods Print_grid(curr_grid) #print the initial state Next_grid = next_state(curr_grid, next_grid)įield_sum += sum(curr_grid) Next_grid = *grid_size for _ in range(grid_size)] #!/usr/bin/env python3Ĭurr_grid = *grid_size for _ in range(grid_size)] I made a few adjustments to consider the cells at the edges of the grid–they will have less than eight neighbors. The code below implements a basic game with a glider. Given the simplicity of its rules, it's easy to program the Game of Life. But, now we can use computer programs to see the patterns evolve. When Conway created the game, he used a board of Go as the grid–he had no computers. There are many more patterns with varying degrees of complexity. Gosper's Glider gun (credit: Lucas Vieira / CC BY-SA) The glider is a pattern that travels diagonally across the grid.Ī more complex configuration, Gosper's glider gun, generates gliders. It switches between horizontal and vertical positions every period. The blinker is a straight line of three adjacent cells. Well-known configurations exist in the Game of Life. As John Conway puts it: "it's not a question of not being able to tell because you haven't got a big enough brain, it's an absolute condition–it doesn't matter how clever you are." This consequence is fascinating, given that the game is governed only by three simple rules. In some cases, it's impossible to tell if a pattern will perish or continue to live forever. The Game of Life can also generate randomness–patterns that show unpredictable behavior. It all depends on that initial arrangement. Some configurations die out after a few generations, others remain still, while others go out producing different patterns and then come back to the original configuration, creating a cycle. Depending on how we choose, patterns emerge–they can get complex, and it's mesmerizing watching the cells rearranging themselves. The fun part is picking the initial arrangement and then watching what happens. The game advances, updating the cells, giving birth to new generations. The game is a zero-player game, meaning it doesn't require any players to proceed. These are all the rules of the Game of Life. All other live cells die (and dead cells stay dead).A dead cell with three live neighbors becomes alive.A live cell with two or three live neighbors stays alive.Then, in the next period, all cells update their state based on the following rules: To start the game we choose an initial configuration of the cells. A cell has eight neighbors–these are the eight squares surrounding the cell.Ī cell in the center, with eight neighbors. Conway borrowed a board of the game Go when creating Life.Įach cell is either "alive" (populated) or "dead" (unpopulated). The Game of Life–or simply Life, as Conway called it originally–consists of a two-dimensional grid of squared cells. That same year–when Martin Gardner featured the game in an article in Scientific American–it became an instant sensation. The game is a cellular automaton–a grid of cells that take a specific state, for example, "on" or "off." It was created by British mathematician John Horton Conway in 1970. Conway's Game of Life falls in this category. Lego blocks and jigsaw puzzles are not the only things that are simple, yet fascinating. The potential in simple things is fascinating. It's the thinking–about how we can arrange them–and the building, creating something new that entertains us. But it's not the individual parts that make them fun and interesting. Yet, we were entertained for long periods. Taken by themselves, they are dull and boring. These are very simple things: pieces of plastic and paperboard in a few different shapes that snap together. You remember spending hours tinkering and rearranging them into different shapes and structures. Most of us played with Lego blocks or jigsaw puzzles when we were kids–maybe you still do.
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