Game of Life
Game of Life
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The Game of Life is a game in mathematical sense rather than a playable game. it is a "zero-player game" which means that you just have to decide initial state/pattern, after that it will be played by itself. It is a cellular automaton, and was invented by Cambridge mathematician John Conway. It is a most famous example of cellular automata.
This game became widely known when it was mentioned in an article published by Scientific American in 1970. It consists of a collection of cells which, based on a few mathematical rules, can live, die or multiply. Depending on the initial conditions, the cells form various patterns throughout the course of the game.
The game takes place on a two-dimensional finite or infinite grid whose cells can take two distinct states: "alive" or "dead".
Why it is called 'Game of life'?
Once we put some cells in living position, the rules determine everything that happens later. Nevertheless, Life is full of surprises! In most cases, it is impossible to look at a starting position (or pattern) and see what will happen in the future. The only way to find out is to follow the rules of the game. So it is called Game of Life.
Rules:
Rules:
For a space that is live or populated:
Each cell with one or no alive neighbors, dies as if by solitude
2. Each cell with four or more alive neighbors, dies as if by overpopulation.
3. Each cell with two or three alive neighbors, survives.
For a space that is empty or dead:
Each cell with three alive neighbors becomes alive, as if by reproduction.
Instruction:
Select the cells you want to be live .
You can try pattern given below or your own patterns like your name etc.
observe your pattern and decide that from which one of given three category your pattern belongs.
Click Start reproducing button to start/stop.
Click Reset button to make all cells dead.
Examples of pattern:
After running game of life for numerous times, we can see that many different type of patterns occur. These patterns are reclassified according to their behaviour.
1) Still lifes: this type of patterns do not change from one generation to the next.
Examples :
Block
Beehive
Boat
Tub
2) Oscillators: this type of patterns return to the same initial pattern after finite number of generations.
Examples :
Blinker
(period 2)
Toad
(period 2)
Beacon
(period 2)
Pulsur
(period 3)
Penta-decathlon
(period 15)
3) Spaceships: this type of patterns return to the same initial pattern, but translated by some steps in some direction.
Examples :
Glider
Light-weight spaceship (LWSS)
Middle-weight spaceship (MWSS)
Heavy-weight spaceship (HWSS)
Undecidability:
Numerous patterns in game of life eventually become a combination of still lifes, oscillators, and spaceships; other patterns may be called chaotic. A pattern may stay chaotic for a very long time until it eventually settles to such a combination.
The Game of Life is undecidable, which means that given an initial pattern and a later pattern, no algorithm exists that can tell whether the later pattern is ever going to appear. This is a corollary of the halting problem: the problem of determining whether a given program will finish running or continue to run forever from an initial input.
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