Conway game of life replicator

Here is a page with some interesting observations about 3D variants of the Game of Life. Cellular automata are also possible to construct in a 1-dimensional space. These types of automata are generally drawn in two dimensions, with the Y axis corresponding to successive generations. Rule 30 , a 1-dimensional cellular automata developed by Stephen Wolfram , is particularly interesting because it produces chaotic and complex patterns from simple rules. Rule 90 , another 1-dimensional cellular automaton, generates a Sierpinksi Triangle pattern when seeded with a single live cell.

Although they have not been studied extensively, Triangular , Pentagonal , and Hexagonal versions of Life have been implemented, replacing the square grid with other tilings and affecting the number of neighbors that each cell has. Multiple Colors Another class of variations on the standard Game of Life is cellular automata involving more than 2 possible colors or states for each cell. The Immigration Game is identical to the original Game of Life, except any newborn cell is colored according to the majority color of its 3 living neighbors.

Although the patterns generated in the Immigration Game are no different than the ones in Conway's Game of Life, the colors can interact in interesting ways--including cyclic patterns. The Rainbow Game of Life. The Rainbow Game of Life is similar to the Immigration Game, only newborn cells instead are colored based on the average color values of their parent cells.

Thus, a cell which is born from two black cells and one white cell will have a dark gray appearance. The Rainbow Game of Life is notable for being somewhat analogous to genetic properties spreading through a population of creatures.

Some investigations on the propagation of colors in the Rainbow Game of Life can be seen here. Cyclic Cellular Automata In cyclic cellular automata , an ordering of multiple colors is established. When Wade posted his self-replicating mathematical organism on a Life community website on 18 May, it sparked a wave of excitement. It might help us understand how life on Earth began, or even inspire strategies to build tiny computers. The Game of Life is the best-known example of a cellular automaton , in which patterns form and evolve on a grid according to a few simple rules.

The rules of the game were laid down by mathematician John Conway in , but cellular automata first took off in the s when the late mathematician John von Neumann suggested using them to demonstrate self-replication in nature. This lent philosophical undertones to Life, which ended up attracting a cult following.

But a pattern that spawned an identical copy of itself proved elusive. A programmer living in Toronto, Canada, Wade first dabbled with Life during the s but eventually lost interest and moved on.

One such discovery was the universal constructor, a pattern of cells that can be programmed to spit out a variety of others in subsequent generations. But the result ran too slowly to be of any practical use. By placing these at precise intervals, he created a program that feeds into the constructor and dictates its actions, much like the punched rolls of tape once used to control the first computers.

This proved a smart move. Dubbed Gemini, his creature is made of two sets of identical structures, which sit at either end of the instruction tape. As the simulation progresses the incomplete structure begins to grow, while the structure at the start of the tape is demolished. The original Gemini continues to disassemble as the new one emerges until after nearly 34 million generations, new life is born see diagram.

As a result of this, and the ability to program universal constructors using simple tape, Gemini has reinvigorated Life. Players are now looking forward to creating ever more novel and complex patterns. But it still has implications for understanding life. Whatever role Gemini ends up playing in the wider world of science, Stepney stresses the importance of those like Wade who experiment with Life in their spare time.

The Game of Life, created in the s by mathematician John Conway has garnered a cult following. It consists of an infinite grid of square cells that can either be live or dead.

It might not sound like much but such humble beginnings can give rise to a zoo of astoundingly complex patterns and processes, which now include self-replicating organisms see main story. How is this possible?