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Cellular Automata

Cellular Automata

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Gosper’s Glider Gun (gif by Keiff). Just one of the amazing ‘complex’ patterns that emerge from simple automata rules.

Cellular Automata are an eye-opening way of conceiving how complexity, given enough time, can emerge from very simple rules. The most famous is Conway’s Game of Life which takes place on an infinite 2-dimensional grid of cells. The cells can be either ‘dead’ or ‘alive’ (black or white) and change as time progresses according to the following very simple rules.

1. A live cell with fewer than 2 live neighbours dies (under-population).
2. A live cell with 2 or 3 live neighbours lives on to the next generation.
3. A live cell with more than 3 live neighbours dies (overcrowding).
4. A dead cell with 3 live neighbours becomes a live cell (reproduction).

To start you populate the grid with however many live cells you like, in whatever configuation you like, and let events take their course. From these very simple rules amazingly complex, and seemingly ‘intelligent’ ‘organisms’ come into existence and go about their business. Sometimes they burst into life and then die, other times, they interact with each other and spawn new ‘organisms’. As you go further and further in time self-replicating organisms are born. Further still and univeral Turing machines arise.

The analogy of course is that this is how the universe actually works. Albeit with extra dimensions and a continuous, rather than discrete, flow of time. The simple rules are the laws of nature. The grid is the fabric of space/time or whatever it is the events of our universe takes place in. Basically the argument goes that some set of initial conditions, govenerned by a few simple laws of nature, could lead to all the complexity of the universe as we know it. While this may in someways threaten our sense of individuality it does not lead to a conclusion of a pre-ordained destiny, as, perhaps most amazingly of all, in Conway’s Game of Life there is no way to predict how things will unfold, you just have to run the programme and see what happens.

The Game of Life was created in 1970 by John Horton Conway, but the history of cellular automata goes back to the 1940s and one of the greatest ever mathematicians John von Neumann.

Cellular automata were the inspiration for Stephen Wolfram’s A New Kind of Science and thought-provokingly referenced in the final chapter of Stephen Hawking‘s Grand Design.

Sombody on YouTube put together this great compilation of some of the incredibly complex “organisms” which can emerge over time when the game is played on a vast grid. Set to the music from Requiem For A Dream. Enjoy.

Epic Conway’s Game of Life

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