Simple Rules Create Cellular Automata

Complex Adaptive Systems: 9 Cellular Automaton

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In this video we are going to discuss cellular automata, we will firstly talk about what they are before looking at a classical example, we will then discuss individually the different classes of patterns that cellular automata can generate before wrapping-up with a talk about their significance as a new approach to mathematical modeling.

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Transcription Excerpt:

Cellular automata are algorithmic models that use computation to iterate on very simple rules, in so doing these very simple rules can create complex emergent phenomena through the interaction between agents as they evolve over time. To illustrate the functioning of a cellular automaton we will take an example from probably the most famous algorithm called the Game Of Life devised by the mathematician John Conway. The Game Of Life is played on a grid of square cells. A cell can be live or dead, a live cell is shown by putting a mark on its square, a dead cell is shown by leaving the square empty, each cell in the grid has a neighborhood consisting of all adjacent cells to it and there are just three rules governing the behavior of an agent.
1. Any live cell with fewer than two live neighbors dies, as if caused by under- population.
2. Any live cell with two or three live neighbors lives on to the next generation.
3. Any live cell with more than three live neighbors dies, as if by overcrowding.
4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.

So lets Input a starting condition and run the program to see what we get, this pattern is called still life for obvious reasons, its product is probably the most simple class of pattern, called class one, where nearly all of these patterns evolve quickly into a stable, homogeneous state and any randomness in the initial pattern disappears.

The second class of pattern we may get is where the system evolves into an oscillating structure. The simplest of these being a blinker that has a period two oscillation. We can also have oscillating structures that cycle over prolonged periods of time for example a pulsar has a period three oscillation, but oscillators of many more periods are known to exist.

Class three patterns are random where nearly all initial patterns evolve in a semi-random or chaotic manner. Any stable structures that appear are quickly destroyed by the surrounding noise. Local changes to the initial pattern tend to spread indefinitely. Here we can get what are called gliders where a group of cells appear to glide across the screen and this is a good example of emergence as we no longer see the simple rules that are producing them but instead this emergent structure of an object gliding.

Lastly automata can also produce patterns that become complex and endure over a prolonged period of time, with stable local structures. With these more complex patterns cellular automata can simulate a variety of real-world systems, including biological and chemical ones.

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