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Stewart Dean's Guide to Artificial Life

Complexity and Entropy

Everything in the universe exists on a sliding scale of entropy. Things very cold and still are at one end and things muddled, hot and moving rapidly are at the other. Life sits in the middle some where. This is possible a gross simplification so I feel it's best to explain what entropy is and what is defined when a system is complex. This is a standard explanation of the second law of thermodynamics, or the rule of entropy, as used in A Brief History of Time:

"It [The second law of thermodynamics] states that the entropy of an isolated system always increases, and that when two systems are joined together, the entropy of the combined system is greater than the sum of the entropies of the individual systems. For example, consider a system of gas molecules in a box. The molecules can be thought of as little billiard balls continually colliding with each other and bouncing off the walls of the box. The higher the temperature of the gas, the faster the molecules move, and so the more frequently and harder they collide with the walls of the box and the greater the outward pressure they exert on the walls. Suppose that the molecules are all confined to the left-hand side of the box by a partition. If the partition is then removed, the molecules will tend to spread out an occupy both halves of the box. At some later time they could, by chance, all be in the right half or back in the left half, but it is overwhelmingly more probable that there will be roughly equal numbers in the two halves. Such a state is less ordered, or more disordered, than the original state in which all the molecules were in one half."

Likewise if one side contains a different gas then removing the partition will cause the gases to mix, creating a uniform mixture of the two gases and creating a less ordered state. This is just a simple example applying to gases but in truth entropy is a rough law that applies to all systems, including those that exchange information. If entropy had its way the whole universe would be a soup of equal density, temperature and composition. The second law of thermodynamics states that, unless a system is a closed system, entropy will always increase and the whole become more chaotic.

Life is about the fight against entropy. As other systems lose information to the surrounding environment (information can be seen as heat or other quantities) life has not only to keep hold of its information but also increase its amount of information. It does this by absorbing, or eating, energy from the surrounding environment. The source of nearly all of Earth's energy is the sun; this keeps things going at the right pace. If Earth was too hot, we'd die, too cold and we'd freeze and also die. It appears that our version of life likes a certain temperature band. This may be obvious but it is an important point as we will see.

Chris Langton is one of the continuing chain of people responsible for major breakthroughs in Alife. Working with Von Nuemann's principles he did much experimentation with Cellular Automata, included Conway's Life. He later went on to produce a simplified reproducing automata that created exact copies of its self. Through his work he began to realise that there was an optimum level of information exchange that was convivial to what we call life.

Life is a complex system, in the dictionary sense of the words. It is a dynamic equilibrium, that can carry on changing and evolving over a great amount of time without dying out or fading away. It occurred to Langton that this optimum level of information could be measured. Langton created the lambda parameter which was the amount of information being exchanged in a system. By varying this figure in a CA he found that to low a value resulted in things freezing up and too high a value led to chaotic behaviour that made stability very difficult. In the middle was a state, a type of system, which became known as a complex system. On the edge of Chaos.Here is a diagram showing where life exists the extremes of complexity. In Langton's words he saw that life existed "on the edge of chaos".

In nature this can be demonstrated by the life that forms around deep sea vents of volcanic heat, black bubblers I believe they are called. Beyond these oases of heat little survives, yet around them mini ecosystems have evolved.

In Alife complexity can be seen at work in Conway's Life. Arrays of cells can be created that either die out, freeze, pulse or behave in a complex way. A glider, for example, lies on the periodic side of complex whilst glider guns and other controlling shapes are truly complex. It easy to see how the program got its name considering that we and the patterns in Conway's life inhabit the same region of logical space, only we are far more able to cope with outside influences. One wrong cell and often a Life array will explode, die out or both.

Please send any corrections, comments or additions to: alife(at)stewdean(dot)com

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