Self organisation

Biological diversity and complexity does not contradict the Second Law of thermodynamics because living organisms are structures that maintain themselves far from equilibrium: They use an inflow of energy to create "order from disorder" within themselves, but dissipate heat and other waste products to increase the net entropy and disorder of the universe. The remarkable self-organisation exhibited by living organisms is also illustrated in simpler non-living systems such as that of Benard cells and the BZ chemical reaction. There are many examples of self-organisation, that is, macroscopic order or pattern formation in a complex system.

A close-up of regular Rayleigh-Benard cells in the
petri dish.

Motion of liquid in a Benard cell. This phenomenon is the manifestation of short range forces acting to create organization over much larger length scales due to convection.

 

 

 

The game of life (Conway, 1960) was the first simple system to exhibit "life like" behaviour based on a few simple rules. This computer simulation followed from the earlier work of John von Neumann's study of self-replicating systems.

The game is run in discrete time-steps, and with the cells of the lattice taking one of two states: alive or dead. At each time-step the state of a cell is determined according to the following two rules:

  1. A living cell will remain alive only if it has two or three living neighbours. It dies from exposure or loneliness if it has less than two neighbours, and from overcrowding if it has more than three neighbours.
  2. A dead (or vacant) cell can come alive if it is surrounded be exactly three live cells. (One can think of this as reproduction)

Though the above rules are a caricature of ecosystems, they lead to surprising and sometimes complex pattern formation. Indeed this game is a beautiful exemplification of emergent behaviour. Starting with a given configuration of live cells, many possible outcomes can result. Three simple types of objects are : static, periodic and moving, as shown in the figures below. More interesting objects are those that breed, mimicking real life, as best seen in the simulations. \epsfbox{107.eps}

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Note the large variety of patterns that are possible from different initial conditions even though the rules for "evolution" are few, local and completely deterministic.

Game of life applet

 

A boids applet

Emergence: A feature that distinguishes complex systems from a simple system  is the presence of behaviours and patterns that result from the interaction of the system with itself and the surroundings

Stock Market Crashes:

Predicting the rise and falls of shares is a lucrative business for Physicists...

Various models have been applied, including both stochastic processes (Black-Scholes theory for option pricing - Nobel prize in economics) to catastrophe theory and self-organization.

Stockbrokers may act like sheep

Predicting stock market crashes