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.
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:
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.
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.
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.