Chaos theory is a study of the behaviour of dynamical systems that are highly sensitive to initial conditions, which determines their future behaviour.
Chaos is ubiquitously spread, from nature's most intimate appearances, to the art of any kind. The chaos theory explores the complex systems of the earth's weather systems, the behaviour of water boiling on a stove, migratory patterns of birds, or the spread of vegetation across a continent.
Complex systems are systems that contain many evolving elements, for which computers are used to calculate all the various possibilities. This is the cause of a shift in theory from the Deterministic Era to the Quantum Mechanical Revolution. In the former, people believed that things were directly caused by other things. What went up had to come down, and that, if only we could catch and tag every particle in the universe, we could predict events from then on.
A Brief History of Chaos Theory
American mathematician, meteorologist, and a pioneer of chaos theory, Edward Norton Lorenz, in 1960, created a weather- model on a computer, at the Massachusetts Institute of Technology. This weather model accounted for an extensive array of complex formulas. Clouds rose, and winds blew, heat afflicted or cold chilled.
The weather system failed when Lorenz designed the program to run from the initial settings and calculate the outcome. Lorenz decided to start half-way down the sequence, by inputting the values that the computer had come- up with, initially.
The Principle's and Applications of Chaos Theory to Nature
The Uncertainty Principle, however, prohibits accuracy, so the initial situation of a complex system cannot be accurately determined, and the evolution of a complex system, can, thus, not be accurately predicted. A tiny particle cannot be accurately pin-pointed, due to the Uncertainty Principle. One cannot define the present situation.
The Butterfly Effect
The Butterfly Effect is a concept in meteorology. It explains that t he flapping of a butterfly's wing will create a disturbance that, in the chaotic motion of the atmosphere, will become amplified. It will eventually lead to a change in the large scale atmospheric motion, so that the long term behaviour becomes impossible to forecast.
Attractors
The triumphant chaos theorists discovered that, complex systems generally run through some kind of cycle, even though situations are rarely exactly duplicated and repeated. Plotting many systems in simple graphs revealed that, often there seems to be some kind of situation that the system tries to achieve - equilibrium of some nature.
E.g., imagine a city of 10,000 people. In order to accommodate these people, the city will generate one supermarket, two swimming pools, a library, and three churches. Thus, equilibrium is achieved. However, then the city intends to construct an ice cream plant on the outskirts of the town, opening jobs for 10,000 more people. The town expands to accommodate 20,000 people; one supermarket is added, two swimming pools, one library, and three churches, and the equilibrium is maintained. That equilibrium is termed, ‘an attractor’.
Self-Similarity
Self-similarity is a fundamental principle that allows building blocks to mimic their own shape in the building they make. A huge amount of particles will display a pattern that is equal to the initial possibilities of a single particle. A self-similar object is exactly or approximately identical to a part of itself, i.e., the whole has the same shape as one or more of the parts.
The objects in the real world, such as, coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity occurs everywhere in nature, and is termed a s a key natural principle, that shapes the world, the way it is.
The chaos theory ultimately reveals that, the nature, most often works in patterns, which are caused by the sum of many tiny pulses.
Sources: Stephen H. Kellert, In the Wake of Chaos: Unpredictable Order in Dynamical Systems, University of Chicago Press, 1993.