How to Understand Chaos Theory

In Science chaos refers to the apparent randomness that exists in a complex nonlinear system. Even though these systems still obey particular laws or rules, complex and unpredictable changes occur. Use these steps as a guide for understanding the complexity of chaos theory.

Instructions

1. Identify the meaning of chaos from a scientific view. A chaotic system is not a state of complete disorder. Chaotic systems can be smooth and ordered. Chaos theory explores whether or not the long term behaviors of this system can be predicted.

2. Study the laws of motion. Before the chaos theory was discovered determinism was used to explain systems in the universe. Determinism systems rely on cause and effect relationships with all actions predetermined. Review determinism through scientist Isaac Newton's three laws of motion. Explore how these laws predict the position and speed of the planets at any point in time.

3. Read about initial conditions. Newton's laws work when placed into mathematical equations. The values in a system at its initial condition should create a predictable outcome. Learn about physicist Henri Poincaré, who proved that in systems involving interaction between three or more bodies in space the laws of motion did not create the predicted outcome.

4. Study the butterfly effect. Meteorologist Edward Lorenz predicts weather patterns over long periods of time and the smallest change creates drastically different results. Discover how a butterfly flapping its wings in a certain part of the world makes a tornado occur 1 year later on the other side of the world.

5. Explore the Lorenz Attractor. Attractors map out evolution of a system over a period of time using a three dimensional graph. The Lorenz Attractor is an example of an attractor capable of showing where the system is located and thereby showing chaotic flow. An animated illustration of the butterfly pattern seen on the Lorenz Attractor can be seen online at the "California Institute of Technology" (see Resources below).

6. Understand fractals are objects that are similar to themselves on all scales. An example of a fractal is the "Sierpenski triangle." Self-similarity of the triangle shows that zooming into any one part of the object shows an object that is very close to the original.

7. Observe chaos in the real world. Chaos theory can be applied to many instances in the real world. Weather patterns, changes in the stock market and the swinging of a pendulum are just a few of the ways that chaos can be found around us.

Tips & Warnings

• Learn about the differences between linear and nonlinear systems to understand chaos.

• Movies such as "The Butterfly Effect," "A Sound of Thunder" and "Run Lola Run" all examine the main principle of chaos theory. Watch the films to see how small changes create unforeseen effects on the future.

• Study of advanced math and physics should be considered to aid in fully understanding chaos theory.

Resources

• Watch an animation of the butterfly effect at Caltech.
• See an example of the Sierpenski triangle.