Questions and Chaos

Life in the 21st Century


Wednesday, July 11, 2007

When you think of chaos, perhaps what comes to mind is something like a group of ten year olds at a birthday party. (yelling, falling, spilled pop, cake on the floor) A state of disorder and confusion is the traditional definition of chaos.

The science of chaos finds order and elegance in turbulent situations. defines chaos as: “A new branch of science that deals with systems whose evolution depends very sensitively upon the initial conditions. Turbulent flows of fluids (such as white water in a river) and the prediction of weather are two areas where chaos theory has been applied with some success.” The study of chaos is the study of systems where multiple variables are interacting. A tiny change in one of the initial conditions can have a disproportionate result in the outcome.

The most over-used metaphor for this phenomenon is the “Butterfly Effect”. The idea being, that a small change in initial conditions, such as a butterfly flapping it’s wings, can set in motion changes in the atmosphere that ultimately escalate into a dramatic change in weather somewhere else in the world.

According to James Gleick in Chaos:Making a New Science, “Those studying chaotic dynamics discovered that the disordered behavior of simple systems acted as a creative process. It generated complexity: richly organized patterns, sometimes stable and sometimes unstable, sometimes finite and sometimes infinite, but always with the fascination of living things.”

Chaos theory helps us understand natural processes such as the unique formation of snowflakes. A snowflake may float in the wind for an hour or more as it grows and falls to earth. The six tips of the snowflake are subjected to the same conditions so they maintain their symmetry. As the snowflake falls, it’s growth depends on such things as temperature, humidity and impurities in the air. Any two snowflakes will experience a completely different path through the turbulent air. Therefore each one will develop its own unique shape.

The pattern of a snowflake is a fractal image. Computers can be used to create fractal patterns from mathematical formulas. The site has over 300 awe-inspiring images such as the one below. (Had I known mathematics could be this beautiful I might have paid attention in high school.)

Fractal patterns exist in clouds, thunderstorms, hurricanes, in the shape of coastlines and the shape of the galaxies. They are found in frost on the window, tree branches, blood vessels, heart rhythms and the shape of the brain. Chaotic behavior exists in population growth, the spread of epidemics and the movement of the stock market.

Nature grows and moves in remarkable ways following mathematical rules and hidden patterns. Natural forms and structures are created in the same way snowflakes are created. We are only beginning to understand patterns present in our world.

Edward Lorenz, the meteorologist considered the founder of chaos theory, was running an early computer program in the 1960s attempting to model and predict weather. He found that when he entered a number rounded off to only three decimal places instead of six the result was not similar, it was completely different. He discovered the sensitivity to initial conditions that unfolds in weather

It used to be thought that given sufficient technology and computing power we could predict the weather months and even years in advance. Four days is about the best that can be done, and not always accurately. We can never measure the world to enough decimal places to accurately predict the complete movements of a chaotic system.

1 Comment »


Comment by Peggy

July 23, 2007 @ 12:27 pm

I love those fractal patterns – although I have no idea how they are created.
This is the most I have ever read about Chaos theory too! You are informing me………….

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