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chaos theory & butterfly effect

Chaos Theory is not chaos.

Chaos Theory states that even in a complex seemingly random and "chaotic" system... There is an underlying order.

The study of Chaos was born out of the realization that not all systems in nature could, or can, be modeled in a linear fashion using linear equations.

Chaos Theory is cross disciplinary. It is an effective tool in the study of economics, earth sciences and even biology. In fact, Chaos Theory can be applied to any complex "natural" system.

Fractal geometry, and the associated pretty pictures, give a visual representation of how order comes out of Chaos.

Fractals when imaged, display a visual representation of a concept that is know as Self Similarity.
In Self Similarity, no matter how much you zoom into the image or how faraway you zoom out,
the image always looks the same. Such as looking at a fern. The plant is the same shape as the leaves, and the leaves are the same shape as a piece of a leaf.
(It would be like you looking at yourself, looking at yourself, looking at yourself;
generating yourself, generating yourself, generating yourself.)
This can be refered to as Self Similarity. It's a recursion thing.

An associated idea of Chaos Theory is the notion of the Butterfly Affect.
An idea borrowed from Eastern Philosophies.

The single wing flap of a butterfly in one part of the world can cause a tremendous wind storm in another part of the world.

Small changes eventually manifest above the white noise of complex systems
and may have profound effects on the entire system.

The temporal reality, is a system like any other natural system.
Temporal reality as it is experienced may seem chaotic and without order.
But like any other complex seeming chaotic system there is an underlying order.

Life, in fact, may be a fractal experience. Layer upon layer of experience.

Layer upon layer of Self Similarity.

This applies to life in general and to personal life as experienced on the individual level.
We are a natural complex system like any other natural complex system within this universe.
And are governed by the same underlying order as the universe.

We are an expression of the Self Similarity of the universe.

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references/resources

"Chaos, Making a New Science". James Gleick
"What is Chaos?". Dr. Matthew A. Trump
"Chaos Theory". MSN Encarta
"Chaos Introduction". Andrew Ho
"In a World of Order, Chaos Rules". ThinkQuest
"Chaos Theory: A Brief Introduction". Greg Rae
"Virtual Chaos". Virtual Chaos
"An Introduction to Chaos". David M. Harrison
"Chaos and Complexity Resources for Students and Teachers". SCTPLS
"Chaos Theory for Beginners". Abarim Publications
"Chaos Theory". TechTarget
"Philosophical Reflections - Chaos". ThoughtWare Australia
"What are Fractals?". Janice Eilken.
"Self Similarity". Paul Bourke
"What are fractals?". The Academy of Science of St. Louis
"Fractals". Cynthia Lanius
"Fractals and Self-Similarity". Jim Loy
"Exploring Fractals". Mary Ann Connors
"Sprott's Fractal Gallery". Julien Sprott
"The Butterfly Effect". Lee Borrell
"Introduction to Fractals". Bonnie Hole
"Real-Life Relevance And Importance of Fractals and Fractal Geometry".

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