"Chaos theory" seems to be one of those misnomers that smell much more of Greek paganism than rational physics. It is safe to say that "chaos theory" was the last thing that Johannes Kepler needed in order to simplify astronomy for high-school students.
Chaos theory (in my opinion) is more appropriately called a theory of equilibrium. The "order in chaos" comes out of some interference pattern that bring an impressive amount of determinism to seemingly disorderly systems. Fractals stand for series of re-iterated operations that approach the equilibria of chaos theory.
Perhaps the universe still does, in a sense, have a mind of its own - but that would not make it any less rational. If anything, having a mind of its own would probably make it morerational.
If you would like to see physics that possibly smells a lot more like Kepler, Newton, and Occam, I recommend the physics site that I have been developing - along with one other site that gave me my inspiration. I especially recommend the papers where I cover fractals.
I say all these things as a theoretician who really believes he has answers - but must bypass standard explanations.
But to a mathematician, it is a neat, neat subject area. Why are fractals important? Fractals help us study and understand important scientific concepts, such as the way bacteria grow, patterns in freezing water (snowflakes) and brain waves, for example. Their formulas have made possible many scientific breakthroughs.
Nobody. Fractals are not owned by anyone!
Self-similarity.
Complex mathmatic equations.
Fractals are situations where the geometry seems best approximated by an infinitely "branching" sequence - used, for example, in modeling trees. For work on fractals that I have done as a theoretician, I recommend the included links. I just happen to have an original answer, and I want to make it known.
Denny Gulick has written: 'Calculus' 'Encounters with Chaos and Fractals' -- subject(s): MATHEMATICS / Number Theory, Chaotic behavior in systems, Fractals, MATHEMATICS / Geometry / General, MATHEMATICS / Differential Equations
Heinz-Otto Peitgen has written: 'Fractals for the classroom' 'Introduction to fractals and chaos'
Chaos Theory and the Theory of the Six Degrees have little to no overlap; they're not really related. There are some mathematical probabilities associated with the Six Degrees, and Chaos Theory is rooted in mathematics. But the former can be looked at as a "probability thing" and the latter an "anti-probability" or "probability resistant" thing.
Stephen Lipscomb has written: 'Fractals and universal spaces in dimension theory' -- subject(s): Fractals, Dimension theory (Topology)
Benoit Mandelbrot made mathematical accomplishments in physics, information theory, and finance. However, he is by far best known for his organization and rigorous development of the geometric objects known as fractals, a word which he invented. Specifically, his studies of fractals lead to his development of what are now called Mandelbrot sets, which provided the spark that started the fire with regards to the research of chaos theory.
M. R. Schroeder has written: 'Number theory in science and communication' 'Fractals, chaos, power laws' -- subject(s): Symmetry (Physics), Recursion, Self-Similarity, Scaling
The Chaos Theory was created on 2002-07-23.
Chaos Theory.
Remedial Chaos Theory was created on 2011-10-13.
No; chaos theory is more useful to explain why hurricanes CANNOT be predicted.
If you follow the link below it will lead you to references and articles on chaos theory.
The general Chaos Theory is plausible given its unpredictability in complex systems.