Fractals and chaos - what do they have in common?

[Tom83B]

I really like fractals and what I find even more amazing, is that something so beautiful can be so useful. I've heard that they can be used for example in chaos.
I've gone through about 10 websites and all were about fractals and chaos. But I couldn't find a single sentence that would tell me HOW can we use them...
Could anyone please try to explain me or send some links why are the fractals so useful and at least a little about how are they used?
Thanks

 

[Office_Shredder]

Like this?
http://en.wikipedia.org/wiki/Fractal#Applications

 

[jackmell]

How about getting the book, "Chaos and Fractals" by Peitgen, et. al. It gets really interesting at chapter 10: Deterministic Chaos. Try and get good at programming to work through the many examples.

 

[Tom83B]

Thanks, I will look for it.

 

[CellCoree]

Fractals and chaos are two concepts that have a lot in common. Both are complex, self-similar patterns that can be found in nature and in various systems. Fractals are geometric patterns that repeat themselves at different scales, while chaos refers to the unpredictable behavior of a system that is highly sensitive to initial conditions.

One of the main applications of fractals in science is in the study of chaos theory. Fractals are used to model and understand chaotic systems, as they can provide insights into the underlying patterns and structures of these systems. For example, fractal geometry has been used to study the behavior of weather patterns, stock market fluctuations, and even the human brain.

Fractals also have practical applications in fields such as computer graphics, where they are used to create realistic and detailed images of natural objects. In medicine, fractals have been used to study the structure and growth of tumors, as well as to analyze the branching patterns of blood vessels.

In addition to their scientific and practical uses, fractals also have aesthetic and philosophical implications. They have been seen as a symbol of the interconnectedness and complexity of the natural world, and have inspired artists and thinkers across various disciplines.

To learn more about the specific applications of fractals and chaos, I would recommend exploring the websites of organizations such as the Fractal Foundation and the International Society for the Arts, Mathematics, and Architecture. These organizations have resources and information on the uses of fractals in different fields, as well as links to further reading and research.