Fractals and chaos - what do they have in common?

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Fractals are not only aesthetically pleasing but also have practical applications in understanding chaos theory. Despite extensive research, clear explanations of how fractals are utilized remain elusive for some. Resources like the Wikipedia page on fractals and the book "Chaos and Fractals" by Peitgen provide valuable insights into their applications. Engaging with programming can enhance comprehension of fractal concepts through practical examples. Overall, fractals serve as a bridge between beauty and utility in the study of chaos.
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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
 
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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.
 
Thanks, I will look for it.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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