MHB Lorenz Attractor: Questions & Answers

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The Lorenz attractor is not classified as a fractal set, although it exhibits fractal-like properties. Its structure is determined by chaotic dynamics rather than strict fractal geometry. The topological dimension of the Lorenz attractor is typically considered to be three, reflecting its complex behavior in three-dimensional space. Understanding these characteristics is crucial for studying chaotic systems. The discussion highlights the intersection of chaos theory and topology in the context of the Lorenz attractor.
dingo
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I have 2 questions about the Lorenz attractor:

1)Is the Lorenz attractor considered to be a fractal set?
2)If it is so, then what is its topological dimension?

Thanks.:)
 
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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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