Calculating Fractal Dimension for the Lorenz Strange Attractor

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SUMMARY

The discussion focuses on calculating the fractal dimension of the Lorenz strange attractor, which is known to lie between 2 and 3. Participants explore various methods for determining fractal dimensions, including Hausdorff dimension, Correlation dimension, and Pointwise dimension, questioning their equivalence and relevance. The reference to the paper by N. B. Abraham et al. from 1986 highlights the historical context and potential methodologies for this calculation. The conversation emphasizes the importance of selecting the appropriate definition of fractal dimension for accurate results.

PREREQUISITES
  • Understanding of fractal geometry concepts
  • Familiarity with the Lorenz attractor and its properties
  • Knowledge of different definitions of fractal dimension
  • Basic skills in computer simulation techniques
NEXT STEPS
  • Research methods for calculating Hausdorff dimension
  • Explore techniques for determining Correlation dimension
  • Study Pointwise dimension and its applications
  • Locate and review the paper by N. B. Abraham et al. (1986) for historical methodologies
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Mathematicians, physicists, computer scientists, and anyone interested in fractal analysis and simulation techniques for complex systems.

broegger
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Hi.

How can I "experimentally" (by way of computer simulation) calculate an approximate value for the dimension of a fractal object? The object in question is the Lorenz strange attractor, which has a dimension between 2 and 3.

Also, I know there is a number of different ways to define fractal dimension (Hausdorff dimension, Correlation dimension, Pointwise dimension etc.): are these equivalent or does it matter which one is used?

Thanks.
 
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My notes have this old citation:

N. B. Abraham, A. M. Albano, B. Das, G. De Guzman, S. Yong, R. S.
et al , Calculating the dimension of attractors from small data sets, Phys. Lett. A 114 (1986) 217.

I no longer have the paper, but I believe it may help.
 
I'll try to locate that one. Thank you!
 

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