Calculating Fractal Dimension for the Lorenz Strange Attractor

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To calculate the fractal dimension of the Lorenz strange attractor through computer simulation, various methods can be employed, including Hausdorff, Correlation, and Pointwise dimensions. The choice of method may affect the results, as these definitions are not necessarily equivalent. The Lorenz attractor's dimension lies between 2 and 3, making it a complex object for analysis. A reference to an older paper by Abraham et al. is mentioned as potentially useful for this calculation. Locating this citation could provide valuable insights for the experimental approach.
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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 dimention 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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