Multifractal estimation---maximum likelihood

Due to a server upgrade some years ago, this web service is not working at the moment. Contact me by email.

Paste your data points into the box below, then click

Also enter the magic word "a z o n a l" into this box:

Enter your data into the box to the left

Your data must represent a 1D, 2D or 3D set of points.
Your data must be one, two or three columns of numbers;
and no more than 400 rows;
then click the submit button above to analyse.

Wait for a minute

Your data is analysed after submission:
taking up to perhaps a minute execution time;
this is compute intensive, so have patience;
and you will then see a data summary returned in a web page.

The theory behind the analysis

A. J. Roberts and A. Cronin, Unbiased estimation of multi-fractal dimensions of finite data sets, Physica A, vol.233, pp.867--878, 1996.
I construct many artificial multiplicative multifractals and remember those that generate fractals that look much like your data. The reported fractal properties are those of multifractals that best look like your data.
Be wary that the Hausdorff dimension is very sensitive to experimental sampling chance: this article explains, Use the information dimension, not the Hausdorff
I thank Thuc Le for the code to handle data embedded in different dimensional space.

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Multifractal estimation---maximum likelihood

by Emeritus Prof. A. J. Roberts

Due to a server upgrade some years ago, this web service is not working at the moment. Contact me by email.

Paste your data points into the box below, then click

Enter your data into the box to the left

Wait for a minute

The theory behind the analysis