Mu-Molecule Metrics  

Robert P. Munafo, 1993 Oct 8.

%%not finished yet This article discusses measurements that can be performed on indivudual mu-molecules. Counting the mu-molecules is discussed under Enumeration of Features.

When comparing mu-molecules to each other, there are a large number of parameters that can measured. Most of these are lengths, areas, positions, or other geometric properties; these are discussed here.

Distortion Measures

These metrics are due to ADGP and KWP (%% reference)

%%illustration of RF(2)S, with 4 keypoints marked.

%%illustration of RF(3)S, with same 4 keypoints marked.

Intuitive Center and Size

These metrics are approximations of obvious visual features that become important to people exploring the Mandelbrot Set, particularly when loooking for embedded Julia sets.

The intuitive center and size are formally defined as the center and radius of the smallest disk that entriely encloses the mu-unit. However, this cannot be measured easily, so we use approximations instead.

The Intuitive Center is located %% of the way from the seed's mucleus to the ".1/2a" atom's nucleus. The Intuitive Size is %% times the geometric mean of the major and minor axes, which were defined above in the definition of AGDP's distortion measures.

Here is a mu-molecule with its intuitive metrics shown, to ilustrate the concept :

%%illustration of another fairly distorted mu-molecule

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2018.     Mu-ency index

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