Mu-atom
Robert P. Munafo, 2000 Feb 4.
Definition : math. Any one of those areas, resembling either a circle or a cardioid, which is the largest connected superset of a subset of M, and possessing the property that all internal points have the same period.
This term was introduced by Benoit Mandelbrot in his description of the Mandelbrot set in The Fractal Geometry of Nature. On page 183, he defines a mu-atom as one of the "maximal connected sets", no two of which overlap, except perhaps in a single point (a bond). The mu-atoms make up Mu-molecules. All mu-atoms are shaped either like a disk or like a cardioid. The former are descendants; the latter are seeds.
For examples of mu-atoms, see the entry R2.
A mu-atom is also called an attractive component, e.g. by Douady in The Beauty of Fractals page 165.
Some colloquial names for mu-atoms are ball, bud, bulb, decoration, lake and lakelet.
To the eye, it appears that all mu-atoms are either perfect circles or perfect cardioids. However, it now known that none except R2a and R2.1/2a are perfect (see Fractal Horizons).
Acknowledgements
non-circular issue: Ken Shirriff
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo. Mu-ency index
Robert Munafo's home pages on HostMDS (c) 1996-2010 Robert P. Munafo. about contact
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