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).

See mu-atom size formulas.


Acknowledgements

non-circular issue: Ken Shirriff


From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo.     Mu-ency index

Creative Commons License This work is licensed under a Creative Commons Attribution 2.5 License .
WWW: http://www.mrob.com/
EMail: mrob at mrob com (If you aren't a spambot you can rewrite this yourself)
© 1996-2008 Robert P. Munafo.s.13