R2a

Robert P. Munafo, 2002 May 8.

R2a is the largest mu-atom in the Mandelbrot Set, and it is the seed of the continent. It is the large cardioid; see the R2 entry for a picture identifying its location and links to other attached features.

Colloquial names for R2a include body, main cardioid, fixed-point cardioid.

The boundary of R2a can be precisely described by a parametrized relation. It is the set of all points P given by the expression

P = ((A + i)/2)2 + 1/4

where A is a point on the unit circle, i.e. A = 1. From this formula it is also possible to derive the location of all secondary continental mu-atoms; see internal angle for details.

All of the points in the interior of R2a have a period of 1.

The Julia Sets of points in the interior of R2a have an interior that is connected. No other Julia Sets have this property.


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

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