Proceed to Safety


Robert P. Munafo, 2023 Jul 1.

Colloquial name used by Milnor as early as 2000, and others such as Romera et al. to describe the Julia set of R2.C(0). Also, by extension, used to describe the same shape as it appears in Julia sets of other cardioid cusps like R2F(1/2B1)S.C(0).

c=0.26 (''dense'')
c=0.26 ("dense")
c=1.0 (''sparse'')
c=1.0 ("sparse")

Embedded Julia set shape

This is the shape of Type CC embedded Julia sets which are thus called cauliflower medallions (see that article for an example). They are distinct from all other embedded Julia sets because of their simple open interior with a very clear binary branching structure of nodes and connecting filaments.

revisions: 20000302 oldest on record; 20080218 "and others", type CC; 20230418 "medallions"; 20230701 add images

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.

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