Distortion

Robert P. Munafo, 2010 Oct 20.

Some features of the Mandelbrot set are often said to be "distorted" when compared to other features¹.

One common example are islands in cusps. In these illustrations, the first island is the slightly asymmetrical R2F(1/3B1)S. The second is R2F(1/15B1)S, located fairly close to the cusp R2.C(0):

-0.15842 +1.03335 i @ 0.03048

Figure 1. R2F(3)S . Coordinates: -0.15842 +1.03335 i @ 0.03048

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Figure 1. R2F(15)S . Coordinates: 0.2925294 + 0.0149698 i @ 0.0006675

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As the R2.C(0) article illustrates, the cardioid is symmetrical, yet the north and south radicals of this island are of quite different sizes and the .1/2 child mu-atom is clearly off-center.

footnotes

1 : (In fact, provided that the software is accurate, no Mandelbrot set feature is truly distorted — they are all exactly the shape that they "should" be).

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