Deepest  

Robert P. Munafo, 2008 Feb 18.



The words "deep", "depth" etc. are often used to refer to the amount of magnification in a view.

The popular program FRACTINT allows arbitrarily deep views, which it implements by using arbitrary precision math routines.

The 1991 book Mm - Much Ado About Nothing - Vol. 1, (A.G. Davis Philip, Adam Robucci, Michael Frame & Kenelm Philip, LC catalog number 91-092943) discusses the midgets on the spike of the sequence R2F(1/2B1)S (period 3), R2F(1/2B1)FS[2]S (period 4), R2F(1/2B1)FS[2]FS[2]S (period 5), etc. (see Utter West)

The last midget in the sequence they picture has period 300, and the image of it is at magnification 1.6×10359, requiring about 362 decimal digits or 1202 binary digits to compute. This is the deepest view I have seen, but with FRACTINT one could easily go deeper.

See also resolution, coordinates.


Here are some Internet pages related to very deep imaging:

Richard Voss' Avogadro Midget, as the name suggests, involves a magnification of about 6×1023.

This zoom movie (wmv video, WMV1 codec), one of several at fractal-animation.net, ends at a magnification of about 3×1027. Coordinates: -1.7499357218920984460646651243594 + 0.0000000890808697365708495087578 i @ 7.1e-28.

Adam Robucci's image of a midget close to R2t, magnification 10359. It is the leftmost midget of period 300.

Deepzooming with Fractint, includes images up to about 101500. The arbitrary Precision algorithms are described here. The 101500 image, located at exactly 0.0 + 1.0 i, exploits a special property of those coordinates which makes deep zooming easier.




From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2017.     Mu-ency index


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