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)FSS (period 4), R2F(1/2B1)FSFSS (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.
Here are some Internet pages related to very deep imaging:
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.
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
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11