Robert P. Munafo, 2008 Feb 18.

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

The 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. Coordinates: exactly 0.0 + 1.0 i.