There have been several posts here about generating animations of the Mandelbrot set, most recently at Display Matplotlib animations in Excel, but using standard 64 bit floats you rapidly run out of precision. However, using arbitrary precision arithmetic, and with sufficient memory, processing power, and time, you can go much further, as displayed here (and accompanied by Beethoven):

For those who want to do their own investigation of this region of the Mandelbrot Set, it is defined by:

Coordinates :
Re : -1.74995768370609350360221450607069970727110579726252077930242837820286008082972804887218672784431700831100544507655659531379747541999999995
Im : 0.00000000000000000278793706563379402178294753790944364927085054500163081379043930650189386849765202169477470552201325772332454726999999995