The Mandelbrot Set and Julia Sets

Scalings in the Mandelbrot Set

Hurwitz-Robucci scaling - the Smallest Thing We've Ever Seen

Here is the smallest midget image Adam generated. The cardioid corresponds to a 300-cycle.

How small is this?

The magnification factor between this and the whole Mandelbrot set is 10³⁵⁹.

How small is this?

Suppose the diameter of the universe is 100 billion (= 10¹¹) light years.

The diameter of a proton is about 10^-15 meters.

Then the diameter of the universe is about 10³⁹ times the diameter of a proton.

Now suppose the 300-cycle midget is the size of a proton.

Suppose the universe containing this proton is itself a proton in a larger universe,

and that universe is a proton in a still larger universe,

and that universe is a proton in a still larger universe,

and that universe is a proton in a still larger universe,

and that universe is a proton in a still larger universe,

and that universe is a proton in a still larger universe,

and that universe is a proton in a still larger universe,

and that universe is a proton in a still larger universe,

and that universe is a proton in a still larger universe.

That last universe is the size of the whole Mandelbrot set.

Return to Hurwitz-Robucci scaling.