🚀 go-pugleaf

The M-set doesn't really contain every Julia set; rather it acts as a 'map'
of all the quadratic Julia sets in this sense:

Refer to by J[c] the Julia set constructed in this manner:
For each point z in the complex plane, calculate the iterations
		z[n+1] = z[n] ^ 2 + c
A point is in the Julia set if z[n] fails to escape to infinity.
(In practice, the Julia is usually computed by seeing if |z[n]| exceeds
some preset threshold value, commonly 2, after a specified number of iterations
n.)  Well, when plotted on the complex plane, some of the Julia sets are
connected and some of them are not.

The Mandelbrot set is constructed similarly--EXCEPT for a few changes in the
meaning of the variables.  To construct M, for each point c (NOT z) in the
complex plane, starting with z[0] = 0, iterate
		z[n+1] = z[n] ^ 2 + c
and a point is in the Mandelbrot set if z[n] fails to escape to infinity.

It turns out that J[c] is connected if and only if c is a member of M.
I don't really understand the math used to prove it, I just like to play
with Fractint :)	Hope this helps.

Chris Jeris	cjeris@imsasun.imsa.edu	The Illinois Math & Science Academy
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