What is the Mandelbrot set?

Question

2001 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-15T18:09:07

On the complex plane the Mandelbrot set is the set of complex numbers #c in CC# such that the sequence defined as:

#z_0 = 0#

#z_(n+1) = z_n^2+c#

is limited in module.

In other words, we have:

#z_0 = 0#

#z_1 = c#

#z_2 = c^2+c#

etc... and if #lim_n norm (z_n) < oo# then #c in M#