16umm001 / mandelbrot

The Mandelbrot set is the set of complex numbers c c for which the function f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z^{2}+c} does not diverge when iterated from z = 0 z=0, i.e., for which the sequence f c ( 0 ) {\displaystyle f_{c}(0)}, f c ( f c ( 0 ) ) {\displaystyle f_{c}(f_{c}(0))}, etc., remains bounded in absolute value.

mandelbrot

The Mandelbrot set is the set of complex numbers c c for which the function f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z^{2}+c} does not diverge when iterated from z = 0 z=0, i.e., for which the sequence f c ( 0 ) {\displaystyle f_{c}(0)}, f c ( f c ( 0 ) ) {\displaystyle f_{c}(f_{c}(0))}, etc., remains bounded in absolute value.