The Mandelbrot Set is built around a simple iterative equation.
z(1) = c z(n+1) = z(n)^2 + c
Mandelbrot numbers remain bounded for n through infinity. These numbers have a real and complex component.
For a vector of real and complex components determine if each is a Mandelbrot number.
If abs(z)>2 then z will escape to infinity and is thus NOT valid.
Input: [-2; 0.22-0.54i ; 0.25-.54i ; 0.26 ;.125+.125i; 0.25]
Output: [1 ; 0 ; 1 ; 0 ; 1 ; 1] ...Where 1 is for a Valid Mandelbrot
Cleve Moler has a whole chapter on the Mandelbrot set in his book Experiments with MATLAB: Chapter 10, Mandelbrot Set (PDF)
Problem based upon Cody 81: Mandelbrot Numbers