It begins with this equation : z ` n +1 = z ` n2 + c. Starting with z0 = 0 , c is in the Mandelbrot set if the absolute value of z ` n never exceeds a certain number ( that number depends on c ) however large n gets .
More technically , the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial z ` n +1 = z ` n2 + c remains bounded . That is , a complex number , c , is part of the Mandelbrot set if , when starting with z0 = 0 and applying the iteration repeatedly , the absolute value of z ` n never exceeds a certain number ( that number depends on c ) however large n gets .