Divergence from the Mandelbrot Set

size of square

2.

center's real coordinate

-1.25

center's imaginary coordinate

0.047

resolution

64

step size

6

run

step6keeps1539candidates out of4096

Consider the mapping

f

c

:z↦

2

z

+c

. The Mandelbrot set consists of those complex numbers

c

such that the iterates of

(n)

f

c

(0)

do not tend to infinity as

n∞

. Points with an iterate greater than 2 in absolute value diverge.

In the left-hand image, the norms of red points reach 2 in the fewest number of iterations, followed by the other colors in order of wavelength. The initial image only takes "step size" number of iterations. Check "run" to let the number of iterations increase.

In the right-hand image, white points have iterates with norms less than 2. These are the remaining candidates for membership in the Mandelbrot set.