Mandelbrot Set Doodle

background

grid

core

disk

run
reset

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.

As you drag the blue point

B

or use "run" to get a random path, the blue line joins

B

's first 20 iterates under

f

c

.

B

also leaves a track of green or red points according to whether

B

is inside the core region of the Mandelbrot set or not.

Iterates that leave the gray disk of radius 2 can be excluded as possible candidates for the Mandelbrot set because their next iteration will again be outside that critical disk.