Generating Julia Sets

real part of c

-0.79

complex part of c

0.15

iterations

200

resolution

0.05

0.03

0.01

0.005

This Demonstration graphs quadratic Julia sets, which consist of the points in the complex plane whose modulus remains bounded under iteration of the map

z⟶

2

z

+c

. Different values of the complex number

c

yield different Julia sets.

The finest resolution image takes longest to plot. The number of iterations also affects the image and calculation time; the greater the iterations, the more detailed the image, but the longer it will take to calculate. 500 is a good number for disconnected sets, while 50 to 100 is usually best for connected sets.