# How to plot the Mandelbrot set

[CG]Maxime

89.5K views

### Open Source Your Knowledge, Become a Contributor

Technology knowledge has to be shared and made accessible for free. Join the movement.

## Julia Sets

Julia Sets also offer great fractals. The definition of the Julia sets is very similar to the mandelbrot set. As a reminder, the Mandelbrot set is the set of the complex numbers c$c$ for which the sequence zn+1=z2n+c${z}_{n+1}={z}_{n}^{2}+c$ is bounded (z0${z}_{0}$ is set to 0$0$). While, the definition of the Julia sets is the numbers z0${z}_{0}$ for which the sequence is bounded, with c$c$ a constant value.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

from math import log, log2

MAX_ITER = 80

def julia(c, z0):

z = z0

n = 0

while abs(z) <= 2 and n < MAX_ITER:

z = z*z + c

n += 1

if n == MAX_ITER:

return MAX_ITER

return n + 1 - log(log2(abs(z)))

Enter to Rename, Shift+Enter to Preview

1

from PIL import Image, ImageDraw

Enter to Rename, Shift+Enter to Preview

I hope you liked this playground. Please leave a comment below!

Suggested playgrounds

Open Source Your Knowledge: become a Contributor and help others learn. Create New Content