# How to plot the Mandelbrot set

[CG]Maxime

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## 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 $c$ for which the sequence ${z}_{n+1}={z}_{n}^{2}+c$ is bounded (${z}_{0}$ is set to $0$). While, the definition of the Julia sets is the numbers ${z}_{0}$ for which the sequence is bounded, with $c$ a constant value.

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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)))

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from PIL import Image, ImageDraw

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