Plot Mandelbrot with matplotlib / pyplot / numpy / python

Question

I am new to python and learning by following Python "Scientific lecture notes Release 2013.1" tutorial. Please help me solve this Mandelbrot problem in the srcreenshot below (Pg 71). Please provide step-wise commands with explanation if possible because programming concepts are new to me.

http://dl.dropbox.com/u/50511173/mandelbrot.png

I tried to solve this as follows:

import numpy as np
import matplotlib.pyplot as plt

x,y=np.ogrid[-2:1:10j,-1.5:1.5:10j]
c=x + 1j*y
z=0
for g in range(50):
  z=z**2 + c

plt.imshow(z.T, extent=[-2,1,-1.5,1.5])

I encountered the following error "TypeError: Image data can not convert to float"

What does this error exactly mean and how to correct it? I am finding it difficult to understand the imshow() function. What do the individual terms inside imshow() mean?

Thank You.

Answer 1

The Mandelbrot set is not the values of z you are trying to plot, which are giving you problems because they are complex numbers. The Mandelbrot set is made up of the points p of the complex plane for which the recurrence relation z_n = z_n-1**2 + p remains bounded. This is checked in a practical way by comparing the result after a few iterations to some threshold. In your case, if you add the following lines after your for loop:

threshold = 2
mask = np.abs(z) < threshold

and then plot mask you should see the set plot on screen.

To understand the general workings of imshow's arguments, you will be better off reading the docs than asking here.