This is a plot of Mandelbrot's completely incomputable set.

mandelplot.py

######################################################
######## mandelplot: plot the mandelbrot set #########
######################################################
import numpy as np # load numerical python
import matplotlib.pyplot as plt # load plotting tools

bailout = 10**62 # bound on the number of iterations
radial_pixels = 512 # resolution of plot
sequence = [-2 + 4/radial_pixels*count for count in range(radial_pixels)]
image = np.zeros((radial_pixels,radial_pixels))

def mandelplot(radial_pixels, bailout):
    def mandelpixel(x, alpha):
        z_n = 0 + 0j
        c = x + alpha*1j
        for n in range(bailout):
            if abs(z_n) > 2:
                return n
            z_n = z_n**2 + c
            if n == bailout - 1:
                #print('n hit bailout; (n,z_n): ',(n,z_n))
                return n
    for i_x in range(radial_pixels):
        for i_alpha in range(radial_pixels):
            value = mandelpixel(sequence[i_x], sequence[i_alpha])
            image[bailout-1-i_alpha][i_x] = value
    figure = plt.imshow(image)#, clim=(0.4, .9))
    plt.set_cmap('spring')
    plt.colorbar(orientation = 'horizontal', shrink = .5)

mandelplot(radial_pixels, bailout)

"How can you plot a set of points that is completely incomputable?" One method is to use a convergence threshold after some number of iterations. This gist was the first thing I threw together to plot this. It could use many obvious improvements. Can you spot them? Please run this, fork this, change this to explore it, and ask me anything. I dare ya! :-)