Mandelbrot fractal

gistfile1.py

"""
This script uses the cplot function in mpmath to plot the Mandelbrot set.
By default, the fp context is used for speed. The mp context could be used
to improve accuracy at extremely high zoom levels.
"""

import mpmath
import cmath

import StringIO
import urllib, base64

import matplotlib.pyplot as plot

def Mandelbrot(ITERATIONS = 50, POINTS = 90000, ESCAPE_RADIUS = 8, 
  	RE = [-2.5, 1.5], IM = [-1.5, 1.5]):
	ctx = mpmath.fp

	# A pretty subplot
	#RE = [-0.96, -0.80]
	#IM = [-0.35, -0.2]

	def mandelbrot(z):
		c = z
		for i in xrange(ITERATIONS):
			zprev = z
			z = z*z + c
			if abs(z) > ESCAPE_RADIUS:
				return ctx.exp(1j*(i + 1 - ctx.log(ctx.log(abs(z)))/ctx.log(2)))
		return 0

	imgdata = StringIO.StringIO()
	ctx.cplot(mandelbrot, RE, IM, points=POINTS, file=imgdata)
	imgdata.seek(0)  # rewind the data
	uri = 'data:image/png;base64,' + urllib.quote(base64.b64encode(imgdata.buf))
	print '<img src = "%s"/>' % uri
	
	return None