It’s impressing how easy it is to draw fractals with Python. Using the ubercool Python Imaging Library (http://www.pythonware.com/products/pil/index.htm) and native complex number support in Python you can code an elaborate and easy to understand fractal generator in less than 50 lines of code:

#!/usr/bin/python import Image, ImageDraw, math, colorsys

dimensions = (800, 800) scale = 1.0/(dimensions[0]/3) center = (2.2, 1.5) # Use this for Mandelbrot set #center = (1.5, 1.5) # Use this for Julia set iterate_max = 100 colors_max = 50

img = Image.new(“RGB”, dimensions) d = ImageDraw.Draw(img)

Calculate a tolerable palette

palette = [0] * colors_max for i in xrange(colors_max): f = 1-abs((float(i)/colors_max-1)**15) r, g, b = colorsys.hsv_to_rgb(.66+f/3, 1-f/2, f) palette[i] = (int(r255), int(g255), int(b*255))

Calculate the mandelbrot sequence for the point c with start value z

def iterate_mandelbrot(c, z = 0): for n in xrange(iterate_max + 1): z = z*z +c if abs(z) > 2: return n return None

Draw our image

for y in xrange(dimensions[1]): for x in xrange(dimensions[0]): c = complex(x scale - center[0], y scale - center[1])

    n = iterate_mandelbrot(c)            # Use this for Mandelbrot set
    #n = iterate_mandelbrot(complex(0.3, 0.6), c)  # Use this for Julia set

    if n is None:
        v = 1
    else:
        v = n/100.0

    d.point((x, y), fill = palette[int(v * (colors_max-1))])

del d img.save(“result.png”)

Some example pictures:

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