It's impressing how easy it is to draw fractals with Python. Using the ubercool Python Imaging Library 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(r*255), int(g*255), 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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