Another Julia Set animation

Click this image to view the Julia Set animation (the gif file is about 5.3MB in size, so I didn’t want to embed it here directly):

This is the Python code I used to generate the 200 individual frames in the animation:

#
# julia_frames.py - Generates Julia Set images
# Written by Ted Burke
# Last updated 10-2-2012
#
# This program generates a sequence of Julia Set images,
# using values of the complex parameter c that lie on a
# circle of radius 0.3, centred on the point -1 + 0j in
# the complex plane. I'm hoping this circular path will
# generate plenty of interesting images since it lies a
# little outside the perimeter of a roughly circular
# lobe (with radius 0.25) of the Mandelbrot Set.
# 

import numpy
import math

# Specify image width and height
w, h = 640, 480

# Specify real and imaginary range of image
re_min, re_max = -2.0, 2.0
im_min, im_max = -1.5, 1.5

# Generate evenly spaced values over real and imaginary ranges
real_range = numpy.arange(re_min, re_max, (re_max - re_min) / w)
imag_range = numpy.arange(im_max, im_min, (im_min - im_max) / h)

# Frame counter
frame = 0

# Iterate over a range of c values
for angle in numpy.arange(0.0, 2 * math.pi, 0.01 * math.pi):
	# Increment frame counter
	frame += 1
	
	# Open file and write PGM header info
	filename = "{0:03d}.pgm".format(frame)
	print filename
	fout = open(filename, 'w')
	fout.write('P2\n# Julia Set image\n' + str(w) + ' ' + str(h) + '\n255\n')
	
	# Generate pixel values
	for im in imag_range:
		for re in real_range:
			z = complex(re, im)
			c = complex(-1.0 + 0.3*math.sin(angle),0.3*math.cos(angle))
			n = 255
			while abs(z) < 10 and n >= 5:
				z = z*z + c
				n = n - 5
			# Write pixel value to file
			fout.write(str(n) + ' ')
		fout.write('\n')
		
	# Close file
	fout.close()

To convert each of the 200 images from PGM to PNG format, I used the following command:

for i in {001..200}; do convert $i.pgm $i.png; done

To combine the 200 PNG images into a single animated gif, I used the following command:

convert -delay 10 *.png julia.gif