#
# vary_ab.py - Written by Ted Burke, last updated 18-1-2016
#

import subprocess
import math

centre = 0 + 0j   # complex value at centre of image
w,h = 400,400     # image width and height
pxw = 0.02        # pixel width
limit = 4.0       # once z reaches this value, iteration ceases

amin,amax = 2.0,4.0
bmin,bmax = 2.0,4.0

# Create a buffer to store a row of pixel values
row = w*[0]


# Generate images
for frame in range(100):
    # Open file
    filename = 'frame{:03d}'.format(frame)
    pgmfile = file(filename + '.pgm', 'w')
    pgmfile.write('P5\n{} {}\n255\n'.format(w,h))
    for y in range(h):
        for x in range(w):
            a = ((amin+amax)/2.0) + ((amax-amin)/2)*math.cos(2*math.pi * (float(x)/w + frame/100.0))
            b = ((bmin+bmax)/2.0) + ((bmax-bmin)/2)*math.sin(2*math.pi * (float(y)/h + frame/100.0))
            c = centre + complex(((x-(w-1)/2.0)*pxw),(((h-1)/2.0-y)*pxw))
            z = 0
            n = 0
            while abs(z) < limit and n < 51:
                try:
                    z = (pow(z,a) + c)/(pow(z,b) - c)
                    n = n + 1
                except ZeroDivisionError:
                    z = limit
            row[x] = int(255 * (0.5 + 0.5*math.cos(math.pi*n/51.0)))
        pgmfile.write(bytearray(row))

    # Close file
    pgmfile.close()
    subprocess.call('mogrify -format png ' + filename + '.pgm', shell=True)
    subprocess.call('rm ' + filename + '.pgm', shell=True)
    print(filename + '.png written')

#
# renamer.py - Written by Ted Burke, last updated 18-1-2016
#

import subprocess

# Create fractal image files
for n in range(100):
    filename = 'frame{:03d}'.format(n)
    print(filename)    
    subprocess.call('convert ' + filename + '.png -resize 50% ' + 'half_' + filename + '.png', shell=True)

To create an mp4 video using ffmpeg:

ffmpeg -framerate 10 -i half_frame%03d.png -c:v libx264 -pix_fmt yuv420p output.mp4

To create a looping gif using ImageMagick’s convert tool:

convert -loop 0 half_frame*.png output.gif