Here are some pictures from my July 13, 2004 talk at the Texas State Honors Summer Math Camp. All images are 2048 x 1536 and in PNG format.
This is the Julia set of z^2 + (0.12 - 0.6i) (each image is magnified 1000 times from the previous).
These are Julia sets of z^2 + c where c is -0.8 - 0.15i and -0.8 - 0.175i, respectively.
c = -i
c approximately 0.395014 + 0.555625i
c approximately -0.564098 + 0.679273i