In the past I had wanted to have multiple mandelbrots in the same image but I didn't want to do image side trickery like the white square method or use an if statement that switched the image from one to the other. I stumbled across a way to do just that using a simple formula similar to the one used to calculate parallel resistance. Anyone that has taken electrical engineering is familiar with the formula for parallel resistance:
rp = 1 / ( 1 / r1 + 1 / r2 )
If you put a mandelbrot equation at r1 and r2 with a different center point you have it. You can use different orders for each mandelbrot and have as many as you like by adding more 1 / rn terms. When the mandelbrots get close they interact in wierd ways. I made a short movie of two mandelbrots flying past each other. Almost like two galaxies colliding.
The parameter file for the center image of the movie is below:
frm:F_20111031_1502 {
; Two mandelbrots
; p1 is the position of mandelbrot 1
; p2 is the position of mandelbrot 2
; time = instant
z=0,
r1=p1,
r2=p2:
z1=1/(z*z+pixel-r1),
z2=1/(z*z+pixel-r2),
z=1/(z1+z2),
|z|<=100
}