Over a decade ago while working with 2D fractals, I wanted to have multiple mandelbrots in the same image but I didn't want to 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 equations 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.

You can see the original web page with a movie here:

Two Mand

Now in October 2021, I have updated my fractal program Fracton to be able to make 3D fractals. I can report that using the parallel resistor formula with 3D fractals works in a similar fashion to the 2D version. The fractals interact with some parts repelling and other parts attracting. The movie below shows two mandelbulbs combined using the parallel resistor formula. I am going to call it a PARABULB or PARAllel resistor formula mandelBULB.

The ray-traced images were created with Fracton. The movie was made with Final Cut.