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 < 1 Mb QuickTime 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:

Two_Mand { ; Exported from Fracton.

 reset=2004 type=formula formulafile=fracton.frm

 formulaname=F_20111031_1502 passes=1 float=y

 center-mag=0/0/0.1904761928571428/1/0/0

 params=0/2.5/0/0/0/0/0/0/0/0 maxiter=500

 inside=1 proximity=0

 colors=000511921D32H43L54P74T85X96`A7dB7hD8lE9pFAt\

 GAxHBvGAtGArFApE9nD9lD9jC8hB8fA8dA7b97`87Z76X76V66\

 T55G00I21L42O63R84UA5XC6_E7bG8eI9hKAkMBnOCqQDtSEwU\

 FzWGyVFwUFvTEtSEsRDqQDpPCnNCmMBkLBjKAhJAfI9eH9cG8b\

 F7`E7_D6YC6XB5VA5U94S84R73P63N52M42K31J21H10G00WGG\

 YHF_IEaJDcKBeLAgM9iN8kO7nP6pQ5rR4tS3vT2xU1zW0wU0sS\

 0pR0lP0iN0eM0bK0ZI0WH0SF0OE0LC0HA1E91A71751C92FB2I\

 D2LF2OH2SJ3VK3YM3`O3cQ3fS3iU4mW4pY4sZ4v`4t_4qY4nX4\

 lV4iU4gS4dR4aP4_O4XM4VL3SJ3PI3NG3KF3HD3G00H11J22K3\

 3M44N55P66Q77S88T99VAAWBBYCC_DD`EEbFFcGGeHHfIIhJJi\

 KKkLLlMMnNNoOOqPPsQQtRRvSSwTTyUUzWWwUUuSSrQQoOOlMM\

 iKKgIIdGGaFFZDDWBBU99R77O55L33I11L44O76QA9TDCWGEYJ\

 H`MJcPMeSOhURkXUn_WpbZse`vhcxkfwhcue`sbZq_WoXTmURk\

 ROjOLhLJfIGdFDbCA`98Z65Y32W00G00I33K66M99ODDQGGTJJ\

 VMMXPPZTT`WWbZZdaafddihhkkkigghddg``fYYeUUdRRcOOaK\

 K`HH_DDZAAY66X33W00000000 }

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

}