two_mand_center_800_5.jpg

Two Mand Center Frame with 5 x 5 anti-aliasing

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:

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\
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F7`E7_D6YC6XB5VA5U94S84R73P63N52M42K31J21H10G00WGG\
YHF_IEaJDcKBeLAgM9iN8kO7nP6pQ5rR4tS3vT2xU1zW0wU0sS\
0pR0lP0iN0eM0bK0ZI0WH0SF0OE0LC0HA1E91A71751C92FB2I\
D2LF2OH2SJ3VK3YM3`O3cQ3fS3iU4mW4pY4sZ4v`4t_4qY4nX4\
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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
}

 

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