Mixed Up Minibrot with 5 x 5 anti-aliasing

Here is an image of a fractal made with a formula similar to the parallel resistor formula. The formula uses parameters to set the power of the z term in two Mandelbrot equations, the location of each equation on the complex plane, and the size of each equation. In this example, using eighth and seventh power Mandelbrot equations of equal size and opposite sign located at -1 and +1 respectively, the formula looks like: z = 1 / (1 / ((-1) * (z ^ 8) + pixel + 1) + 1 / (z ^ 7 + pixel - 1)) The image consists of several normally formed 7 arm 6 internal bud minibrots that you would expect from a z ^ 7 equation but the minibrot in the center is clearly something different. Rather than try to explain it, click on the link below and watch the movie to see what is happening.
To make the movie, I slightly changed the location of the left equation from 1.0 to 1.00000005. Note that the fractal is rotated 90 degrees to better fit the screen so the x and y axis are reversed. Another thing to notice in the movie is that the x axis seems to eat features and spit them out along the y axis. It reminds me of a conveyor belt. These areas along the x axis with two way symmetry are very common with this formula. Zooming into them instead of moving the equation location usually causes the "conveyor belt" to appear to move and features appear to pop out. Usually the x and y axis conveyors run at a different speed and have different features on them so you get an infinite variation of the same repeating features interacting with each other. In this example, the chance alignment of mixing the two equations caused the combined minibrot. In general, this formula allows you to make fractals with lots of closely spaced minibrots that just aren't possible with the pure z ^ n + c form. When you zoom way out and look around the fractal you notice the 8 armed minibrots are on the left in the area where the z ^ 8 equation is located and the 7 armed minibrots are along the center and on the right in the area where the z ^ 7 equation is located. Minibrots using the lower power of z seem to be a lot more common. With some parameters I have been unable to find any minibrots of the higher power. If you want undistorted minibrots, the best area to search is on the x axis. I think it is possible to find minibrots with up to twice the number of arms of the higher power by combining two minibrots like in this example. |

The parameter file for the fractal is: MixedUpMinibrot { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121101_1707 passes=1 float=y center-mag=-0.3871042832031641/-1.169807668188325e\ -12/1333333350/1/90/0 params=-1/1/8/7/-1/0/1/0/0/0 maxiter=4000 inside=0 periodicity=6 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\ 40C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40\ C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C1\ 0000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C100\ 00C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000\ C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C1\ 0O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O\ 40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40\ ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA\ 0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0h\ I0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0\ oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS\ 0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0u\ a0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0\ ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0ym\ 0zy0ym0ua0oS0hI0ZA0O40C10 } frm:F_20121101_1707 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*(z^b)+c1)+1/(d*(z^f)+c2)), |z|<100 } |