Mixing Cosine with 5 x 5 anti-aliasing

Here is another fractal using the parallel resistor formula. The basic formula combines any two powers of z. It seems to make a fractal with pretty much any coefficients you pick. I wondered what would happen if I substituted a cosine for one of the z terms. The cosine seems to add a lot of intricate detail. Here is a link to a web page with an image and a description of what I found: The equation for this fractal is: z = 1 / (1 / ((-1) * cos(z) + pixel + 1) + 1 / (z ^ 4 + pixel - 1)) I like fractals with lots of intricate detail and even more so when there is a lot of variation as you look around in the image. This image has a lot going on that is not visible unless it is drawn at a much higher resolution than fits on a webpage. I made a high resolution anti-aliased image (4000 x 3000 and 6.1 Mb) which is available in the link below. It may be too large for some browsers so right click (option-click Mac) and download the file for viewing in an image editing program if you have problems. If you do open it in a browser, make sure to click the screen to zoom in so the image is at full size. http://drive.google.com/uc?export=view&id=0B46h4FB5HYJdeWNXM0NiS1MtMW8 Looking around in the high resolution image reminds me of looking at some of the Hubble deep sky images. Everywhere you look there is some interesting feature. I didn't realize the right side was so different from the left side until I saw it at high resolution. There are dozens of places that would be interesting to zoom into. Each time I have made one of these large images I have noticed things I missed when searching the area. |

The parameter file for the fractal is: Mixing_Cosine { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121102_1156 passes=1 float=y center-mag=0.5475442691084866/-2.413982470836851e-\ 06/3333.333375/1/0/0 params=-1/1/0/4/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\ 40C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40\ C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C1\ 0000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C100\ 00C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000\ C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C1\ 0O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O\ 40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40\ ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA\ 0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0h\ I0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0\ oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS\ 0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0u\ a0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0\ ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0ym\ 0zy0ym0ua0oS0hI0ZA0O40C10 } frm:F_20121102_1156 { ; 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*cos(z)+c1)+1/(d*(z^f)+c2)), |z|<100 } |