I released a new version of Fracton with a unified user interface and an improved color editor. The fractal I am posting today came from a search I started back in 2012. I was experimenting with a 3 term parallel resistor formula and I tried moving the terms along the imaginary axis instead of the real axis that I usually use. Moving the terms created a lot of interesting parent fractals but one alignment in particular stood out. The colors are from two color maps in Paul Lee's map collection. I used Fracton's new color editor to combine the maps and fit them to the fractal. I liked how the purple areas look like a meandering river. Here is a link to an image: http://dl.dropboxusercontent.com/u/33642054/image/pr_2-2-2_J_1200_5.jpg The FractInt compatible PAR file for the image is: pr_2-2-2_J { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20150409_1343 passes=1 float=y center-mag=-9.290328008454884/0/983.2889626222531/\ 1/0/0 params=0/6.16666666/0/0/0/0/0/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=22376BCAIHEQLIXQMdVQk_UsbYuYUmUQePMYKHQFDIA\ 9A65223327B2AI2DQ1HX1Kd1Nk1Rs0Tv0Pn1Mf1IZ2FS2BK38C\ 344000862HC5PI7XPAdWDlbGthIxjIrfHj`FcVCWPAOJ8GD587\ 300030681EC2MG2TK3`P4hT4pY5xW5tR4lN3eJ3YE2Q92I50A1\ 02630E81MD1VH1bM2jR2rW2z_2rW2jR1bN1WI1OE0G90840000\ 2864GC7OIAVOCbVFj`HrgKzmHrfFj`CcVAWO7OI4GC28622376\ BCAIHEQLIXQMdVQk_UsbYuYUmUQePMYKHQFDIA9A65223327B2\ AI2DQ1HX1Kd1Nk1Rs0Tv0Pn1Mf1IZ2FS2BK38C344000862HC5\ PI7XPAdWDlbGthIxjIrfHj`FcVCWPAOJ8GD587300030681EC2\ MG2TK3`P4hT4pY5xW5tR4lN3eJ3YE2Q92I50A102630E81MD1V\ H1bM2jR2rW2z_2rW2jR1bN1WI1OE0G908400002864GC7OIAVO\ CbVFj`HrgKzmHrfFj`CcVAWO7OI4GC28622376BCAIHEQLIXQM\ dVQk_UsbYuYUmUQePMYKHQFDIA9A65223327B2AI2DQ1HX1Kd1\ Nk1Rs0Tv0Pn1Mf1IZ2FS2BK38C344000862HC5PI7XPAdWDlbG\ thIxjIrfHj`FcVCWPAOJ8GD587300030681EC2MG2TK3`P4hT4\ pY5xW5tR4lN3eJ3YE2Q92I50A } frm:F_20150409_1343 { ; Similar to the parallel resistance formula z=0,c1=pixel-p1,c2=pixel+p1,c3=pixel: f1=z*z+c1, f2=z*z+c2, f3=z*z+c3, z=1/(1/f1+1/f2+1/f3), |z|<100 } -- Mike Frazier www.fracton.org
Dear Mike (and/or anyone else if interested), I like the math approach in your F_20150409_1343 fractal formula. I experimented a lot with multiple variable systems, mainly with one I found somewhere included with an old 80's fractal program. This formula might be included in other programs as well but my search for an other name, original purpose (if there is any) or creator resulted in nothing. Here I post this original formula (AB-) with a bailout value way larger than the original, that is the only main change I've made to it. You'll have to zoom out a bit if you load the formula. An other formula I post is from my experimentation branching from this one, with two parameter files (DLs08-0101 and DLs08-0102). If anyone knows more about systems acting similarly, please point me to the right place. Have a nice day, B.D. ---formula-start------------------------------------------- AB- { a = b = pixel bailout = 1E+100 : a = sqr(a /b) +a b = sqr(b /a) +b |a|+|b| <= bailout } ---formula-end--------------------------------------------- ---parameters-start---------------------------------------- DLs08-0101 { reset=2099 type=formula formulaname=DLs08-01 center-mag=-3.88284/0.696062/0.2224559/1 params=-0.0032/1.0368/0.992/-0.006/-1/0/0.0025/0.0046875/11/0 float=y maxiter=300 inside=0 periodicity=0 colors=000<24>00n00p00r<2>00x00z00z<24>nnzppzrrz<2>xxzzzzzzz<24>CCzAAz88\ z<2>22z00z00z<24>00C00A008<2>002000000<24>0an0cp0dr<2>0ix0jz0jz<24>nwzpx\ zrxz<2>xzzzzzzzz<24>CnzAmz8mz<2>2kz0jz0jz<30>000 } DLs08-0102 { reset=2099 type=formula formulaname=DLs08-01 center-mag=-2.24553/1.05099/0.2127981/1 params=1.0404348100300811/-0.095741680046563471/1.12/-0.12/1/0/0/-0.01875/8/0 float=y maxiter=500 inside=0 periodicity=0 colors=00000C<18>00n00p00r<2>00x00z00z<24>nnzppzrrz<2>xxzzzzzzz<24>CCzAA\ z88z<2>22z00z00z<24>00C00A008<2>002000000<24>P0nQ0pR0r<2>U0xW0zW0z<24>tn\ zupzvrz<2>yxzzzzzzz<24>aCz`Az_8z<2>X2zW0zW0z<24>60C50A408<3>000<4>00A } frm:DLs08-01 { a = pixel b = pixel +(2.5 +flip(-3)) c = pixel +5 n = m = n_t = 1 n_iter = 0 n_level = real(p5) bailout = 1E+100 : n_iter = n_iter +1 IF (n_iter == n_level) n_t = n n = n +m m = n_t n_iter = 0 ENDIF a = a +(n *p4), b = b +(n *p4) a = sqr(a /b /c) +a *p1 b = sqr(b /a /c) +b *p2 c = sqr(c /a /b) +c *p3 |a|+|b|+|c| <= bailout } ---parameters-end------------------------------------------
Nice fractals, thanks for posting them. Here are the images I got, if anyone is curious to see what they look like. http://dl.dropboxusercontent.com/u/33642054/image/DLs08-0101_640_2.jpg http://dl.dropboxusercontent.com/u/33642054/image/DLs08-0102_640_2.jpg The AB- is particularly striking. There was no par for the formula so I used one of the others and zoomed out a bit to get this image. http://dl.dropboxusercontent.com/u/33642054/image/AB-_640_5.jpg -- Mike Frazier www.fracton.org
Hello, Thank you for your reply. I didn't want to include a parameter for AB- and have mentioned that you'll have to zoom out a bit to see at least part of the possible graph. I found the formula originally here: http://archives.math.utk.edu/software/msdos/fractals/frcal040/ It is listed as a user formula and has the name of "Flower Power". I really liked the look of that equation. Now I remember that the other change I made apart from the bailout was setting both a and b to pixel, because originally it was: a = pixel, b = flip(pixel). If you are interested in formula AB- you can play with it the most easily by setting up a multiplier, or any kind of modifier to either a or b as: a = sqr(a /b) +a *modifier. If you load evolver, I can advise the application of the spread function to the modifier, or searching around the borders similar as the Julia x/y evolver setup, where the parameters corresponding to the border of the Mandelbrot set yield the most interesting results. Have a nice day, B.D.
participants (2)
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B.D. V.C. -
Mike Frazier