I haven't posted any fractals for a few months while I was testing Fracton's 3D model code. I really need a faster computer (or faster code) to make them practical. I stopped one model after two weeks of calculations when it still hadn't finished. Doubling the resolution of the model often takes 10 times longer to calculate. Changing the resolution of a model from coarse to good often changes the execution time from minutes to months. Luckily, there are still plenty of fractal adventures to be had in the 2D space where calculations finish in a much more reasonable time. I recently explored fractals using the parallel resistor formula I have posted in the past. I noticed a few things, although there are still many more behaviors to be discovered. Here is a link to a web page with an image and a description of what I found: http://www.fracton.org/fmlposts/mixed_up_minibrot.html I will also list the PAR file here for people collecting them from the mail list: 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 } -- Mike Frazier www.fracton.org
Amazing - very golden! On 11/01/2012 04:11 PM, Mike Frazier wrote:
I haven't posted any fractals for a few months while I was testing Fracton's 3D model code. I really need a faster computer (or faster code) to make them practical. I stopped one model after two weeks of calculations when it still hadn't finished. Doubling the resolution of the model often takes 10 times longer to calculate. Changing the resolution of a model from coarse to good often changes the execution time from minutes to months. Luckily, there are still plenty of fractal adventures to be had in the 2D space where calculations finish in a much more reasonable time.
I recently explored fractals using the parallel resistor formula I have posted in the past. I noticed a few things, although there are still many more behaviors to be discovered. Here is a link to a web page with an image and a description of what I found:
http://www.fracton.org/fmlposts/mixed_up_minibrot.html
I will also list the PAR file here for people collecting them from the mail list:
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 }
-- David gnome@hawaii.rr.com authenticity, honesty, community http://clanjones.org/david/ http://dancing-treefrog.deviantart.com/
Thanks for the comments. I have a few more fractals coming in the next few days. With regard to the speed issue, the slow part is making the model. Once you have the model it only takes a minute or so to render even the most complex model I can make. The biggest problem with the speed concerns dividing the calculation into parts. I thought my "layer cake" approach of making the model one iteration band at a time divided the problem well enough. Even with that, I still end up with individual polygons with 10's of thousands of points. Many of the calculations in making the model take N x N operations (or even N cubed) where N is the number of points in the polygon. The solution may be to divide the large polygons into smaller ones but that adds even more complexity since the large polygons often have many long thin arms and holes. When large polygons are cut into smaller polygons, holes could overlap more than one polygon. I will probably revisit the algorithms and code in another few months. I had thought about possibly adding network rendering but it wouldn't help me that much. Over the years I usually have one relatively new computer and one or more really old ones that are much much slower. Unless I can divide the problem into a lot more pieces it probably isn't worth it. -- Mike Frazier www.fracton.org
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