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makc
Strange Attractor
Posts: 272
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« Reply #1 on: February 01, 2010, 08:17:11 PM » |
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attached essential part
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makc
Strange Attractor
Posts: 272
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« Reply #2 on: February 01, 2010, 10:43:13 PM » |
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tried to up the number of iterations but that site times out after roots of (((((x²+x)²+x)²+x)²+x)²+x)²+x
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lkmitch
Fractal Lover
Posts: 238
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« Reply #3 on: February 01, 2010, 11:08:05 PM » |
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You may already know this, but what you'd get if you could continue the process indefinitely would be a point for the center of each cardioid and each disk, which would approximate the boundary of the Mandelbrot set.
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makc
Strange Attractor
Posts: 272
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« Reply #4 on: February 01, 2010, 11:18:13 PM » |
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I was entering random garbage into this form over and over until I came up with signs alteration idea. I wonder what's going to happen with traditional Mandelbrot set rendering algos modified this way?
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makc
Strange Attractor
Posts: 272
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« Reply #5 on: February 01, 2010, 11:30:34 PM » |
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I wonder what's going to happen with traditional Mandelbrot set rendering algos modified this way? It appears nothing particularly interesting, except that there are now "islands". I am going to try one with random coefficients now...
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makc
Strange Attractor
Posts: 272
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« Reply #6 on: February 01, 2010, 11:46:15 PM » |
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I am going to try one with random coefficients now... This turned out to be much more fun than typing stuff in Wolfram Alpha
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makc
Strange Attractor
Posts: 272
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« Reply #7 on: February 02, 2010, 01:05:32 PM » |
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added manual coefs control to the code in last post and without page reloading. (shift+)click to zoom (out) btw. not too fast, but it's only flash. could be more fluid in c.
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kram1032
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« Reply #8 on: February 02, 2010, 02:52:58 PM » |
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really a nice little program
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Timeroot
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« Reply #9 on: February 07, 2010, 10:26:37 AM » |
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I made a quick formula(s) for UF that implement this. It calculates an "angle" to multiply c by each iteration. With angle=0.5, you get ((z^2+c)^2 - c)^2 + c etc... with angle=0.25, you get ((((z^2+c)^2+ic)^2-c)^2-ic etc... The incredible thing is, unless the angle has an imaginary part of exactly zero and a real part not close to a multiple of 2, the mandelbrot set loses basically all its interior. At angle=0.0001, it's a full Mandelbrot set with not visible deformation. At angle=-0.00001 or angle=1.99999, it has no deformation, but it has lost all it's interior. Weird, just weird. In fact, I think this might be a viable inside coloring algorithim for the Mandelbrot set due its lack of deformity and interesting shapes. Code: ChangingSignsMand{ init: sign=-1^(2*@Angle) iter=0 z=0 loop: z=z^@Power + (sign^iter)*#pixel iter=iter+1 bailout: |z|<=@Bailout default: title="Changing Signs (Mandelbrot)" complex param Angle default=(0.05,0.0001) endparam complex param Power default=2 endparam float param Bailout default=4 endparam }
ChangingSignsJulia{ init: signedC=(-1^(2*@Angle))*@C iter=0 z=#pixel loop: z=z^@Power + signedC iter=iter+1 bailout: |z|<=@Bailout default: title="Changing Signs (Julia)" complex param Angle default=(0.05,0.0001) endparam complex param Power default=2 endparam float param Bailout default=4 endparam }
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« Last Edit: February 07, 2010, 10:28:59 AM by Timeroot »
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
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jehovajah
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« Reply #10 on: February 07, 2010, 11:22:25 PM » |
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If this does become a colouring algorithm i just want to say i was first to respond to your insight to this wholly serendipitous train of events!
Delightful.
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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Timeroot
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« Reply #11 on: February 08, 2010, 07:51:06 AM » |
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Well, I made a "coloring algorithim" of that idea, if you can call it that. Basically it just iterates this other formula with a very very small angle (which the user can change) and then colors based on iteration, magnitude, angle, real, or imaginary. But I think I've made an incredible discovery. With any option other than iteration, if produces PURE NOISE. Zooming in to any level doesn't simplify it. It fills the entire MSet. I zoomed in to E11, with only 100 iterations (that's relevant, because more iterations mean more chaos), and there was still pure noise. I may have messed something up in the code, but either way, I see some applications in encoding and security considering how much noise is generated by such little computation... anyone have thoughts???
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
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makc
Strange Attractor
Posts: 272
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« Reply #12 on: February 08, 2010, 11:57:09 AM » |
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your typical random() code doesn't involve much computations either.
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Timeroot
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« Reply #13 on: February 09, 2010, 12:43:58 AM » |
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Okay fine, but the amount of chaos it produces is quite surprising I find.
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
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