Schlega
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« on: March 21, 2010, 09:35:08 PM » |
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This was inspired by Paolo's conjecture in the triplex algebra thread, combined with my inability to get anything but a black screen for exp(2*ln(z))+c using the triplex definitions. Define exponentialish functions by expish(x,y,z) = exp(x)*(cos(y)*f 1(x,y,z), sin(y)*f 2(x,y,z), f 3(x,y,z)), where f 1(x,y,0) = f 2(x,y,0) = 1 and f 3(x,y,0) = 0. Similarly, define logarithmish functions by logish(x,y,z) = (ln(x^2+y^2) + g 1(x,y,z), atan2(x+iy)+g 2(x,y,z), g 3(x,y,z), where g 1(x,y,0) = g 2(x,y,0) = g 3(x,y,0) = 0. Here is what you get for expish(2*logish(z))+c for f 1(x,y,z) = f 2(x,y,z) = cos(z), f 3=sin(z): g 1 = ln(x^2+y^2+z^2) - ln(x^2+y^2), g 2=0, g 3 = asin(z/r).
http://www.youtube.com/v/q9ncR-Hbl4Y&rel=1&fs=1&hd=1I played with some other choices, but youtube doesn't seem to like them at the moment. I'll try again later.
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« Last Edit: March 21, 2010, 10:04:00 PM by Schlega »
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kram1032
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« Reply #1 on: March 21, 2010, 09:40:08 PM » |
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pretty much 2D-Mset-ish... But nice
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Schlega
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« Reply #2 on: March 22, 2010, 06:46:47 AM » |
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Schlega
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« Reply #3 on: March 22, 2010, 09:05:56 AM » |
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This also gives a definition for triplex powers. z (2,1,0): z (2,1,1): z (2,0,1): z (8,1,0): z (8,1,1): z (8,0,1):
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Sockratease
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« Reply #4 on: March 22, 2010, 11:25:19 AM » |
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I really enjoyed the "higher powers" animation! It's like watching a time-lapse video of a flower blooming
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Life is complex - It has real and imaginary components. The All New Fractal Forums is now in Public Beta Testing! Visit FractalForums.org and check it out!
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kram1032
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« Reply #5 on: March 22, 2010, 03:59:01 PM » |
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very nice animations and still and I have to agree with Sockratease
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kram1032
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« Reply #7 on: March 23, 2010, 03:14:59 PM » |
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that's pretty nice
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Timeroot
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« Reply #8 on: March 24, 2010, 02:19:17 AM » |
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Sweeet! :thumbsup1 After seeing those stills, I was just about to request a video of parameter space exploration of z^(a,b,c), and there it was when I scrolled down! Pre-request gratification is fun!
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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: June 09, 2010, 12:03:53 PM » |
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Hi schlega. I am pretty excited by the form you have developed. The animations are a great tool to understanding what you have done. Again it is pretty cool that ideas sparked from this forum are at the cutting edge of visualisation of relativistic forms. I can't explain myself now but i will later when i have explored the notions of polynomial multiple operators. A simpler idea is the taylor expansion operator or the Fourier polynomial transforms .
What you are showing is something fractal woman said: our computing power has arrived at a place where the computaional error is not significant enough to mask the relationships we are exploring; i think she said we are close to plank length!
Good luck and good fortune in your explorations!
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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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Schlega
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« Reply #11 on: June 09, 2010, 01:43:53 PM » |
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Thanks, jehovajah. I must admit I don't know what relativistic forms are, but I like the sound of it.
Good luck in your own exploration as well!
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KRAFTWERK
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« Reply #12 on: June 10, 2010, 09:03:02 AM » |
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Very nice animations Schlega! Some seem to be totally new versions, but these two looks exactly like our familliar Positive z: and cosine mandelbulbs: Wicked...
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kram1032
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« Reply #13 on: June 10, 2010, 12:53:17 PM » |
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very interesting but when thinking about how the exponential is related to angular functions, it's somehow expected.
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