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matsoljare
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« Reply #1 on: June 16, 2010, 03:15:50 PM » |
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That seems very close to the Barnsley formula...  |
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KRAFTWERK
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« Reply #2 on: June 16, 2010, 03:30:38 PM » |
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Cool!
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johandebock
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« Reply #3 on: June 16, 2010, 06:33:51 PM » |
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Interactive deep zoom version: http://seadragon.com/view/14f5This is very nice software, maybe I'll used it for my website. |
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« Last Edit: June 16, 2010, 06:36:14 PM by johandebock »
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Dinkydau
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« Reply #4 on: June 17, 2010, 03:21:30 PM » |
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The borders remind me of sierpinski triangles.
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kram1032
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« Reply #5 on: June 17, 2010, 08:52:03 PM » |
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I saw such root images before. They look great  |
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johandebock
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« Reply #6 on: June 19, 2010, 03:32:52 PM » |
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Roots of polys with degree=30 and coeffs=-1,1 , 50% calculated. A x128 zoom on 0.7071, 0.7071:  |
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« Last Edit: June 19, 2010, 06:52:27 PM by johandebock »
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johandebock
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« Reply #7 on: June 19, 2010, 03:57:00 PM » |
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If somebody is interested in the program, I can make it available like BuddhaBrotMT.
I still have to work a bit on the status saving, it's a bit different than for a buddhabrot.
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kram1032
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« Reply #8 on: June 19, 2010, 05:05:10 PM » |
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really nice  |
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johandebock
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« Reply #9 on: June 21, 2010, 08:09:00 PM » |
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Finished plot:  |
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kram1032
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« Reply #10 on: June 21, 2010, 08:51:52 PM » |
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not much different, it seems^^
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johandebock
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« Reply #11 on: June 21, 2010, 09:51:57 PM » |
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not much different, it seems^^
Indeed. The roots of the most important polynomials were already calculated. |
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kram1032
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« Reply #12 on: June 22, 2010, 12:12:57 PM » |
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I just wonder how those roots are exactly calculated. Is is a regular grid or more randomly?
Because in theory you could create Polynomials for any zeros by multiplying linear factors (Vieta)
So how does it work that an actual pattern emerges? With that you could easily fill the plane uniformly with roots I'd assume...
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johandebock
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« Reply #13 on: June 22, 2010, 02:16:26 PM » |
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It seems that if you fix the possible coefficients for each degree in the polynomial to a fixed set, you get patterns.
With the coefficients fixed to [-1,1] the roots are located around the unit circle, donut structure:
-strange moonlike textures on the surface
-different types of fractal around the edges.
If you would not fix them you would indeed get a uniform filling of the complex plane.
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kram1032
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« Reply #14 on: June 22, 2010, 10:17:09 PM » |
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ah, I see |
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