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Contrasting ValuesWoodland GardenLiving Blocks
Woodland Garden
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Description: Created with the Fractal Science Kit fractal generator. See http://www.fractalsciencekit.com/ for details.

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Discussion Topic: View Topic
Keywords: fractal art abstract chaos Julia 
Posted by: Ross Hilbert October 01, 2011, 10:32:56 PM

Rating: ***** by 5 members.

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Comments (8) rss
Ross Hilbert
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October 03, 2011, 03:36:25 PM
Thanks Fractalisman :-)
Fractalisman
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db


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October 03, 2011, 10:26:36 AM
Agree with RCPage
Ross Hilbert
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October 02, 2011, 05:55:22 PM
Thanks Paul!

This is a Julia set based on an equation inspired by, and similar to the KaliSet and 2D MandleBox equations.

The heart of the equation is:

Code:

  z = Affine.TransformPoint(s1, z)
  z = Complex(p1p(m1p(z.x)), p1p(m1p(z.y)))
  z = Affine.TransformPoint(s2, z)
  z = CircleFoldIn(z, 0, Radius)
  z *= c
  z = Affine.TransformPoint(s3, z)


where:

Code:

  Complex p1p(r) = LRFold(r,  1)
  Complex m1p(r) = LRFold(r, -1)

  CircleFoldIn(z, center, radius) {
    return IIf(Abs(z) > radius, Geometry.Inversion(center, radius, z), z)
  }

  Complex Geometry.Inversion(center, radius, z) {
    return center + radius^2/Conj(z-center)
  }

  Complex LRFold(r, v) {
    return Abs(r - v) + v
  }


s1, s2, and s3 are affine transformations defined by user options,
and Affine.TransformPoint(s, z) applies affine transformation s
to z and returns the result.

In this fractal Radius is 12, s1 and s3 are the identity transformation,
and s2 is a reflection in a line through the origin inclined -22.5 degrees.
Pauldelbrot
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October 02, 2011, 04:31:33 PM
Are these Kaliset fractals? Or 2D Mandelbox? The resemblance to those is strong. Very nifty BTW.
Ross Hilbert
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October 02, 2011, 03:27:37 PM
Thanks Johan!
KRAFTWERK
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October 02, 2011, 08:41:42 AM
Very nice Ross!
Ross Hilbert
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October 02, 2011, 05:08:12 AM
Thanks RC :-)
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October 02, 2011, 05:05:54 AM
 Repeating Zooming Self-Silimilar Thumb Up, by Craig

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