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Serpentine Labyrinth Previous Image | Next Image
Description: This image was created with the Fractal Science Kit fractal generator. See http://www.fractalsciencekit.com/tutorial/examples/examples.htm for details.

It is based on information given by penny5775 at:
http://penny5775.deviantart.com/art/Mobius-Dragon-Script-104021373
http://penny5775.deviantart.com/art/Mobius-Design-Pack-104115613

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Total Favorities: 1 View Who Favorited
Filesize: 372.4kB
Height: 700 Width: 1050
Discussion Topic: View Topic
Keywords: fractal art abstract chaos attractor IFS symmetry dragon mobius circles kleinian Apollonian gasket
Posted by: Ross Hilbert March 11, 2011, 07:50:30 PM

Rating:     by 7 members.

 Comments (8) Ross Hilbert Fractal Phenom      Posts: 469   December 24, 2011, 01:47:31 AMHi bib,I didn't base this fractal on the other one you referenced.I used the code given below with the options set as follows:Order: 12Pattern: 1PatternWeight: 1HorizontalWeight: 0.25VerticalWeight: 0.12LineWeight: 0.05Power: 16Weight: 0.98RossCode:comment:    This program generates a Mobius Dragon IFS.    2 options are available to control the pattern: 'Order' and   'Pattern'. Order is an integer that ranges from 1 to 12 and   controls the complexity of the pattern. Pattern is an integer  that ranges 1 to 3 and is used to vary the pattern.    You can speed up the display and improve the results by adding  a symmetry transformation to match the symmetry inherent in the  attractor.    I recommend using the 'Color Map - Index' controller with this equation  so that you can control the index/color mapping. The index values range  from 0 to 2 as follows:      0 pattern attractor 1    1 pattern attractor 2    2 vertical shift attractor    you will need to use the controller's Attractor Opacity property   to favor index 2 since the weight for the pattern attractors   is so much larger.    This program is based in part on information given by penny5775 at:    http://penny5775.deviantart.com/art/Mobius-Dragon-Script-104021373    http://penny5775.deviantart.com/art/Mobius-Design-Pack-104115613  global:    Complex shift[] = \    Complex(0.4995, 0.6772), \    Complex(0.3195, 0.3668), \    Complex(0.2252, 0.2512), \    Complex(0.1648, 0.1939), \    Complex(0.1223, 0.1589), \    Complex(0.0909, 0.1339), \    Complex(0.06741, 0.11389), \    Complex(0.0502, 0.0969), \    Complex(0.0378, 0.0828), \    Complex(0.02898, 0.071), \    Complex(0.0226, 0.0613), \    Complex(0.01784, 0.05323)      Complex dy1[] = \    2.3228, \    2.6332, \    2.7488, \    2.8061, \    2.8411, \    2.8661, \    2.8861, \    2.9031, \    2.9172, \    2.9290, \    2.9387, \    2.9468      Complex dy2[] = \    2.7381, \    3.0482, \    3.1636, \    3.2206, \    3.2558, \    3.2807, \    3.3006, \    3.3180, \    3.3319, \    3.3437, \    3.3535, \    3.3616      Complex dy3[] = \    2.6460, \    3.2668, \    3.5, \    3.6, \    3.66, \    3.71, \    3.75, \    3.78, \    3.8, \    3.81, \    3.82, \    3.83    const Complex d = shift[Order-1]    switch (Pattern) {    case 1: dx = d.x : dy = dy1[Order-1]    case 2: dx = d.x : dy = dy2[Order-1]    case 3: dx = 0   : dy = dy3[Order-1]  }  const Mobius m = Mobius.Multiply(Mobius(1, 0, -1i, 1), Mobius(1, Conj(d), 0, 1))  const Affine s[] = \    Affine(-1, 0, 0, -1, -d.x, d.y), \    Affine(1, 0, 0, 1, -1, 0), \    Affine(1, 0, 0, 1, 1, 0), \    Affine(1, 0, 0, 1, -dx, -dy)      const Complex pLine[] = 1, d.y-1 ' vertical position of 2 horizontal lines  const Complex indexLUT  const Complex count = 5 ' number of transformations  const Complex p[] = PatternWeight, PatternWeight, HorizontalWeight, HorizontalWeight, VerticalWeight, LineWeight, LineWeight  const Complex k[] = 0, 1, -1, -1, 2, -1, -1  Math.NormalizeWeights(p[], Array.Dim1(p[]))  Math.GenerateIndexLookupTable(p[], Array.Dim1(p[]), indexLUT[])  powerChain = 0  Debug.Print("Mobius Dragon IFS, Y coordinate of top/bottom lines: +/- {0}", 1-d.y/2)  iterate:    if (powerChain = 0) {    powerChain = IIf(Random.Number() < Weight, 0, Random.Integer(Power))    index = Math.GenerateIndex(indexLUT[])    idx = k[index]        if (idx >= 0) {      attractorIndex = idx    }  } else {    powerChain -= 1  }  z.y += d.y/2    if (index < count) {    if (index = 0) {      z = Mobius.TransformPoint(m, z)    } else {      z = Affine.TransformPoint(s[index-1], z)    }  } else {    z.y = pLine[index-count]    powerChain = 0  }  z.y -= d.y/2  properties:    divider {    caption = "General Options"  }  option Order {    type = IntegerEnum(1,12)    caption = "Order"    details = "Order of complexity of pattern"    default = 9  }  option Pattern {    type = IntegerEnum(1,3)    caption = "Pattern"    details = "Used to vary the pattern"    default = 1  }  divider {    caption = "Weights"  }  option PatternWeight {    type = Float    caption = "Pattern"    details = "Weight applied to pattern transform"    default = 1  }  option HorizontalWeight {    type = Float    caption = "Horiz Shift"    details = "Weight applied to horizonal shift"    default = 0.25  }  option VerticalWeight {    type = Float    caption = "Vertical Shift"    details = "Weight applied to vertical shift"    default = 0.12  }  option LineWeight {    type = Float    caption = "Line Weight"    details = "Weight applied to line generation"    default = 0.05  }  divider {    caption = "Power Options"  }  option Power {    type = Integer    caption = "Power"    details = "Maximum length of generator power chain"    default = 16    range = [1,32]  }  option Weight {    type = Float    caption = "Base Weight"    details = "Weight applied to base transformations (0-1)"    default = 0.98    range = [0,1]  } bib Global Moderator Fractal Senior      Posts: 2070 At the borders...  December 24, 2011, 01:28:13 AMI am curious to see how this one would turn out in 3D. What did you do to get these spirals if you started from this one? http://www.fractalforums.com/index.php?action=gallery;sa=view;id=2222 Ross Hilbert Fractal Phenom      Posts: 469   July 03, 2011, 07:31:43 PMThanks Erisian, Thanks Kam, Yeah when I first saw an example of this style, I was instantly hooked. kameelian Iterator Posts: 181  June 30, 2011, 06:17:45 PMI really like this one - and some of the derivatives you've done. It was one of the first ones that caught my eye (ifnot THE first) when I first came to this site.It has a kind of middle eastern watchmaker's feel to it for me.cheersKam Guest March 14, 2011, 11:25:24 PMTotally stunning! Ross Hilbert Fractal Phenom      Posts: 469   March 14, 2011, 06:37:24 PMThanks guys! Guest March 11, 2011, 08:01:53 PMYeah, awesoem... dainbramage Iterator Posts: 165  March 11, 2011, 07:57:58 PMAwesoem image Ross! 