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Bivariate Newton Kaleidoscopemorbid fashion of self-devotion
Bivariate Newton Kaleidoscope
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Description: Bivariate Newton fractal with the kaleidoscope mapping, functions \( f(z_1) = z_1^3 - 1 \) and \( f(z_2) = z_2^3 - 1 \)
Code: [Select]
2DNewton3 {
init:
  z = @z10_fix+@z10_pix*pixel
  z1 = @z20_fix+@z20_pix*pixel
  i = sqrt(-1)
loop:
  f1 = z^3 - 1
  f2 = z1^3 - 1
  d1f1 = 3*z^2
  d2f1 = 0
  d1f2 = 0
  d2f2 = 3*z1^2
  zold = z
  zold1 = z1
  factor = (1 / ((d1f1*d2f2) - (d2f1*d1f2)))
  z = z - @relax * factor * (d2f2 * f1 + -d2f1 * f2)
  z1 = z1 - @relax * factor * (-d1f2 * f1 + d1f1 * f2)
bailout:
  |z - zold| >= @bailout || |z1 - zold1| >= @bailout
default:
  title = "2D Newton 3"
  helpfile = "Uf*.chm"
  helptopic = "Htmlformulasstandard
ewton.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  maxiter = 100
  center = (0, 0)
  param z10_fix
    caption = "z1_0, fixed factor"
    default = (0.0,0.0)
  endparam
  param z10_pix
    caption = "z1_0, pixel factor"
    default = (-1.0,0.0)
  endparam
  param z20_fix
    caption = "z2_0, fixed factor"
    default = (0.0,0.0)
  endparam
  param z20_pix
    caption = "z2_0, pixel factor"
    default = (1.0,0.0)
  endparam
  param bailout
    caption = "Bailout value"
    default = 0.00001
    min = 0
$IFDEF VER40
    exponential = true
$ENDIF
    hint = "This parameter defines how soon a convergent orbit bails out while
            iterating. Smaller values give more precise results but usually
            require more iterations."
  endparam

  param relax
    caption = "Relaxation"
    default = (1, 0)
    hint = "This can be used to slow down or speed up the convergence of
            the formula."
  endparam
}


Rendered with Ultra Fractal 6.03.
Stats:
Views: 57
Total Favorities: 0 View Who Favorited
Filesize: 617.57kB
Height: 1080 Width: 1920
Keywords: Newton multidimensional kaleidoscope 
Posted by: FractalAlex December 11, 2020, 03:46:04 PM

Rating: *** by 1 members.
Total Likes: 1

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