 • May 06, 2021, 06:46:11 AM

Bivariate Newton Kaleidoscope Next Image
Description: Bivariate Newton fractal with the kaleidoscope mapping, functions $$f(z_1) = z_1^3 - 1$$ and $$f(z_2) = z_2^3 - 1$$
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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| >= @bailoutdefault:  title = "2D Newton 3"  helpfile = "Uf*.chm"  helptopic = "Htmlformulasstandardewton.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.
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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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