Bairstow beanstalksSchroder fractal with a 4th power MinibrotNova Householder Mandelbrot
Schroder fractal with a 4th power Minibrot
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Description: This fractal, the Schroder fractal, uses the Schroder method to calculate the roots. This variation contains Minibrots, but these are raised to the 4th order, although the method itself has a quadratic convergence. The formula is similar to Halley's method, minus the 2's on the formula, aside from the 2's on the exponents of the powers of the derivatives and function.

The code:
Code: [Select]

MandSchroder1 {
  z = p1
  c = pixel:
  z2=z*z
  z3 = z*z2
  fz = ((z*z*z*z) + (c-1) * z - c)
  dz = (4*(z*z*z) + c - 1)
  dz2 = 12*z*z
  f1 = fz*dz
  f2 = (dz^2)-fz*dz2
  oz = z
  z = z - (f1/f2)
  |oz-z|>10^(-10)
  }

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Views: 21
Total Favorities: 0 View Who Favorited
Filesize: 544.61kB
Height: 649 Width: 1349
Keywords: schroder multibrot minibrot 
Posted by: FractalAlex May 21, 2020, 12:24:12 AM

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

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