Nova Householder Mandelbrot
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Description: This is a Nova fractal, but instead of the typical Newton method or Halley method, it is based on the Householder method. Note here that due to its cubic (3rd) order of convergence, the minibrots are miniature Cubic Mandelbrot sets, just like Halley's method, instead of being quadratic (or 2nd order), in the case of the Newton or Schroder method. Rendered with ManpWIN 4.00e. This is the first in a series of new Nova fractals that I discovered a while ago.
Function: $f(z) = z^3 - 1$
Formula: $z_0 = 1, c = pixel,$
$z_{n+1} = z_n - (f(z_n)[2f'(z_n)^2 + f(z_n)f''(z_n)])/(2f'(z_n)^3) + c$
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Filesize: 360.74kB
Height: 649 Width: 1349
Keywords: householder nova mandelbrot
Posted by: FractalAlex May 20, 2020, 06:38:16 PM

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