09/05/2026
New Movie at YouTube: mixing it up
https://www.youtube.com/watch?v=Fc0XUnzWJIg
Mostly Cubic, Quartic, Pentic and Hexic symmetrical Mandelbrot bezier Julias with 3d Elliptical between...
I was looking for a Julia Mandelbrot "Longbrot" and found one.
The Julia movies I did this morning at about 2 Am...
as the spirit moved me, LOL.
Recent fractal Jazz music.
The Mandelbrot Julias started with the cubic and the Fiegenbaum reverse,
and I found an polynomial inverse trick to use with the beziers.
Cubic polynomials:
p[z_] = 1/3 (2 - z + z^2 + z^3)
q[z_]=1/3 (-2. - 1. z - 1. z^2 + z^3)
Quartic polynomials:
p[z_]=1/12 (2 + z) (-1 + 4 z) (1 + (-1 + z) z)
q[z]=1/3 (-0.5 - 2.25 z - 1.25 z^2 - 0.75 z^3 + z^4)
Pentic polynomials:
p[z_]=1/48 (2 + z) (-1 + 4 z) (3 + 4 z) (1 + (-1 + z) z)
q[z_]=1/3 (0.375 + 1.1875 z - 1.3125 z^2 - 0.6875 z^3 - 1.5 z^4 + z^5)
Hexic polynomials:
p[z_]=1/2 (-0.46875 + z (1.10938 + z (2.82812 + z (0.453125 + z (1.1875 + z (2.75 + z))))))
q[z_]=1/2 (-0.46875 - 1.10938 z + 2.82812 z^2 - 0.453125 z^3 + 1.1875 z^4 - 2.75 z^5 + z^6)
By mistake I used the Cubic Inverse on them all:(z^3 instead of z^n)
pi[z_]=z^3*p[1/z]
qi[z_]=z^3[q[1/z]
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