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Hi, I was just thinking about using a parabola-type version of the Newton iteration when I read about the Irrational Halley formula. Does anyone know some code for it? I can't seem to find any or right any functional code myself... 

Anyway, I was thinking about doing something even further with a cubic or quartic polynomial (quintic don't have a closed form solution) fit to the given function. That is, to solve for example Y=i*X^7-(2+i)*X^3-6*X^2-i , we'd fit a quartic polynomial to any point z, with the height and the first four derivatives equal, and then use the "quartic" formula to find the roots of this polynomial. I'm hopeful this could produce some interesting results - probably somewhat like the Newton fractal. Help is appreciated!