Fractals From Newton Method

Generalized Newton, by Myriam Mahiques

Newton's method, also called the Newton-Raphson or Newton iteration method, is a root finding algorithm of a real function. It can be used to find the minimum and maximum of a function.

Isaac Newton discovered what we now call Newton's method around 1670. Although Newton's method is an old application of calculus, it was discovered relatively recently that extending it to the complex plane the result is a boundary set, a very interesting fractal pattern.

My interest in this type of fractal is its analogy with urban morphogenesis with a center and radial avenues. It can be applied to urban morphology simulation exercises.

All images generated by Myriam Mahiques.

REFERENCES
http://www.chiark.greenend.org.uk/~sgtatham/newton/

http://facstaff.unca.edu/mcmcclur/mathematicaGraphics/Newton/index.html