Newton Fractal Dynamics

Status

Width: Height:

Roots:
Iterations: Min x: Max x: Min y: Max y:
Colour Centre x: Colour Centre y: Click to Set: Hue is Magnitude: Magnitude Shading: Magnitude Saturation: Hue Rotation: Iteration Time (ms):

An adaptation of Mandyn to the problem of Newton Fractals, largely inspired by this page about it. As with Mandyn, the idea is to watch the fractal grow iteration by iteration, representing the value at each point using colour.

This particular fractal uses the Newton-Raphson method to find roots of a complex polynomial, which for convenience is (z-c₀)(z-c₁)... - the idea is that c₀ are the roots of that polynomial. The "Roots" variable above represents the values of c₀ as an array of arrays, where each inner array contains the real and imaginary part of c_n. So [[0,1],[1,0],[0,-1],[-1,0]] represents the polynomial (z-i)(z-1)(z+i)(z+1). The value of Roots is sent to eval, so you can include javascript code there to generate your roots for you if you want.

Thanks go to Simon Tatham for introducing me to these fractals.

Peter Corbett, 2014

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