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Fractal Math, Chaos Theory & Research => General Discussion => Topic started by: lapinot on December 13, 2016, 08:38:38 PM

Title: Running derivative
Post by: lapinot on December 13, 2016, 08:38:38 PM

Can someone explain to me what a 'running derivative' refers to ?

How is it different from simply a 'derivative'.

Does it have anything to do with Taylor/McLaurin series i.e. linear approximation to a function through derivatives ?

Thanks! O0

Title: Re: Running derivative
Post by: quaz0r on December 14, 2016, 01:53:28 AM

maybe one of the resident math professors has more to say about it but i think running derivative just means a derivative that is iterated

Title: Re: Running derivative
Post by: claude on December 14, 2016, 06:06:19 PM

I think it just means that you calculate the derivative while you iterate, something like this Mandelbrot loop for example:

Code:

dzdc = 0;
z = 0;
n = 0;
while (|z| < 25 and n < 1000) {
  dzdc = 2 * z * dzdc + 1;
  z = z * z + c;
  n = n + 1;
}
de = 2 * |z| * log |z| / |dzdc|;

Title: Re: Running derivative
Post by: DarkBeam on December 14, 2016, 07:54:53 PM

Exactly- it helps in raytracing programs, or using a "smooth" coloring of the outside of the fractal etc :beer: