This is a sample of applying the secant method to the cosine function cos(z)=0.

A few more images are at http://www.hpdz.net/StillImages_Convergent.htm

This operation turns out to give images with a surprising amount of variation with size and location, unlike Newton's method with its rigid self-similarity.

I think my next large animation will be a tour of this thing. I can't zoom very deeply into it right now because I don't have high-precision floating-point math in my software yet. I have been holding off on extending my bignum fixed-point functions to floating point (fixed point is adequate for divergent fractals and iterated maps that never cause a division by a small number). This may be the thing that gives me the incentive to do it....

SecantMethod1


SecantMethod2


SecantMethod3


SecantMethod4