Title: Secant method for cosine function Post by: HPDZ on February 02, 2009, 06:41:51 PM 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 (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 (http://www.fractalforums.com/gallery/0/359_02_02_09_9_24_48_2.jpg) SecantMethod2 (http://www.fractalforums.com/gallery/0/359_02_02_09_9_24_47_1.jpg) SecantMethod3 (http://www.fractalforums.com/gallery/0/359_02_02_09_9_24_46_0.jpg) SecantMethod4 (http://www.fractalforums.com/gallery/0/359_02_02_09_6_32_10.jpg) Title: Re: Secant method for cosine function Post by: cKleinhuis on February 03, 2009, 09:51:16 PM nice coder colors :D |