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Fractal Art => Images Showcase (Rate My Fractal) => Topic started by: HPDZ on February 02, 2009, 06:41:51 PM




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