Recommended books or other sources for fractal geometry algorithms

[jmacclure]

Hello all -
I am new to this forum, although I have been reading for some time and am amazed at the expertise this community has with respect to fractal geometry. I have a math background, am a proficient programmer, and am determined to dive into dynamic fractal generation. Are there any recommended books or other sources (papers, online sources) that any of you use as a reference or learning tool? Yes I know how to use Google, I am interested in your expert opinions.

[cKleinhuis]

hello and welcome to the forums,

what i liked very much, and in my eyes is somehow the new century/decade/millenim fractal techniques, in my own viewing it is from
the late 90's, or beginning of 2000's, the document describing "flame fractals", this is a very good starter for experienced programmers,
because results are quite cool check this one:
http://flam3.com/flame.pdf

second i can recomend the "chaos" book by james gleick as a perfect reading for introduction of chaos theory in general, from mid 80's but holds still true ,
http://www.amazon.de/CHAOS-Making-Science-James-Gleick/dp/0749386061/ref=sr_1_3?ie=UTF8&qid=1291931825&sr=8-3

[jmacclure]

hello and welcome to the forums,

what i liked very much, and in my eyes is somehow the new century/decade/millenim fractal techniques, in my own viewing it is from
the late 90's, or beginning of 2000's, the document describing "flame fractals", this is a very good starter for experienced programmers,
because results are quite cool check this one:
http://flam3.com/flame.pdf

second i can recomend the "chaos" book by james gleick as a perfect reading for introduction of chaos theory in general, from mid 80's but holds still true ,
http://www.amazon.de/CHAOS-Making-Science-James-Gleick/dp/0749386061/ref=sr_1_3?ie=UTF8&qid=1291931825&sr=8-3

thanks for the reply. i should have noted i am already familiar with fractal geometry, i have read mandelbrot's book as well as some of his papers. i am more interested in algorithms implementing the math. i recently ordered Fractal Programming in C, an older book from 1989.

[Tglad]

I think the main block to anyone trying to render their own 3d fractals is getting an approximate distance function (getDistanceToNearestPointInFractal(pos)), once you have this you can take steps down each ray (each pixel on the image) and reduce the step size as you get closer to the fractal, until you find the point within the minimum radius of your choosing.
The distance function is a little tricky, and there are a few threads in this forum about approximating it for different formulas. Maybe someone else can give a summary or link to them.

Good luck!

[lkmitch]

The Ultra Fractal formula database is a tremendous collection of formulas implementing various fractal types and coloring methods.  The formulas are written for Ultra Fractal, but may be sufficiently general for translation to your favorite platform.

http://formulas.ultrafractal.com/

[Adam Majewski]

http://en.wikibooks.org/wiki/Fractals