Not New To Fractals, But New To Fractal Mathematics

[o0megaZer0o]

So I am pretty familiar with several different fractal programs including Mandelbulber, Xenodream, and Mandelbulb3D. I understand that an algorithm runs through a loop infinite amounts of times creating the iterations (or you can set a cap for how many times the equation runs through the loop). Besides that, everything else about fractal mathematics I am pretty much stumped. I am used to adjusting knobs, having absolutely no idea what they do, and waiting for my brain to get tickled by the next result. Trial and error are the only ways I know how to use these programs until my artist mind seems something pretty that it likes.
I am aware that fractal mathematics is a a very broad topic, but if someone can point me in the right direction so I can learn what important algorithmic symbols mean, I would greatly appreciate it.

Does any experienced fractal programmer, script writer, or mathematician have any inspiring stories of how they got into this? Everyone had to start somewhere and we are all n00bs when we start something new.

I will also accept a quick link that will head me toward the right direction.

Thank You!

[o0megaZer0o]

Wiki helps only sometimes for understanding what the basis of certain definitions mean, but wiki is notorious for busting out like 4 lines of code when describing some things and all that is currently beyond me. It's the code that I want to understand. Like what is the proper name for the code? Are they algorithms?

[o0megaZer0o]

Lastly I would like to add that I am an artist and have never been a mathematician, but as Einstein said:

"People should be ashamed to use the wonders
of science and technology if they don’t
know any more about it than a cow
knows about the botany of the
grass it relishes in eating."

Hence my reason's for wanting to learn the math behind fractals

[David Makin]

Very basic information can be found on my site, on the homepage here:

http://www.fractalgallery.co.uk/#anchor1

And more in my "blog":

http://www.fractalgallery.co.uk/cantor-set.html
http://www.fractalgallery.co.uk/peano-curve.html
http://www.fractalgallery.co.uk/orbits.html

One of the keys to visualising fractals is how the software/programming/algorithms identify the attractors of a particular fractal i.e. the attractors as in the section above on "Orbits and Attractors".
The standard Mandelbrot and Julia Sets and other related fractals are generally visualised by simply identifying where the attractor is tending to infinity (diverging) and where it isn't - in fractal software parlance with respect to normal escape-time fractals the diverging areas are normally said to be "outside" the set and the rest is "inside".

For more on fractals I'd recommend the following....

http://library.thinkquest.org/26242/full/index.html
http://classes.yale.edu/Fractals/

For learning how to do the math relating to the commonest complex number escape-time fractals then I'd recommend the Fractint help-file - the section on how to do complex arithmetic (entitled "Trig identities"):

http://www.nahee.com/spanky/www/fractint/append_a_misc.html

[o0megaZer0o]

Hey thanks a lot David! I greatly appreciate it

[GKStill]

Hi,

New to this forum - so sorry for adding to an old thread. My story was published by Ian Stewart in "Disovery" (USA Science Magazine). The fractal work came from watching a cobweb while paralysed from the waist down (I got better!).

http://www.xenofractals.com/Cobweb.html

'I know who you are.' Jack Cohen, an avid science fiction fan and freelance alien designer, has just been introduced to my new research student. 'You're Hari Seldon.'

Jack is referring to Isaac Asimov' s science fiction series Foundation, in which Seldon was the genius behind 'psychohistory' - a mathematical scheme for predicting the behaviour of large groups of people. But Seldon was frail, bald, and walked with a limp, whereas G. Keith Still is solidly-built biker and vigorous with short dark hair. Nevertheless, Jack has a point, for Keith shares Seldon's fascination with the mathematics of 'the human conglomerate'. And his own entirely factual scientific brainchild is Legion, a method for predicting crowd movements which would have turned Hari Seldon's bright blue eyes green with envy.

Happy to talk to mathematicians/programmers on how to develop more with these fractal patterns. Been 18 years since I last played with them.

Keith
www.XenoFractals.com