I’ve been very low on free time recently, so I’ve been goofing around with fractals. I’ve never really payed attention to them before and it’s doable in very small time slices.
http://glsl.heroku.com/e#9994.2
http://glsl.heroku.com/e#9903.1
http://glsl.heroku.com/e#9904.1
http://glsl.heroku.com/e#9915.1
http://glsl.heroku.com/e#9916.2
http://glsl.heroku.com/e#9971.0
Set the sampling down to .5. You can pan & zoom with the mouse.
These are trippy as hell! I really need to learn how fractals work one day.
I don’t know if I’m learning anything…but it’s kinda fun.
My eyes… blacks out
I’ve done something like this, but on a much simpler scale. It was just a player, in my game, but I mixed up with and x, and started messing around with is. What I got was a crazy looking person who got fatter and fatter as he moved to the right. But that is nothing compared to what this is. Bravo! I love how you can edit code as well!
More goofing around: http://glsl.heroku.com/e#10873.3
(EDIT: The above won’t compile for me in chrome, but works fine in Firefox…go figure).
and some stills: http://roquendm.deviantart.com/gallery/
Funny that, me too (Julia sets; f(z) = z^2 + c through to f(z) = z^5 + c and so forth). I’ve been working on making a Android live-wallpaper out of them. Although I think your representation of them is far, far ahead of mine. The colour schemes look beautiful and almost other-worldly. In fact, I’ll delve deeply into your code over the next few days and try to work out how you’ve done it.
Well done, it’s very impressive.
The coloring scheme is by IQ. Mostly I’ve been screwing around with domain deformations. So for a julia or m-set style fractal:
c = T(s)
where ‘c’ is the standard additive (translation) term, ‘s’ is the sampling point and T(s) is a change of domain function…aka the standard is T(s)=s.
So that in that last link, the T(s) code is after the comment “perform the domain mapping”. You can use about any analytic function here.
I have some domain plot of some functions here: http://s824.photobucket.com/user/RoquenDM/library/DomainPlots?sort=9&page=1.
Cheers muchly Roquen. After reading your post, code and IQ’s website I realised I was only scratching the surface of fractals & their representation. Been goofing around myself the past week and have had some good results; although still have plenty of more goofing around to do before I produce anything fancy.
Nice! @Roquen.
Used to delve into these things when democoding was big.
www.rel.phatcode.net/junk.php?id=34
The orbit algo to do the rings was from an article I found that applies the same coloring to the mandelbrot. I just applied it to my julia animator out of curiosity and was surprised it looked fantastic.
Strange attractors are fun too.
The animation works by changing the parameters of the equation and not all combinations of parameters result in chaos, so be patient 
It uses Processing.js and the source is in the html file.
Oh yes. There are tons of interesting structures, both visually and mathematically.
Here’s another: http://www.josleys.com/show_gallery.php?galid=346
and the math is here (google translate does okay, but the equations get borked):
http://images.math.cnrs.fr/Les-ensembles-limites-de-groupes.html
It looks very interesting.
Only 4 million pixels and an infinite precision image! The anti aliasing! It does nothing!