There is a great set of renderings, high-rez, on Wikipedia.
Also, Bert has just found an interesting attempt at rendering it in three dimensions. Very cool.
This one is awesome in full size:
(The site/author sells it in high-rez render poster.)
Tommy asked:
OK, for the rest of us uninformed low-lifes, could you please explain what this is..
Woa, that's a tall order. It's a whole science. I recommend Wikipedia for the lowdown.
But it's the study of finding order in apparent chaos. It turns out that many apparently chaotic things, like many shapes in nature, can be repeated by pretty simple mathematical formulas, you take two numbers in reiterative calculation (you take the result and put it into the formula again, and if it at length approaches zero, you color the node in the two-dimensional grid black, and if it approaches infinity, you color it white). You will find shapes like leaves and snow flakes and so on.
(What I get from this is that maybe god or nature uses a big computer to make the immense detail in nature.)
One of the characteristics of these drawings is that they are infinitely detailed. But also that you tend to see repetition of shapes at various scales.
The Mandelbrot Set is one of the most famous of the graphics generated this way, and so far as I recall, from one of the simplest formulas.
Regular two-dimensional fractals are very fascinating, but this thing here is... a mathgasm!
ReplyDeleteEO "If you followed your stuff in the eighties, you'll have an idea of Chaos theory, and know the Mandelbrot Set."
ReplyDeleteOK, for the rest of us uninformed low-lifes, could you please explain what this is..
See update to post.
ReplyDeleteVERY COOL the 3D's!! And THANKS for 'splainin' fer us "low-lifes"! (Thanks fer defining fer me what I couldn't put my finder on, Tommy! And...this one's for YOU!! "LOL!!!!!" ;-)
ReplyDeleteThat first one brings back memories.
ReplyDeleteI can remember loading the program into my BBC Micro (early '80's) and then leaving it overnight to run through the maths and draw it in screen. Shame that there was no way to save them - not that i can remember.
Can't also remember whether i had to type the program in from a magazine or load it from cassette tape or 5.25" floppy
Those were the days
I'm not trying to induce envy or anything, but these graphics (not the least the 2D ones) look totally amazing on a 30-inch monitor. Wow.
ReplyDeleteWikipedia says: "The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and for being a complicated structure arising from a simple definition."
ReplyDeleteBut that's by far not enough. In the update it's explained a bit more. It's about gaining insight into the cyclic structure of nature, created by endlessly iterating the same quite simple algorithms, growing/flowering into more and more complexity. A big paradoxon. Maybe also a simple example of the Ouroboros symbol - life feeding itself on life.
If somebody wants to play with the classic "chaos images", you may download WinCIG (Windows Chaos Image Generator) from www.hoevel.de/e_wincig.htm - it's a pretty old freeware program, but still nice to play with it. Very simple to use (sorry, only for Windows), no need for mathematical skills.
BTW: In the Greek mythology "chaos" is not in any way meant in a negative way (as often understood today), it is simply the "pool of all but not yet formed structures", similar to the "virtual ocean of particles" in quantum mechanics.
The development into 3D in the field of fractals was new for me - amazing pictures! Thanks for sharing.
Yeah, like the guy says on the site, it's only in recent years that we've had the computer power for it.
ReplyDelete"maybe god or nature uses a big computer to make the immense detail in nature"
ReplyDeleteI'd think of it more like the processes of nature are a form of computer. It's like an massive automaton forging ahead as reality. We haven't noticed anyone stepping in to alter it or tweak the computer from time to time. And I don't want to be around when it's rebooted. If it is, will we all live again the same way as part of the program?
EO "look totally amazing on a 30-inch monitor. Wow."
ReplyDeleteShow off....
After reading this, I'm gong to have to do a little studying. I'm not sure if there is any practicle use for this, but it is very interesting.
Practical use I don't know, but I feel it has helped me understand the universe and life better. There are many things in life which echo the principles of fractals.
ReplyDeleteThere are many things in life which echo the principles of fractals.
ReplyDeleteYes. For example the old principle "as above so below". But others, too.
Practical use
Getting better understanding of life IS of course a practical use.
But I have also heard, that it was used to generate naturally looking landscapes in computer simulations needing relatively small computer power. Maybe no more, because computer power has increased very much.
I'm sure it's still used, it's a very powerful way of getting tons of detail fast.
ReplyDeleteI believe it's also used in some compression methods. Not sure how but I remember someone saying wavelet compression was fractal based. And also in texturing to create more believable graphics. There used to be a program called WinFrac (or, well, something like that) I used to explore them. I found them fun but after a while they start to look more or less the same.
ReplyDelete