I hate to sound like a dumbass, too late, but what is a fractal. I've seen some of the images and the gallery and was wondering what exactly is the technical definition of a fractal?

You don't see only fractals in the fractal gallery. There are images created with fractal generators, but they do not need to be fractals at all :-)

heheheh didn't answer the question though ;) we used to have a screensaver on the old mac that did fractals. it'd make a symmetrical shape, then zoom in on it, refine and antialias it, then zoom in more, and more and more and it went forever was pretty cool heheh

Attached Link: http://www.ultrafractal.com/

Hmmm??? Well first of all RobWolf...Welcome to the Fractal Page...I would like to complement you on your work???It looks awesome!!!I only wish that I spent as much time on my stuff... A Fractal is a math formula...This math formula can be Algebra,Calculus,ect...This math formula is computed as many times as the user(me)would like for it to compute?If I wonted the computer to calculate my fractal 1000 times, I would enter into a fractal program's ((itterations box)) to calculate my math formula 1000 times.. This would give me a computed JPG that I could work on in other programs..Paint shop pro..ect..I would then come up with a finished Render &/or print for my Renderosity gallery.. Here are some links of software companies that have Fractal Software packages available.Free & Trial... http://www.fractalus.com/ Below is the link to Ultra Fractal & here is the Library link; http://formulas.ultrafractal.com/ Let us know what turns up...

Hmmm... you can recalculate a formula 1000 times but you'll get the same answer 1000 times. The key is that this formula is reiterated, meaning that the result of the formula calculation is input back into itself and the formula recalculated. This can be done as often as wished. The answers derived from these calculations are used to plot the fractal image which is essentially nothing more than a graph, albeit often a very beautiful graph. The fractal formula is often exceedingly simple yet can be the source of extremely complex imagery. These patterns are without limit so can be enlarged endlessly, each enlargement showing more and more detail. Fractals show similar detail at various enlargements, referred to as fractal scaling. Many fractals are also self-similar. As you dive into (enlarge) a fractal image the pattern may disappear only to reappear in various guises as you continue to dive. The degree and frequency of self-similarity may vary from formula to formula. The foregoing is extremely simplistic. Mandelbrot, discoverer of the formula bearing his name, defined fractals in terms of the mathematics used to calculate fractal dimensions. He later expressed regret for having done so, preferring to leave the definition of fractal open. Curiously, within the context of fractals as art what we call a "fractal" is not the actual fractal. Rather, it is a visual representation of the effects of the fractal on surrounding geometric space and determined by how the artist has chosen to colour such effects. - Jack

whoaaaa, alright, i think that's a good enough definition heheh so you can enter actual mathematical formulas and have it calculate fractals out of them?

Attached Link: http://fractals.iuta.u-bordeaux.fr/f-art-faq/

Fractal Art FAQ: http://fractals.iuta.u-bordeaux.fr/f-art-faq/

A fractal isn't a re-iterated formula at all... A fractal is a geometrical shape with scale-invariant self-similarity, a "broken" dimension - hence the name fractal. You can create some of the fractals be re-iterating something, a formula, a graphic process, ...
But the definition of a fractal can be found in Mandelbrot's books for example...

WOAH!!!!!! Ok, so some of you say that my precalc homework would graph with fractals, and others say that I need a special program to create them with formulas. Still others say its just an image with a broken dimension. Is it all of these?!?!

A fractal isn't a re-iterated formula at all... Correct. A slightly better definition would be that a fractal is a geometric object possesssing a regular or uneven shape, repeated over infinite measurement scales and that also has a fractal dimension greater than its spatial dimension. But Renderosity is an artists' forum and I choose to present a usable definition within that context. Programs such as Bryce and MojoWorld make intensive use of fractals. But art created from such programs is not what the "man in the street" commonly envisions when thinking of fractal art. Instead, assuming they are even aware of fractals, they are more likely to recall the abstract imagery so often reminiscent of the 60s era. As reiteration is a fairly significant component in creating such fractal imagery I generally include it when discussing fractals as art. As noted, this "artistic" fractal isn't even the fractal thus further compromising the definition of fractal from an artist's viewpoint. As abmlober says, Mandelbrot defines the fractal in his seminal book The Fractal Geometry of Nature, 1977. But in a subsequent edition he regrets this attempt and writes "... for me, the most important instrument of thought is the eye. It sees similarities before a formula has been created to identify them." If one desires a full definition of "fractal" one might ask Doc Mojo, who frequently inhabits the MojoWorld gallery. He undoubtably knows more about fractals then anyone else here and worked quite closely with Mandelbrot. Indeed, I believe M referred to him as the "first true fractal artist." Significantly, the beauty of "fractal art" is that the fractal artist need not know anything about fractal mathematics to pursue the form. While such knowledge may lend a further level of appreciation I rather doubt that it will in itself engender superior "art". Personally, I find this quite comforting. Although I majored in math, my adult years have found little need for anything beyond subtraction, addition, multiplication and division. Regrettably, I have long ago forgotten almost all the rest. It has been years since I've experimented with fractal imagery but as proof that mathematical knowledge is not essential I offer our old gallery at: http://www.fractalus.com/jack/ (ps. Margaret knows even less about the math than I yet I far prefer her efforts.) - Jack

...so some of you say that my precalc homework would graph with fractals... No, at least I hope I did not say that. While the classic artistic fractal image is effectively a graph not all graphs are fractals. (or did I misunderstand the question?) ...others say that I need a special program to create them with formulas. I suppose that one could plot a fractal image using an abacus, graph paper and coloured pencils but it would be tedious at best. Depending upon the reiteration level this could take a significant portion of one's life. A specialized program and attendant computer is what makes fractal art a practical endeavour for mere mortals. - Jack

I think im beginning to understand you strange mortals. What I meant by that precalc thing is that I have recently run into interations within my homework. I can understand the math part. However, you could make a fractured geometric shape and call it a fractal? Is that what some of you are trying to tell me? I'm not half as confused as I was but I'm still alittle lost. I have the map, now where's that compass?

...you could make a fractured geometric shape and call it a fractal? Perhaps... if it exhibits self-similarity regardless of scaling and has a fractal dimension greater than its spatial dimension (the famous "what is the length of England's coastline?" question.) Entire books have been written exploring the meaning of "fractal" so do not become disillusioned if you fail to find a simple answer here. If you want anything more than a simplistic answer you will probably have to spend some serious time with these books. There are also numerous fractal oriented websites although the majority of them tend to be image galleries. Judicious use of a search engine will probably find some sites that do a good job of answering your questions. A reasonable place to start is: http://www.fractalus.com/info/layman.htm - Jack ps Fractals are chaotic and you can see fractals in the real world daily. These patterns (mountains, trees, etc) are the evidence of the dynamic activity that gives rise to fractals- an activity where objects interact and feed back into themselves and each other. I'm honestly not sure if the shape is the fractal or merely the visible manifestation of the chaotic process. For example: a human footprint in the sand is evidence of the human's passing but it is not the human itself.

"Significantly, the beauty of "fractal art" is that the fractal artist need not know anything about fractal mathematics to pursue the form. While such knowledge may lend a further level of appreciation I rather doubt that it will in itself engender superior "art". "

Perfect.

Ok. I've started one of these big, "Is poser a real tool?" kind of arguments. Hehe... I guess I get it. Map, compass, ah here I am. Wait a tick, wheres that protracter for my back asimuth. Still lost, I'm somewhere on this map and looking north. I think I understand the principles behind a fractal now, but what makes a fractal other than a mathamatical formula, an iterated piece of art, or something that just looks kool and can't be described as anything other than a fractal? BTW, thanks for the links fractals are kool looking. Did I stumble upon something, trip over that protractor maybe. I dunno. Help!?! Send a GPS!

I understand these things now, thanks for all the help you guys. Great art! Now if any of you know 3DS Max, head over to that forum and read PYRO! I could use a little help there.

A fractal is an object or quantity which displays self-similarity, in a loosley technical sense, on all scales. The object does not need to exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. Note that self-similarity means that the object looks "roughly" the same on any scale.

AHA! Thats a pretty simple answer. Is that it?