PaulWay got me into messing with fractal software again. Grr.

I used to play with Fractint a lot in the old days. But I want more than what Fractint could offer. What I want is a windows program which does:

- Anti-aliasing, like in Fractal eXtreme.

- 24-bit high color, and can cycle those colors, like in Ultra Fractal.

In fact, Ultra Fractal seems to kick ass all over Fractal eXtreme (including having photoshop-style features like transparency and layers), it just doesn't seem to have the antialiasing option.

Fractint will do high color in its latest incarnation (20), but that version hasn't been ported to WinFract yet. And the VESA modes don't work in a DOS window for me, even when I load the DOS VESA drivers in that session.

Anyone got any better fractal software? Actually, it's hard to imagine something better than Ultra Fractal after seeing it...

Never mind, found Anti-Aliasing in the Ultra Fractal Help file.

If you guys haven't seen this one, check it out. Pretty nifty. Look at the gallery at their web page...

I don't get fractals. They're pretty enough, but it's not like they're great art or anything.

Please explain.

Or did your pot dealer just get out of jail?

They're pretty enough, but it's not like they're great art or anything.

I don't consider them art, either. But they are pretty, fun to explore, and fun to play with. That's the only attraction. Nothing more complicated than that.

Stop bogarting and pass it to me Tony!

-Zeke

OMG, fractals are the coolest thing! It's not that they are pretty or art, but that they can be so incredibly complex but so incredibly simple. The Mandelbrot set is probably the grandaddy of them all, and can be represented with just ONE equation.

zn = (zn - 1)^2 + c

(It's hard to represent that in here, but basically reads z (sub n) = (z(sub n-1))^2 + c)

What this means, is take a number, square it, then add the original number to the result.
Then take that result, square it, then add the original number to the result.
Then take that result, square it, then add... you get the point.

You can see that if you started with the number 2, it would approach infinity very fast. The progression would be:

2, 6, 38, 1446, 2090918

But if you started with .25, it would eventually get to a point of stasis, somewhere around .36 or so. This number never "escapes" to infinity, but stays around a certain result.

Now apply the same calculation on imaginary numbers like 1 + 1i. Make the real part of the number the x-axis of a graph, and the imaginary part of the number the y axis of a graph. Now calculate points at regular intervals, and display them as pixels on a screen. If the number never escapes to infinity, then paint that pixel black. If the number does escape to infinity, then paint it a color depending on how fast that number escapes to infinity (how many iterations did it take to get beyond a certain limit, like 1000?). You will get the Mandelbrot set!



Explore the Mandelbrot set on this webpage (where the above image comes from)

Here is a paper I did on this topic in college for a writing class. Fractals may become more useful as we begin to understand what they mean.

I'm not saying that fractals aren't mathematically (potentially) useful and interesting, but just playing with a fractal program for more than 5 minutes seems to me like a waste. Maybe my brain doesn't grasp the images in the way yours and Tony's do.

OTOH, they are pretty to look at as a screensaver, I suppose.

Edit: I'm being a jerk. Because they're pretty or they're cool is, of course, a perfectly good reason. Not that you need a reason. It's just that so many people seem so interested beyond what I can rationalize that I sometimes feel like I'm missing something obvious.

Whilst I rarely spend much time playing with them (since I first found them way back when I were a lad, anyway), I quite like writing them, since they're a) pretty and b) simple!

Give me a new language to play with and it's probably the first thing I'll write - it was certainly my first exposure to both VB (back in the 16-bit v4 days), C++ and (most recently) C#. It's something that can combine a simple UI, lots of (recursive) maths, screen painting, saving as graphics files, and so on; it can give you quite a nice overview of a language.

That's why I like them, anyway. And did I mention that they're nice to look at?

Bryan.

I read that "Chaos" book back in college during a very slow summer of working security. As an artist with a passing interest in math and computers I found it a very interesting read. If you haven't, and are really curious about why people are facinated by them you should give it a try.

After the book detailed the math side of fractals to me, it made them all the more interesting. The book also explores some of the politics involved around the "discovery" of them...

What makes chaos theory and fractals interesting (beyond the art) is that they have an interesting phenomenon - a basic equation can have very complex results. And that mimics much of nature.
Anyone studying trees for instance, cannot fail to recognise that, despite every tree being different, every tree within the species follows the same rules for it's 'random' growth.
Another example - a pile of sand. Everyone knows that if you put one grain of sand on top of another, it is likely to fall off. But if you add more grains, eventually a pile starts to form, ie, the grains are not falling off. And then when you have a nice large pile something strange starts to happen. One grain might sit on top, or it might slide completely down the side and end up on the floor. Or, it might start a chain reaction, an avalanche.

Now both of these systems are starting with a fairly simple set of known rules. Trees grow to follow the sun. They bud offshoots with an alarming regularity. Gravity makes things fall. Friction can stop them. Given these rules, why don't all trees of the same species grow identically, or all sand piles avalanche at the same height?

It has been shown that both of these examples can be modelled with fairly simple equations, and such equations are basically what comprise chaos theory. Fractals are used in computer graphics to draw trees, plants, coastlines etc.

I've always thought they were pretty cool looking. A friend of mine, about 5 years ago, was using two programs. This was one of them. I'm sure it's not as good as the one you're talking about, Tony, but it's just fun to look aroung these things. The other program was DOS based, and the fractals didn't look as good and crisp, but it was much more visual. The fractals would rotate, zoom, and change colors. It made for a cool thing to project at dances

That Xaos program has the coolest zooming system I've ever seen. It's FAST at the calculations, too. Very impressive!

Doesn't seem to have anti-aliasing, though.

Well, there's a thing under "filters" for it, but I don't know if it works. What is it supposed to do?

Those filters are kinda fun, too. It's kinda neat to see the Mandelbrot set in emboss or "3D"

Well, there's a thing under "filters" for it, but I don't know if it works. What is it supposed to do?

That's a post-processing filter, it doesn't really do true antialiasing. All it does is blur the image after it's been calculated. A true antialiasing system renders a given pixel multiple times with different position offsets, and averages those renders. It doesn't simply smear the image.

The best example of true real-time fractal antialiasing can be seen in Fractal eXtreme. It works well in Ultra Fractal, too, but since that program only does it for disk-renders, you can't easily see it as an A/B comparison. So if you really want to see what AA does, load up the demo of Fractal eXtreme.

I gotta tell you. Making those movies n fractal eXtreme kicks butt.

I gotta tell you. Making those movies n fractal eXtreme kicks butt.

What amazes me, is that that Xaos program will zoom in as you hold your mouse button down, in real time, almost as fast as Fractal Extreme can play back a fully pre-rendered movie. Open Xaos and try it, just click and hold, and watch how fast it goes. I dunno how they do it. Rather impressive.

It IS cool, but if you'll notice, it cheats, drawing only about a quarter of the screen per frame, then leapfrogging to the next quadrant. Intelligent, but it makes it jiggle. It also used pixel doubling when zooming, since you can't see the difference anyway when it's moving. Still, all in all a cool effect.

And example of the eXtreme movie here

fixed link

You can also adjust the zoom speed. Its default is 1.

OK, I haven't had much experience with Ultra Fractal since it was in version 1, so I'll look at it tonight when I get home and get off my SparcStation 5 workstation. They may have improved the speed and the zoom capabilities since then.

Since Fractal eXtreme development hasn't moved in the last three years or so, I think Ultra Fractal is probably the way of the future, though...

I have a fair few Fractal eXtreme movies; I'll upload them onto my d0gz.net server and make a page for them sometime soon.

Have fun,

Paul

OK, I haven't had much experience with Ultra Fractal since it was in version 1, so I'll look at it tonight

I checked out both 2.5 and 3.01, and there were significant changes and improvements between those two versions, so I imagine that going from 1->3 you'd notice a huge improvement.

The part about fractals that I think is cool is that not only does the simple equation yield complexity, but the complexity is both infinitely varied and repetitive at the same time. If you look at that picture of the Mandlebrot set and then go zooming down into "seahorse valley" between the two big circular portions, as you zoom and zoom, you will eventually find a thing that looks (almost) exactly like the original set -- with its own seahorse valley and everything. Every time I do that it blows me away. It is like a very tangible way to have a "holy sh*t" experience about the nature of infinity.

FWIW,
Jim