Fractals

[Turwaithien]

Something I've been very interested in this past school year was fractals. Mathematically they intrigue me greatly ('cause they're just SO COOL). Fractals, as images at least, are (basically) self-repeating pieces. Maybe I should just link to Wikipedia.
So, I found this program Apophysis that creates fractal flames, which are somewhat different. Making (or discovering) the images that could be created was a very meditative process for me. I ended up with a lot of beautiful and meaningful (to me at least) images.
I'd like to share some of them here.

http://lh6.ggpht.com/_qBnUdXLHrBU/SpST2 ... /Silms.jpgThe Silmarils

http://lh3.ggpht.com/_qBnUdXLHrBU/SpST2 ... 0Wings.jpgThis one doesn't really have a name (except in a porfolio, there I call it Wings).

http://lh5.ggpht.com/_qBnUdXLHrBU/SpST2 ... /Manwe.jpgManwe

http://lh5.ggpht.com/_qBnUdXLHrBU/SpST2 ... 20Star.pngShooting Star (I don't even remember how I ended up with this one.)

http://lh5.ggpht.com/_qBnUdXLHrBU/SpST2 ... 282%29.jpgI generally call this one Priestess, though I actually associate it with memories (I don't know why).

So.Yeah. I want to explain how they are meaningful for me, but I don't know that I can. It's like going through a constant sea of moving lines and colors and every now and then something solidifies and is real. Or something like that...

I've (some the times) been trying to get more images that are related to the Legendarium, but it's not something I can just make happen. Though I could probably learn how to get the exact shapes I want mathematically, I much more enjoy (and feel more artistic) in just letting the images happen.

[Meneldur Olvarion]

Very nice!

Yes, fractals are fascinating.  I used fractal math in some of my calculations in the "Quendian Calendar II" (Venus) document.

///Dave

[Calantirniel]

Wow, these are great!  I never knew this existed hehe!  Thanks tons for sharing!

[Arodring]

I am unable to see the first three and the last two are quite beautiful.  Any chance you could upload them at higher resolutions so I can view them in higher detail.  Thanks for sharing these!

[Meneldur Olvarion]

I have uploaded them from the URLs in Turwaithien's original post.

[Turwaithien]

Thanks for that.

[Lomelindo]

Very nice.  Those are amazing pics.  I like the Silmaril association you brought up with the first pic.

I think these pics could be used for meditative/trance purposes as an aid.  Maybe I will try that one of these nights.

Lomelindo

[Llefyn Mallwen]

Beautiful pictures!  My other half is also very keen on fractal art and has been experimenting with making them in Photoshop.  I especially like the one you call "Priestess", and can actually see a figure in the work....the face, arms, chest area, hair, aura around her head, and appears to be sitting in a cross-legged fashion.  Wonderful stuff, thanks for sharing! :-)

[Lúthien]

I found this fractal image somewhere on the internet while looking for Earendil related pictures when I was making that Earendil video. It is indeed uncannily "Earendil-like".
http://img.skitch.com/20091019-gme19ind ... gymq6t.jpg

[Turwaithien]

Woah. That is really Earendil-ish. It's really different from the ones I've made too. I wonder what program was used for this one.

[José]

It makes me think about Ea's beginnings, if not even the Music of the Ainur.
It's very beautiful indeed. Is it easy to make these fractal images?

[Meneldur Olvarion]

[...] It's very beautiful indeed. Is it easy to make these fractal images?

Probably.

Although I did not make these, there is this wiki on Fractal Flames which lists various free software packages at the end (under the "See also" section):

http://en.wikipedia.org/wiki/Fractal_flame

///Dave

[Lúthien]

Fractal flames are one type of Fractals. There are other types as well; here is a list of fractal creating software: http://www.google.com/Top/Science/Math/ ... /Software/

[Lúthien]

when I was in art school in '98 I wrote a C program that created 3D fractal images. It was very slow because the computer wasn't all that fast, and the program had to basically probe a 3D space in order to create the image - so that for a 100 x 100 size image (a small one) it didn't need to go through 10.000 pixels, but probe every one to on average half the depth of the field as well (and on 'empty' pixels the whole depth), so that would multiply the time needed by at least a factor 50.

I thought I lost all the images but I found one on the wayback machine:

http://aandachtuit.nl/img/veryoldsite/jul8.gif

together with one thumbnail of a painting I made

http://aandachtuit.nl/img/veryoldsite/xmage1.gif

and an animated GIF file of a hypercube rotating through 3D space.

http://aandachtuit.nl/img/veryoldsite/aku3.gif

the math behind the 3D images is not that complex .. it is merely an extension of complex numbers which I named "hypercomplex" numbers, and was explained on my then website as follows:

=================================================================

About 3-d fractals

The fractals shown here are Juliasets, named after Gaston Julia, a mathematician who, in the beginning of this century, described the principles of fractal geometry.
I assume you already know about how 2-dimenional Juliaset (and the related Mandelbrot-set) are made, and that they exist in the (x,i) plane of complex numbers. What I did (and who knows how many others, but I've never seen it anywhere else) is to extend the idea of complex numbers one dimension further.
When complex numbers can be regarded as twodimensional, you could think of something like hypercomlex numbers, having three dimensions. The first dimension (unit 1), the second (unit i) and a third (unit m)

In complex arithmetic, the basic rule is:

i ² = - 1

In hypercomplex arithmetic, I called this third unit m. The basic rule that applies to m is, simple enough:

m ² = - i

Whith this in mind, it's easy to construct the algorithm that draws these threedimensional Juliasets.

=================================================================

I found out later that there is something called Quaternions - a four-dimensional generalisation of complex numbers. The fractals created in quaternion 4D space are virtually identical to what I made up. I found a little freeware program called Gaston that creates them and raytraces them to make them look all nice and shiny:


http://aandachtuit.nl/img/gastons/1.png


http://aandachtuit.nl/img/gastons/2.png


http://aandachtuit.nl/img/gastons/3.png