Tuesday, 18 June 2013

Furute, fractals and everything else...

 And thus we've arrived to the final stage. To top of Watchtower Iteration, from where an anthropomorphic fractal being I named "The Sentient" gazes into the horizons of cyberspace. Today, the more complex 3D fractals I could upload were 3D julians or IFS but I had to stay under 3 iterations and iterate the simplest base shapes. But look back at the times when 3D wasn't even possible or within reach... and look at the future, where things like a 100000 iterations L-system fractal with 100000 iterations Julian four-dimensional quaternions in it's formal grammar will be possible. How complex can that get? Technology will some day make it possible to create systems of such a complexity that they will match a human brains and may be, why not, this system will become sentient just as a side effect of their own complexity as writers like William Gibson have stated. Crazy eh? but their crazy, impossible visions back in the 80's are today real and sometimes I dare say, with all their enlightenment... they fell short.
 So here's my vision of the future, The Sentient. Today a simple fractal collage created on Incendia using IFS and Gumowski attractors. Tomorrow... who knows?

Sunday, 16 June 2013

3 Dimensions - Fractals fill the cyberspace!

 With the arrival of new features fractals became volumetric. No longer flat fractals became in many cases vital components on several of my buildings.

Sierpinski-Menger  I'll begin with the simplest types, the Sierpinski Pyramid and the Menger Sponge. You will find the two of them linked in one single object on the Main Deck. I built this ones manually. The Sierpinski Pyramid was built using the free version of Sculpt Crafter so it's made of sculpties. This was my very first 3D fractal I created inworld, long before the arrival of meshes. I used to have my personal chambers inside a giant version of this pyramid. The Menger Sponge was the first mesh fractal I uploaded. Created manually using Blender it's first copy was rezzed inworld on the mesh test sandboxes on the first hours of mesh deployment in Second Life.

The Industrial Building
Upper Watchtower Julian Fractal The second group of fractals over the Main Deck I call "The Industrial Building" (image to your left). This two fractals are very different kinds. The first one is the terrain. It's what many call a "heightmap" type of sculptie. Many builders use this kind of sculptie to add detail to the parcel terrains. I've just used a simple Mandelbrot Fractal texture to generate the height information. The second fractal is the "building". It's a heavily edited IFS Reflection fractal created using Incendia and Blender. I've also used this method to create the whole structure of the Watchtower, which is actually two Julian 3D fractals created on Incendia and lightly edited on Blender. Most of the other fractals were also created like this. The Stars Platform contains three types of "Stars and Hedra" fractals generated on Incendia and the Apollonian Flower belongs to Incendia's Apollonian Gasket sets.

Stars and Hedra Fractals

L-System Trees The Lindenmayer Platform holds 4 very simple trees. This trees were generated on a very old app people used to generate trees for POV-Ray scenes. It can also export .obj files. The app name is Arbaro, free to download. It can generate much more complex trees and even foliage, I kept them simple to stay low prim. The app is an L-System (Lindenmayer System) tree generator. Aristid Lindenmayer used L-systems to describe the behaviour of plant cells and to model the growth processes of plant development. L-systems have also been used to model the morphology of a variety of organisms and can be used to generate self-similar fractals such as iterated function systems (IFS). Sierpinski triangles and Menger sponges are created like this.

NOTE: All textures were created using either Incendia or Apophysis and some GIMP post, exept for the terrain texture on "The Industrial Building" which belongs to SL Library.


Have I already used this quote?
"Fractal Geometry plays two roles. It is the geometry of deterministic chaos and it can also describe the geometry of mountains, clouds and galaxies." - Benoit Mandelbrot
Well... consider it a second iteration somehow. Now about the geometry of galaxies here's a fractal flame I rendered this morning. I call it the "Looking Forward Looking Back Nebula" cause it pretty matches SL10B event theme!

Friday, 14 June 2013

Start of the journey: flat fractals

 The first stage of the exhibit consists of a few simple objects where fractals have been used just as textures. Not much more could be done with fractals in the early days of SL, not without using hundreds of prims for a single fractal. So the first fractals I've worked with inworld were no more than textures. 2D fractals mostly on the Mandelbrot Set and Julia Set which were like the big colourful ones you'll see on the walls underwater in the exhibit. The green sea floor is also one of this kind of fractals, edited with GIMP to remove the seams. There's also some small glowing plants, the red ones use the most common and known Mandelbrot fractal, the cycling ones use a "Fractal Flame" as texture as well as the vortex floor you land on when you teleport underwater.

The Mandelbrot and Julian Fractals

The "Flame Fractal" Vortex

For Julian, Mandelbrot and a few other fractals I've used Fractal Explorer.
Flame fractals were created using Apophysis.

Now, as I've mentioned, there was already a way to play with 3D fractals even in the early days. If you feel curious check the Second Life Geometry section Paul Bourke's site. There's lots of pictures there and even a few LSL scripts to generate fractals using prims.

Thursday, 13 June 2013

It all begins with a Mandelbrot (a little bit of history)

The term "fractal" was coined by Benoit Mandelbrot in 1975. It comes from the Latin fractus , meaning an irregular surface like that of a broken stone. Fractals are non-regular geometric shapes that have the same degree of non-regularity on all scales. Just as a stone at the base of a foothill can resemble in miniature the mountain from which it originally tumbled down, so are fractals self-similar whether you view them from close up or very far away.
"Fractal Geometry plays two roles. It is the geometry of deterministic chaos and it can also describe the geometry of mountains, clouds and galaxies." - Benoit Mandelbrot
Mandelbrot set images are made by sampling complex numbers and determining for each whether the result tends towards infinity when a particular mathematical operation is iterated on it. Treating the real and imaginary parts of each number as image coordinates, pixels are colored according to how rapidly the sequence diverges, if at all.

The Mandelbrot set has its place in complex dynamics, a field first investigated by the French mathematicians Pierre Fatou and Gaston Julia at the beginning of the 20th century. The first pictures of this fractal were drawn in 1978. On 1 March 1980, at IBM's Thomas J. Watson Research Center, Benoit Mandelbrot first saw a visualization of the set.

Wednesday, 12 June 2013

Welcome to Watchtower Iteration!

The Watchtower Iteration is a virtual exhibit built and textured using fractals with the exceptions of a few prims and one single texture I had no time to replace for a similar fractal texture. In this blog I'll try to explain a bit about each fractal, the creation process and the programs employed, all of them totally freeware!