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 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.
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.