Cubic pyramid

A nice pyramid of cubes was modeled and rendered by David Pearson (fpsurgeon). Each lower level of the pyramid consists of smaller cubes, which are four times more than above. So we see a simple but elegant fractal. This nice rendering was created as a further development of studing by author an open source program Structure Synth, which provides creating 3D structures from a set of user rules. One of preliminary studies you can see below.
Imagine if the top cube of the pyramid is too heavy, and the whole structure will collapse.

Hilbert curve

Hilbert curve is a continuous fractal space filling curve, which was first described by German mathematician David Hilbert in 1891. Below you can see 5 first steps of the plane Hilbert curve.

But the Hilbert curve looks more interesting if it represent in three dimensions. Carlo H. Séquin, a professor of Berkley, created a small 5" metal sculpture of Hilbert curve, which he called "Hilbert 512". You can see it below.

It was also be modeled by Torolf Sauermann in the program Maxwell renderer. Below, you can see the second step of the three-dimensional Hilbert curve and two versions of cubic Hilbert curve.

Triangle vortex

A nice rendering of triangle vortex was found at forum WooYah, which was created by member Heidi. This image is interesting by shapes of triangles, which look like Penrose tribar, but they are not. If looking attentively we see that these triangles are more distorted than classic Penrose triangle. So these figures cannot be named 'impossible' because they don't make sense possible figure. It sounds paradoxically, but all impossible figures makes sense common possible object at first glance.

Below you can see another rendering with the same kind of triangle.

Structures by Rinus Roelofs

Holland artist and mathematician Rinus Roelofs constructs charming mathematical structures. He constructs his structures in computer but some of them became sculptures in various Holland towns.

The sculpture above was erected in Borne (Holland) in 2005. It consists of 26 tetrahedrons or 104 triangles. Triangles are just slid together. Construction is stable and need no further fixing.

Bet he created a lot more computer models of three-dimensional structures. One of them (below) shows Hamiltonean path of polyhedron. Hamiltonean path is a sequence of edges that visits all vertexes of a polyhedron exactly once.

Besides three-dimensional structure Rinus Roelofs created a set of two-dimensional tessellation structures for Escher Centennial Congress in Rome in 1998. They represents regular structures that constitute infinite impossible figures. He insists not to call them tessellations but joins.

Fractal temple

In this raytraced image by unknown author we can see a strange sea temple. The temple consists of many similar platforms of various sizes. Every platform stands on four squared columns. The main cupola of the temple stands on platform which in one's turn stands on four platforms raised from water. There are four platforms smaller size on every of these main platforms with cupolas smaller size. Also, there are four platforms even smaller size on these small platforms and so on. This is a fractal temple with infinite count of cupolas!

Update 08.02.2009

Thanks to Greg M. Johnson, now I know who is the author of this image. His name is Christoph Hormann. The original image can be found at http://www.imagico.de/pov/gallery3_g.html.