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.

Anamorphic art

The word anamorphic is from the Greek "ana" (again) and "morphe" (form). It refers to images that are so heavily distorted that they are hard to recognize without the use of a mirror, sometimes referred to as an anamorphoscope. When viewed in the anamorphoscope, the image is "formed again", so that it becomes recognizable.

Anamorphic art as known from middle ages. European painters of the early Renaissance were fascinated by linear anamorphic images, in which stretched pictures are formed again when viewed on a slant. A famous example is Hans Holbein's "The Ambassadors" (1533), which contains a stretched-out skull.

Nowadays anamoprhic art is rised again because of works of such famous artists as István Orosz, Kelly M. Houle, Julian Beever and Felice Varini.

Hungarian artist István Orosz is well known for his artworks with impossible figures and constructions. He also tries to renew anamorphosis art. Frequently he uses etching tecnique for his artworks. Below you can see two views of his artwork "The Well" (1998). You can see the original image to the left, and a part of the same image with cylindrical mirror in the center of the well. We see face of M.C. Escher in the mirror.

Kelly M. Houle also creates anamorphic images for cylindic mirror. She working on projects including illustrating a children’s book manuscript, writing and illustrating a trilogy of fictional correspondence with an anamorphic theme. Below you can see anamorphic portrait of Leonardo da Vinci.

Julian Beever creates his artworks by chalk on roads and streets. His paintings can be viewed as real image from one point of view only.

Felice Varini paints (lines, concentric circles, triangles) on things (tunnels, castles, groovy interiors). A seemingly random smattering of elements that, viewed from a specific point in space, coalesce into a tangible planar element.

Platonic solids with Escher's mosaics

With Escher's mosaics we can cover not only flat plane but also surfaces of platonic solids. Some Escher's tessellations can be divided into simple shapes such as triangle and square. Using these simple shapes we can cover facets of polyhedrons. Below, you can see several examples of covering of Platonic solids with Escher's mosaics.

These images was found at http://www.math-inf.uni-greifswald.de/mathematik+kunst/polyeder.html

Visage of War

In 1940 Salvador Dalí created his painting Visage of War where eyes and mouth each contain a face, whose eyes and mouth each contain a face and so on. Painting this artwork Dalí thought about Spanish Civil War, and eyes are filled with infinite death. Perhaps Dali decided the infinite horrors of war were better depicted in a bounded canvas through self-similarity, though most certainly he had not been exposed to this as a mathematical concept.

Analogous fractal of order four can be viewed to the right.

Interestingly, a preliminary study (below) of this picture had a face within only one face within the mouth of the largest face.

Sculpture of Sierpiski triangle

This giant sculpture represents three-dimensional version of fractal named Sierpinski triangle. This large tetrahedron that consists of 1024 smaller tetrahedrons was created by students of Alan A. Lewis School. Order of fractal is 6.