Sunday, March 25, 2007

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.

Friday, March 23, 2007

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

Monday, March 19, 2007

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.

Thursday, March 15, 2007

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.

Friday, March 9, 2007

Pythagoras tree

The Pythagoras tree is a plane fractal constructed from squares. It's named after Pythagoras because each triple touching squares encloses right triangle, traditionally used to depict Pythagorean theorem. If triangles of the tree have equal sides, the Pythagorean tree is symmetric, as you can see above, otherwise the tree is asymmetric. The illustration above shows eight iterations of tree construction progress.

Below it's shown asymmetric Pythagoras tree.

The shape of the tree can be used for creation of infinite impossible figure. Some parts of the fractal can be replaced to impossible triangles or squares. Illustrations below show symmetrical and asymmetrical impossible fractal tree.
Flemish artist Jos de Mey created many artworks with Pythagoras tree as main motif. Below you can see his artworks.
Three dimensional effect can be applied to the Pythagoras tree. Illustrations below by Koos Verhoeff shows trees with applied various parameters.
Below you can bronse sculpture of Pythagoras tree which also created by Koos Verhoeff. the sculpture based on computer sketch above right. 
Upd 25.11.2008.
A very nice Pythagoras tree was created by hyperion_00001. Note, that younger leaf generations are located below older ones, which increase convexity of the figure.

Sunday, March 4, 2007

Pre-fractal islamic art

Representations of fractals appear in human art of the Religious and Spiritual varieties. Above left you can see an Ottoman illustration of sacrifice of Ishmael dated to 1583. Above right you can a Mandelbrot fractal image with very similar shape and proportions.

Thursday, March 1, 2007

Corpus Hypercubus

Crucifixion (Corpus Hypercubus)
Salvador Dalí (1954)

Salvador Dalí, the master of surrealism, had a keen interest in natural science and mathematics. He was fascinated by hypercube, and it is featured in the painting Crucifixion (Corpus Hypercubus). Here Christ is crucified on figure of unfolded hypercube.

Hypercube is four-dimensional analogy of three-dimensional cube. It comes in by shifting three-dimensional cube perpendicular to three axis of our space. It consists of eight cubes. Frequently it depicted in it's frontal view as you can see in the image right. As cube can be unfolded into flat figure of six squares, hypercube can be unfolded into three-dimensional construction of eight cubes. This construction we see at Dalí's artworks, in particular.