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.

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.

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.

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.