Fractal Painting

By Nathan Garletts

• Fractals can be found in paintings for a few different reasons. Some are due to an unconscious use of fractal components such as finding self-similarity, or a bifurcation process. Others were done on purpose to mimic chaotic shapes.

Egyptian Temple Column

• This shows the capital of an Egyptian temple column. In Ancient Egyptian cosmogony the white lotus flower often represents the development of the universe. The petals within petals within petals represents the cosmos on smaller and smaller scales, and is a clear example of self-similarity.

Hokusai• Hokusai was best known for his

painting The Great Wave (at the top). Hokusai saw the complex patterns that occur in nature and would repeat these. Many of his pictures remind us of the detail of Julia sets. Notice the self-similarity on the edge of the waves.

• The picture on the bottom is his famous Fuji in a Thunderstorm painting. It is odd that there is such little detail in his lightning, yet the rest of the picture is so complex. This may be due to the fact that photography was not discovered at the time and he had only ever gotten brief glimpses of lightning.

Bifurcation

Visage of War

• Salvador Dali’s Visage of War was done in California in 1940. This image is probably inspired by the Spanish civil war, considering WWII had not yet provided many frightful images. The heads eyes and mouth are full of “infinite death.”

M.C. Escher

• Many wonder what Escher could have done if he was familiar with fractals.

• Escher did many creative images using tessellations. This is defined as a collection of plane figures that covers the plane with no gaps or overlaps.

Border Limits

• As you can see here we have the same tessellation that was in the previous slide, however there is a border limit at the bottom.

Real Border Limit

• This is Escher’s Circle Limit III. In this picture there is a complete border limit.

Jackson Pollock

In the 1940’s Jackson Pollock created abstract art by dripping paint from a can onto vast canvasses across his floor. His art is considered to be a fractal, reflecting the fingerprint nature. Over the years Jackson Pollock refined his dripping technique. As time went on the fractal dimensions of his artwork slowly increased. In his early stages the dimension was close to one and as he got older it went all the way up to about 1.72. This is due to the fact that later on he covered a higher percentage of the canvas’s surface, and used more layers.

• This piece of art was done by Pollock in his early stage, somewhere from 1942-1944. Notice how it is much less dense than the previous one, covering less of the canvas. Also note that there are fewer layers. If you calculated the fractal dimension of this it would be much lower than t he previous image.

Vincent Van Gogh

• Vincent Van Gogh is known for his chaotic paintings. Mathematical studies have shown that Van Gogh’s stormy paintings almost perfectly imitates real turbulence.

• Many researchers say that the skies of The Starry Night, Road with Cypress and Star, and Wheat Field with Crows all contain statistical characteristics of turbulence. These works were actually created while Van Gogh was mentally unstable.

All the artists we have looked at so far used fractals in an unconscious way, at the beginning of the new century a more conscious use of fractal geometry came about. It can be used to create, excitement, and chaos in a picture, mimic nature, or create complex patterns.

Max Ernst

• Max Ernst applied a method of viscous fingering to form interesting textures in his artwork. This method became known as “decalcomania.”

Oscar Dominguez

• Oscar Dominguez also used Ernst’s method of decalcomania, but used ink rather than paint.

Decalcomania

• 1. The stiffness of the paper.

• 2. The viscosity of the paint.

• 3. How quickly you pull apart the two papers.

• 4. How hard you press.

WORKS CITEDWorks Cited

http://classes.yale.edu/fractals/WorldOfFractals/Art/Decalcomania/Decalcomania.html http://www.uoregon.edu/~msiuo/taylor/art/Nature1.pdf http://books.google.com/books?id=nmPyLJoRjiMC&pg=PA186&lpg=PA186&dq=oscar+dominguez+fractals&source=web&ots=NiZfnqcJ4-&sig=TSmEJpwv8VVAqV_DxXitXjXupDQ&hl=en&sa=X&oi=book_result&resnum=1&ct=result

 http://www.arttalk.com/archives/vol-15/artv1502-1.htm 

 http://classes.yale.edu/fractals/Panorama/Art/Hokusai/Hokusai.html http://dali.urvas.lt/page17.html  http://classes.yale.edu/fractals/Panorama/Art/Tilings/Raedeschelders.html http://www.ma.ic.ac.uk/~hjjens/Math_Paint.pdf

http://www.bioedonline.org/news/news.cfm?art=2642