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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.

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Fractal painting

Fractal Painting

By Nathan Garletts



Egyptian temple column
Egyptian Temple Column 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.

  • 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 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.

  • 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
Bifurcation 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.


Visage of war
Visage of War 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.

  • 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
M.C. Escher 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.

  • 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
Border Limits 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.

  • 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
Real Border Limit 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.

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


Jackson pollock
Jackson Pollock 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.

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



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


Oscar dominguez
Oscar Dominguez 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.

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


Decalcomania
Decalcomania 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.

  • 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 CITED 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.

Works 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


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