Week 2 - Math and Art
In this week's readings, we look at how mathematics influences art concepts. Speaking from experience, I know that mathematics has quite the role in computer graphics. Using matrices to manipulate the size, shape, and position of objects is central to computer graphics. Expanding on simple manipulation of objects, computer graphics aims to create some sort of realistic scene; in this, notions such as vanishing points come into effect.
Vanishing points is a concept not unique to computer graphics only. In fact, vanishing points occur in any piece of art depicting "parallel lines" put into perspective. For example, take the drawing "Road do Schlessheim", by Theodore Clement Steele:
This drawing depicts a road stretching off into the distance. We know that roads consist basically of two parallel lines, but the concept of vanishing points makes it so that these two lines converge when put into perspective. The mathematics behind where the "point" should be are clearly defined for use in computer graphics and is one example of how math is used in art.
Another example of math-turned-art is fractals. Fractals are repeating patterns that appear across different scales. Due to this, creating fractals may seem to be a task uniquely suited for computers. However, many artists create fractals; for example, Jackson Pollock creates fractal paintings by using a drip technique that creates repeating patterns at different sizes.
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| One of Pollocks paintings. While it may seem random, if you look closely, you will see that it is made up of repeating patterns. |
Tesselations are another example of math in art. Tesselations are described as "regular division of the plane" that "completely cover the plane without overlapping and without leaving gaps." Once again, we can see that since tesselations are governed by predictable patterns, we can use math to generate them.
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| Tiles in the Alhambra, a tesselation |
From these examples, we can see that mathematics are important to many aspects of art, whether it be creating the entire artpiece itself, recognizing a pattern in the art, or determining how an object should look within the piece of art.
Resources:
Road do Schlessheim - Theodore Clement Steele - The Athenaeum (Road do Schlessheim - Theodore Clement Steele - The Athenaeum)
http://www.the-athenaeum.org/art/detail.php?ID=121540
Full Fathom Five - Jackson Pollock - WebMuseum, Paris
http://www.ibiblio.org/wm/paint/auth/pollock/pollock.number-8.jpg
Ouellette, Jennifer - Pollock's Fractals Discover Magazine May 2015
http://discovermagazine.com/2001/nov/featpollock
The Mathematical Art of MC Escher - Platonic Realms 2015
http://platonicrealms.com/minitexts/Mathematical-Art-Of-M-C-Escher/
Frantz, Marc - Vanishing Points and Looking at Art - 2000
http://www.cs.ucf.edu/courses/cap6938-02/refs/VanishingPoints.pdf
Hi Victor,
ReplyDeleteI thought that you had a very interesting point regarding tesselations. I had never heard of them before but now that I see what they are I believe that they are a great depiction of math in art. They are pretty cool to look at and now I know what the FedEx logo is called.
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ReplyDeleteHi Victor, thanks for your post! I thought your connection of math and art to matrices and computer graphics was interesting. I had a class this year, Chemistry 171, that used matrices to depict atom orbital symmetries to physically explain bonding of molecules. It is especially gratifying that we can explain and describe the natural world around us through mathematics. Do you have any of your own computer graphics projects were you used the vanishing point technique? I would be interested to see that. I wasn’t aware of fractals before your discussion; however, I couldn’t find the repeating pattern in the picture, what is it?
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