Modular Arithmetic Project
The goal of this project was to visually represent
arithmetic patters exhibited in traditional Cayley Table in an informative and
creative matter. My group and I chose to represent modular arithmetic in the
form of modular art but also in combination with the idea of an artistically
represented Cayley Table. This decision was made after researching different
styles of modular art and coming across a Cayley table with specific patterns
inserted in the spaces corresponding with each number. This opened us up to the
idea of using this process to create a separate art piece using the same
concepts exhibited in the modular arithmetic pattern.
The project was initially divided into four parts, one part
per group member. Each individual was
given a specific color to base individual designs off of. Each member was also
given the freedom to arrange their Cayley table in whatever pattern they chose
provided that it remained mathematically correct and that no patterns resembled
another group member’s pattern. Each Cayley table modeled a MOD 5 (numbers
ranging from 0 to 4) system. Within each table, a specific design was assigned
to each number in the table. This created a repeating modular pattern that
remained constant with the other group members’ modulations. Each Cayley table,
being of a different color, was then solidified to create a uniform image. All
four tables were then grouped together in a 2 by 2 arrangement and solidified
as a new MOD 2 table. This “new” table was then visually flipped horizontally
and again vertically to form a final, unified image. Consequently, each colored
pattern was in the vertical and horizontal opposite side in the final image.
The most challenging aspect of this project was finding a
creative image per number in my Cayley table that resulted in a visually
striking final pattern. I went through several drafts of the final image by
selectively manipulating each pattern corresponding with the appropriate
number. It was particularly difficult finding a pattern that was visually
pleasing and did not affect the overall outcome of the picture. It was also
somewhat challenging deciding what pattern looked best when all four images from
each group member were placed together. Eventually the decision was made to
reflect the image in the horizontal and vertical directions transformed it look
very uniform but there was some initial hesitation as what rotations would be
made. If I were to repeat this project I would try to accommodate for more
tables to create a more visually striking final product. I would also account
for the same pattern sizes per individual patterns.
Sources
Britton, Jill. Interactive Mathematics Modula Art Aug. 15, 2009. Nov. 12, 2012
Modular Arts Gallery Jun.
2, 2011. Nov. 12, 2012
Wikipedia The Garden
of Earthly Delights Oct. 8, 2012. Nov. 12, 2012
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