Stars of the Mind’s Sky

I just submitted some art for exhibition at Bridges 2013, the world’s largest mathematical art conference.  I’m extremely hopeful that it will be accepted.  I actually submitted art for exhibition at the Joint Mathematics Meetings, but it was denied, I think, because I hadn’t figured out how to get the right image size and resolution.  Whoops.  Anyhow, I’m proud of what I put together, and I wanted to share it with you here, so I’ve pasted the art, description, and my artist’s statement below.  (And yes.  I will sell you a print if you’d like.)

* * *

My earliest love of mathematics came when I realized its utility in creating beautiful things. As a third grader (and ever since), I spent countless afternoons drawing stars and patterned shapes with a protractor or compass. In my work as a teacher I get to share that beauty in creation with my students. In my art I sometimes try to illuminate the complex structure and interconnectedness of simple, patterned objects. I’m compelled to understand complete spaces of related works and how my choices as an artist locate me within that space.

Stars of the Mind's Sky22.75 in x 22.75 in digital print 2012

Stars of the Mind’s Sky
22.75 in x 22.75 in
digital print

Stars of the Mind’s Sky is the title of a series of works exploring the space of regular star polygons. Here we see 300 stars “in orbit” along concentric circles. The number of points on a star increases with the radius, and stars of a given number of points are spaced evenly along their circle according to “density,” or the “jump number” used in generating them. Algebraically, these represent the subgroups and cosets generated by elements of a cyclic group. They have been colored on a gradient to indicate the number of cosets; a red star signifies a generating element. As a consequence of these structural choices, we may observe congruent stars with increasingly many cosets, shifting their way to blue along central rays through any red star.


8 responses to “Stars of the Mind’s Sky

  1. Pretty, Paul. I’d love to purchase a print of the Stars of the Mind’s Sky. Please email me what and where to send payment. Good luck with your submission!

  2. Paul,
    This is great. What software did you use to create this?

    • Thanks, John! This was a lot of Mathematica. Had to learn lots and lots of code to make it happen. Amazing how much you can learn when you’ve got something you actually want to do/make!

  3. Ooh this is fascinating! Mind if I write a blog about your art? Keep us posted on this exhibition!

  4. Pingback: Stars of the Mind’s Sky with Diagrams | The Math Less Traveled

  5. Pingback: Math Teachers at Play #62 | Let's Play Math!

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