Pictures from Dresden

This is Graybear, the not-quite-gray chew toy stuffed animal I received as a gift on my (twenty-) second birthday, from none other than my now girlfriend (and her roommate). (The name "Graybear" is rumored to have some connection with my last name.)

Graybear and I went on a trip to Dresden, Germany. I was busy at a math conference, so I sent Graybear out to take pictures of the city for me. This is what he came up with.


(Graybear in the Ibis Hotel Bastei.)






(Ampelmann--and Ampelwoman!)


(Frauenkirche)




(Martin Luther)


(Friedrich August III)


(I know it's childish, but I can't help but be amused by this.)




(The Elbe.)










(The Cathedral)






(Pragerstrasse)


(Graybear liked to take pictures of himself.)
















(Graybear has an especially nice smile in this one.)


















Blargh!




(That almost looks like my name!)


(Is there a Postmodernism Shop?)




(It was really difficult to get this one. It's very pretty at night, but difficult to adjust the camera to the appropriate setting.)

After all that picture taking, I think Graybear deserves a nap.



Next time you get a chance to go to Germany, be sure to visit Dresden!

Math Art

This picture represents a good deal of what I accomplished my senior year of college. I didn't make this picture; that credit belongs to my former Professor, Jacob Siehler, who is quite amazing at using computers to represent mathematical data.

Basically this picture represents a result of my senior thesis. Here's more or less what I did:

Take a positive integer m. Make a table with m columns and infinitely many rows. Label the columns 0, 1, ... , up through m - 1. Now place a ball in the 0 column of some row, say row x. Then define a sequence of rotation remainders as follows:

• When the ball is in row x, you move it x spaces to the right, and if there aren't that many spaces left in the row, just wrap around to the next row (just like reading a page left to right, top to bottom)
• After each move, write down the column position the ball is in

This sequence of column positions is called the sequence of rotation remainders, which is a term I made up, and it's what I titled my thesis. Surely I could have picked a more exciting and/or cute name for it, but what can you do...

So you might ask how the above picture represents this sequence at all. In fact, each row of pixels in the picture represents an integer (1, 2, 3, 4, 5, ...) and the pixels in a given row represent the numbers in the rotation remainder sequence corresponding to x. In this picture, m = 63.

Isn't it pretty? I promise there's a lot more complicated stuff behind it, too. I'm sure you'd be very impressed.