Exponential sums can make intricate patterns. Last year I made a page that displays a different page each day, using the month, day, and year as parameters in the expression below. The images plot the partial sums of this sum.
This was yesterday’s image.
Today’s image is surprisingly plain if we use y = 18.
This is in part because the least common multiple of 1, 1, and 18 is 18. The image could have no more than 18 vertices. In fact, it has only 6 vertices because the summand above has period 6.
But if we use y = 2018 we get something much more complex.
The Exponential Sum of the Day page will use y = 18 this year. There will be a few simple images this year but there will also be lots of surprises.