Exponential sums in 2019

I’ve made a small change in my exponential sum page. I’ll need to give a little background before explaining the change.

First of all, you can read exactly what these exponential sums are here. These plots can be periodic in two senses. The first is simply repeating the same sequence of points. The second is repeatedly producing the same pattern of points, but shifted. Here are a couple examples from last year.

The sum for New Year’s Eve was periodic in the first sense. Plotting more points would make no difference.

The sum for Christmas Eve was periodic in the latter sense, repeating the pattern 12 times as it moves down the page. If we increased the value of N in the formula that generates the plots, we’d see more repetitions extending further down.

Since 19 is a prime, there will be more exponential sums this year that are periodic in this latter sense. I doubled the value of N so the plot will always display at least two periods.

The fact that 19 is prime also means there will be more intricate plots this year. For example, here’s the plot for March 17, 2019

compared to the plot for March 17, 2018.

There will also be a few simpler but strange plots. The plot for January 19 is unlike anything I’ve seen since starting this page.

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