Explanation of exponential sums

The exponential sum plots on this site draw lines between the consecutive partial sums of

$\sum_{n=0}^N \exp\left( 2\pi i \left( \frac{n}{m} + \frac{n^2}{d} + \frac{n^3}{y} \right ) \right )$

where m is the month, d is the day, and y is the last two digits of the year.

I have used different values of N over time. Currently I use N = 2 lcm(m, d, y) + 1.

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