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# Seismographs

On the theme of using a single path to shade an image, one idea is to use a wiggling line. A shorter wavelength will result in a darker area, and vice versa. So I threw a little math at the problem, and here are the results of using square, triangle waves, and sine waves:

## A little math

Let’s say that the line width, wavelength, and peak-to-peak amplitude are $w, \, \lambda \, H$. If we ignore the overlap of the lines and the round edges due to a circular pen tip, this makes it much simpler. For each pattern, the approximate darkness is:

\begin{aligned}\overline{K_{square}} &\approx \frac{\left(\lambda + 2 H \right) w}{\lambda H} \\ \overline{K_{triangle}} &\approx \frac{w \sqrt{\lambda^2+4 H^2}}{\lambda H} \\ &\approx K_{sinusoid} \end{aligned}

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