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# More Fourier Noise Contours

Previously, I used single-frequency Fourier noise to do some halftoning. This time, I’ll use broad-frequency noise.

I’ll filter 2D white noise with a gaussian with standard deviation $\sigma$. This reduces the high-frequency content. Let’s call the filtered noise $h$, and the gradient-scaled version$r$. Skipping all the tedious probability work, the pdf of the gradient-scaled noise is

$f_{r} = \frac{\sigma^2}{\left(2 \sigma^2+x^2 \right)^{3/2}} .$.

So the curve length per unit area is $f_r(x=0)=1/(\sigma 2 \sqrt{2}) \approx 0.3536/\sigma$.

How’s this look in comparison to the other style?

The broad-spectrum noise is patchier, but kinda feels more ‘natural’ due to its unevenness. How about using it for halftoning?

They patchiness isn’t helpful. It works, but the single frequency method looks better, I think.

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