How can we plot the Fourier transform of a sampling pattern?

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In Cook, Stochastic sampling in computer graphics, the author is showing distribution patterns like jittered samples

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and the corresponding code to produce the output:

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He's also showing the plot of the corresponding Fourier transform:

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But what exactly does this last picture show? I guess we take the discretete Fourier transform of the data which is formed by the 512x512 pixel grid (and either a value in that grid is 0 (black) or 1 (white)). The discrete Fourier tranform of such a grid (i.e. a two-dimensional array) is another two-dimensional array. But what is the plot showing? And how can we plot it using Python?