Three-cross DFT

Amplitudes of the discrete Fourier transform (DFT) of a 3x3 greek cross recursively replaced with either itself or its complement.

[Originally I had incorrectly described this in terms of checkerboards. Some of the comments reflect this error.]

The lowest spatial frequencies are represented at the center. The rounded square lines are formed by contiguous zero amplitude spatial frequencies, but I don't know the exact shape, or why they might be that shape. Nothing in the generating cross suggests these rounded squares. The shape might be a supercircle/squircle.

"In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it’s the exact opposite. The two are incompatible." Paul Dirac, criticizing J. Robert Oppenheimer's interest in poetry

This image demonstrates a nested structure, not obvious to the eye, embodied by a recursive cross pattern. I don't know any precise reason or meaning of the structure, I just found a clear expression of its existence. Is it more art or science, visual poetry or diffraction pattern? I'm a mathematical Platonist -- I believe this pattern has a firm reality external to my perception or expression of one of its forms. I didn't make it up, I found it. Some people think that these patterns are only my construction, a metaphor for how I think about math or art. This difference of opinion makes it difficult to participate in this discussion of the "Delineations between Math and Art".

Download for 2100 x 2100 px. version.


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