3 ms·
naively, could any percieved symmetry in these images be the effect of constant iteration over some input, where the self-similarity emerges as a kind of artifa
by motohagiography 2y ago
naively, could any percieved symmetry in these images be the effect of constant iteration over some input, where the self-similarity emerges as a kind of artifact of the lens, and not of the underlying numbers? Like how everything viewed through a kaleidoscope looks kaleidoscopic, but this doesn't reveal hidden symmetries in the object in the lens.
I'm suggesting it because even when you use other iterative tools (method of differences, phase space analysis[1], etc) you can percieve symmetry in the images even over random'ish data that mainly indicates limited or periodic inputs, but the output of these images don't provide any net new information about number theoretic relationships. It does suggest fractals may be a kind of lens artifact and not an actual property of nature though.
[1] e.g. https://lcamtuf.coredump.cx/newtcp/ https://lcamtuf.coredump.cx/newtcp/
- throwaway211 2y agoAre you suggesting it's a problem of seeing a sheep in a field?
- codebje 2y agoThe function gives the same result regardless of the sign of the two components, so there's axes of symmetry around the lines defined by (x ± xi): in the first image that gives four axes on the horizontal, vertical, and diagonal lines through the origin. The two zoomed images are along the diagonal extending up to the top left and so there's diagonal symmetry visible. I think that would probably count as it revealing symmetry in the underlying object rather than in the lens, it's not a consequence of rounding or asymptotes or floating point errors or any such.