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Lipton -> Julesz’ vision conjecture kinda highlights what you’ve been saying for a while about human perception of large data series, right? That pic reminded me of Wolfram’s cellular automata graphs for some reason.. probably related somehow, but definitely over my head.
I think a disproof of the Julesz conjecture could have been done by a 2D analogue of the de Bruijn/matrix-tree shuffling algorithms I did for retaining local statistics while destroying long-range correlations. The problem there is that the relevant structures (de Bruijn tori and their attendant generalizations) are not well understood, and there is no known analogue of the matrix-tree theorem for this sort of thing. In fact such a thing would allow a solution of the 2D Ising model with an applied field, which indicates just how hard such a construction must be.
Lipton -> Julesz’ vision conjecture kinda highlights what you’ve been saying for a while about human perception of large data series, right? That pic reminded me of Wolfram’s cellular automata graphs for some reason.. probably related somehow, but definitely over my head.
I think a disproof of the Julesz conjecture could have been done by a 2D analogue of the de Bruijn/matrix-tree shuffling algorithms I did for retaining local statistics while destroying long-range correlations. The problem there is that the relevant structures (de Bruijn tori and their attendant generalizations) are not well understood, and there is no known analogue of the matrix-tree theorem for this sort of thing. In fact such a thing would allow a solution of the 2D Ising model with an applied field, which indicates just how hard such a construction must be.