[FRIAM] what complexity science says ...

[jon zingale]

To continue my howling in the wilderness, what the *intrepid follower of
links* would find from the lecture on Meyer's[φ] wavelets is that wavelet
transforms offer up much better fidelity than Fourier's, with fewer
artifacts, better data compression, and from fewer resources. Why wouldn't
nature prefer it? Again, perhaps because nature found yet a more suitable
transform than either.

FWIW, waveguides offer up a third instance of impedance matching, that of
characteristic impedance.

[φ] The first part of the lecture is also interesting to the *lover of
complexity* as Meyer was the first to realize that quasi-crystals, and
aperiodic tilings more generally, can be manifest as projections of
higher-dimensional periodic structures. Tao, in passing, mentions how the
Fourier spectrum, OTOH, obscures the details of aperiodic structures this
way, as they do not look different than the periodic case. OTO this detail
provided insight into the connection between these higher dimensional
periodics and their lower dimension aperiodic representations.



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