Thought it might interest some to see how FFT works.

 

“Natural phenomena we can relate to, like sound waves, heat transfer, weather patterns, and those of a more esoteric sort, like quantum particle interactions and cosmic objects moving through gravitational fields governed by general relativity, can all have their interactions approximated by classes of functions called orthogonal functions.”

Source: Video explaining Fourier Transform Used in Spectrum Analysis

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One mathematician who’s got first-hand experience of the fascinating interplay between physics and geometry is  Shing-Tung Yau. In a new book called The shape of inner space (co-authored by Steve Nadis) Yau describes how the strange geometrical spaces he discovered turned out to be just what theoretical physicists needed in their attempt to build a theory of everything.  Plus met up with Yau on his recent visit to London, to find out more.

Source: Greenfield.pdf

Gary R. Greenfield
Department of Mathematics & Computer Science University of Richmond

Abstract
I provide a brief survey documenting the inclusion of cellular automata, periodic tilings and op-art in mathematical art. Then I give an overview of the history of Turing-like patterns in mathematical art. I describe a cellular automaton for producing Turing-like patterns and introduce some new variations. This leads to an open problem concerning the convergence of such patterns.