Many equations

This is mix of various linear, polar, Fourier, equations and methods. The scale of what is possible is so overwhelming sometimes. It is difficult to grasp that a single image that is 1000 by 1000 can have states of existence that exceed 2 to the millionth power. Underneath all that is :
f(x)=sin(ex) [ In polar coordinates ]
, and that is the butterfly wing like yellow fan.

I have been doing Fourier analysis of various images I find on the web and it is interesting, what lies behind the images.

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