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Today I found a program, which does Fourier transforms on pictures and tried it on some basic patterns. One of those was a lattice of dots and I have attached this and its Fourier transform to the thread.

I would very much like if someone in basic details could explain what is going on. Why the Fourier transform of the picture looks as it does. Mathematically I understand what there is to know about the Fourier transform and how we represent a function in its frequency domain by writing it as a superposition of sinusoidal functions with different frequencies.

In terms of the mathematical idea behind the FT what is it then, that I observe on the picture? What is my original function (the brightness?) and what does the frequency represent? Please don't hesitate to write a long answer.

I would very much like if someone in basic details could explain what is going on. Why the Fourier transform of the picture looks as it does. Mathematically I understand what there is to know about the Fourier transform and how we represent a function in its frequency domain by writing it as a superposition of sinusoidal functions with different frequencies.

In terms of the mathematical idea behind the FT what is it then, that I observe on the picture? What is my original function (the brightness?) and what does the frequency represent? Please don't hesitate to write a long answer.