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We can define an image representation using parametrized functions in the following way:
f(x,y) is the color of the pixel (x,y), given that very small numbers are darker colors, and very high numbers are bright colors. To obtain different colors, we can start from predefined set of 3 basic colors, and multiply them by the values give by function f. Then we can tweak the output by playing with hue and saturation. We use a clamping operator to restrict the values to [0,255] range.
This is an enhancement to the mathematical 2D representation of a function that we use in elementary school.
A few examples can contain: a constant function will represent into a uniform screen of a single color. A sinus function would then create some stripes:
We can then get into more complicated images, like the following:
The question at hand is how to get more images, and how to create such functions?