File:Height Map.png

English: This is a Height Map of a function that I use for testing optimization algorithms. I am placing it here in the hopes that my optimization art will make more sense in context. Basically a height map just shows the height of some 2D function, for every input point. Here the low points are colored black, and the high points are colored white.

When we preform optimization, we start with an arbitrary point, and try to find another point that minimizes the function. That is, the point where the function is lowest. You can tell from this map that there are two global minima in the image, indicated by the two dark regions. What's not as clear is the fact that there are also six local minima, which occur at the bottom of valleys. Because optimization always converges to a local minima, we cannot guarantee we always find the global minimum.

By coloring each point, based on which minimum it eventually converges to, we can create art from functions like this, utilizing various optimization algorithms.