Gallai's theorem

Gallai's theorem is a concept in geometry about dividing shapes into parts. It states that if you color the points of a geometric grid with a certain number of colors, then no matter how you do that, you'll always find a smaller, similar pattern (like a scaled version of a basic shape) made up of points all the same color. This means that in any coloring, some ordered, repeated structure is guaranteed to exist, highlighting an inherent regularity within seemingly random distributions of points.