Over the real numbers, it's easy to visualize a linear transformation as a series of continuous rotations and stretches/compressions of Euclidean space. Over small, finite spaces (N=6,7) they produce many simple patterns and over large spaces (N=100,101) they produce interesting visual artifacts.
The only rotation we have is a flip about the x-y diagonal. Instead of compressing the space, it can be twisted vertically and horizontally (like a ribbon) which produces visible bands. Instead of stretching the space, higher rows/columns get interleaved with lower rows/columns.