You've most likely heard about gradient noise through the name Perlin noise, which refers to one particular implementation with various CPU optimizations. Because it's an incredible tool for creative work, it's used virtually everywhere: visual effects, video games, procedural mathematical art, etc. While getting it right can sometimes be subtle, a "broken" implementation can still look good or interesting. After all, "it looks fine, and I'm an artist". In order to gain a deeper and more meaning...