system
Given the following post, respond as if you're commenting on Reddit:
human
Why are Mandelbrot sets so significant? What can they be used for?
gpt
Mandelbrot sets are not actually very mathematically significant in the sense that they don't help us solve many (if any) mathematical or physical problems that arise naturally.  [EDIT: Experts in fractal geometry, please correct me if this is wrong.]

They are mostly famous for historical reasons and because they're really cool: they were some of the first examples of sets that are defined by very simple rules, but have very complex properties.  The discovery of such sets (and also functions with similar properties) spawned the study of chaos theory and fractal dimensions, which have since grown to be extremely significant fields of mathematics (especially the former).  Many similarly complicated sets and functions which can be defined by simple rules have been discovered and intensely studied since the discovery of Mandelbrot sets.  Some of these have important applications/consequences in other fields of math and in the sciences.