Don’t worry, this article in Scientific American explains how fractal geometry will save us from any possible future shortage of cute cat photos on the internet. I know you were concerned about that, so I wanted to set your mind at ease. The Julia set, in particular, can be made into a cat, so we can revel in the cat cuteness as well as the mathematical beauty.
Fractals will save us all!
(Read the article to see the cat fractal.)