Many of these graphs are inspired by graphs other people have made, or Desmos has shared (example: the interpolations on the Desmos homepage), or inspired through teaching my amazing students.
For example, the picture below was inspired by a discussion with a student, who wanted me to create a picture of a velociraptor with protractors for claws, which we decided to name Protractiraptor:
Here’s a graph of a problem I’ve given my geometry students for extra credit, the shortest-way-to-help-grandma problem:
A few years ago, I was amazed and fascinated to see a beautiful visual way of identifying prime numbers that I’d never seen before. Here’s a graph I made to replicate the “Sieve of Matiyasevich” for eliminating composite numbers to find primes:
Many of these graphs were created with me just playing around to see what would happen, and then gawking in amazement, and wondering — “Wait, what??” These are only a small selection of the graphs I’ve created.