Earlier this week I was proofreading a book that mentioned Pythagorean spirals. I had seen them before but never thought about them too deeply, so I gave them a try in GeoGebra. I filled them in with curves of pursuit, just for fun!
Week 7 of my Sunday Maths Animations is another one that started out as a cardioid. Varying a different parameter gives a completely different effect.
Week 6 of my Sunday Maths Animations started out as a cardioid, but quickly became something else.