This is really cool! I found you thanks to @katharsisdrill! These are like using the old spirograph! I had old toys from before my own generation thanks to having really old older siblings and I remember the old carboard box, like a boardgame box, full of these little plastic discs and wheels and putting in a pen or pencil and making wonderful seemingly random patterns.
Heh, I have the same memories of spending so much time trying different patterns! Now, try to realize that all those "seemingly random" shapes are in fact perfectly described by mathematical formulas; changing the numerator and denominator of the formula gives the different shapes (in the first picture above, the numbers on the sides are numerator and denominator, n/d).
It is baffling. I have a dear friend who is a bit of a Math genius and he can go on and on about fractals, though I don't always get it, I do see the beauty in Maths, even poetry, in some way, is Maths, I believe.