Polar coordinates are beautiful

Just go over to desmos and type a random equation with polar coordinates. There is a very good chance, you see something visually interesting.

Examples (try with −12π ≤ θ ≤ 12π):

• r = θ: the simplest form is already a spiral
• r = θ²: sqaure it, something that looks like infinite hear shapes
• r = e^θ: try zooming into it, it goes on forever
• r = sin (0.3θ): some floral shape. mess around with the factor (0.3) to watch it unravel in really cool ways.
• r = e^{θ(sin (θ)cos (θ))6}: would make a really cool visualizer for music

Designing a logo? Just play around with polar coordinates till you find a shape inside it that looks interesting. Won't take long.