I was curious if I could form a hexagon like the one on Saturn using polar coordinates. Here’s a picture of Saturn’s hexagon from Wikipedia[1]:
My red blob logo[2] uses polar coordinates to form a nice shape. I used the equation r = 5 + cos(5 * angle). I’m going to use the same pattern here, r = base + cos(6 * angle). When base is small, it forms a star shape; when it’s large, it forms a circle. In the middle, it forms a rounded hexagon! I’ve highlighted r = 30 + cos(6 * angle):
A sine wave in polar coordinates can form this shape. There are sine-like waves in Earth’s atmosphere around the poles; they’re called Rossby waves[3].