Pi and phi (both irrational numbers) visualized as turn ratios. Also compare e (another irrational number). Select a turn angle ratio. Select pi, or phi (golden ratio). Spacebar to pause. Phi fills space most efficiently and has inherent Fibonacci spirals. Pi spirals around, but is less space filling, because it isn't as irrational a number as Phi. Using seven colors shows the closest denominator approximating pi is seven (22/7 is an approximation to Pi). With Phi, the spirals number as Fibonacci numbers. The ratio of clockwise to clockwise spirals roughly approximate Phi. There are many ways to show off the spirals with colors. If your turn ratio has a whole number N in the denominator, the clones will go out in N straight arms. But pi, golden angle and e, don't have a whole number in the denominator, so what will happen? We also compare 22/7, commonly used to approximate π.
