Making Mathematics: Inspi Research Project

Here’s a Logo program that draws some shapes:


								to inspi :s :a :i 

								  fd :s rt :a 

								  inspi :s :a+:i :i 

								end

Sometimes inspi produces a shape that is "back and forth": (The numbers under the pictures show the inputs.)

What about the patterns you get when you divide by other numbers?

curve bending back and forth, like one or more copies of the letter S, connected together

Sometimes the shape is poly-like:

And sometimes it just marches away, never to be seen again:

Are other behaviors possible? Develop a theory to explain how the shapes depend on the inputs.