What's "really really" awesome about Fibonacci spirals? They're just log spirals whose growth factor is phi. I can generate an infinite number of log spirals with different ratios. What's so awesome about generating them with a ratio of (one plus root five) over two? Would one generated with a ratio of pi be even more awesome? what about e?

Sure, phi is the solution to x - 1 = 1 / x. That just means it's the solution to x^2 - x - 1 = 0. It's just the answer to a polynomial. It's not even the unique answer! both phi and 1/phi answer it.

What about x^3 - x^2 - x - 1 = 0? That seems to be related, and it has a unique real solution - 1.839. Maybe that number has magic properties when used as the ratio for a log spiral?