# Peano Curves

1. Apr 26, 2005

### Ed Quanta

Can anyone point me towards an online link or some books where I can study these bad boys? I am supposed to write like a 5-10 page paper on Peano curves in which I prove a few interesting things regarding them.

2. Apr 26, 2005

### saltydog

"Chaos and Fractals", by Peitgen, et.al. I quote:

"In Nature, the organization of space-filling structures is one of the fundamendal buliding blocks of living beings". You know, lungs, kidneys, vascular system. But I digress. Suppose you just want to prove how they fill the plane. Looks like a good N-epsilon proof. Like, for any (x,y) in the plane, curve comes epsilon distance away from it whenever the iteration is greater than N. Thus as N goes to infinity, distance goes to zero. Never proved it though. Suppose Peano and Hilbert did.