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Peano Curves

  1. Apr 26, 2005 #1
    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. jcsd
  3. Apr 26, 2005 #2


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    "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.
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