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Can all patterns in 3D have an equivalent equation in polynomial?

  1. Jul 20, 2011 #1
    Please Help me out with this one.

    Can all patterns in 2D or 3D, have an equivalent equation in polynomial?
     
  2. jcsd
  3. Jul 20, 2011 #2
    Would you like to elaborate on what you mean by that?
     
  4. Jul 20, 2011 #3
    for example the is a pattern in 3 Dimensional form. An obviously repeating or sequence of pattern like fractals. Can we create an equation for that pattern in polynomial?
     
  5. Jul 20, 2011 #4
    Would it count if a pattern were the result of an exponential or trig function? y = sin x is a pretty nice 2D pattern, but it's not generated by any polynomial. If you wanted 3D you could do something similar.
     
  6. Jul 20, 2011 #5
    Actually, I can't think of any repeating pattern that would be represented by a polynomial (at least in Cartesian coordinates). Maybe I don't understand what you mean by "have an equivalent equation in polynomial". Did you have some particular example in mind when you asked this question?
     
  7. Jul 20, 2011 #6

    Mentallic

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    I thought for a second that maybe the OP meant to ask if the patterns be generated in polynomial time, but I re-read the first post and I doubt he did mean that.
     
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