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

1. Jul 20, 2011

flamingyawn

Can all patterns in 2D or 3D, have an equivalent equation in polynomial?

2. Jul 20, 2011

yenchin

Would you like to elaborate on what you mean by that?

3. Jul 20, 2011

flamingyawn

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?

4. Jul 20, 2011

SteveL27

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.

5. Jul 20, 2011

pmsrw3

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?

6. Jul 20, 2011

Mentallic

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.