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

[flamingyawn]

Please Help me out with this one.

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

 

[yenchin]

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

 

[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?

 

[SteveL27]

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?

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.

 

[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?

 

[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.