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

In summary, the question is about whether all patterns in 2D or 3D can have an equivalent equation in polynomial form. The conversation discusses the possibility of creating equations for repeating patterns like fractals and whether patterns generated by exponential or trig functions would count. It is also mentioned that there may not be a repeating pattern that can be represented by a polynomial in Cartesian coordinates. The conversation concludes with considering the possibility that the question may be about whether patterns can be generated in polynomial time.
  • #1
flamingyawn
12
0
Please Help me out with this one.

Can all patterns in 2D or 3D, have an equivalent equation in polynomial?
 
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  • #2
Would you like to elaborate on what you mean by that?
 
  • #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?
 
  • #4
flamingyawn said:
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.
 
  • #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?
 
  • #6
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.
 

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

1. Can all 3D patterns be expressed using polynomial equations?

No, not all 3D patterns can be expressed using polynomial equations. Some complex or fractal patterns may require more complex mathematical equations to accurately represent them.

2. What is the relationship between 3D patterns and polynomial equations?

Polynomial equations can be used to represent certain 3D patterns, but not all of them. It ultimately depends on the complexity and nature of the pattern.

3. Are there any limitations to using polynomial equations for 3D patterns?

Yes, there are limitations to using polynomial equations for 3D patterns. As mentioned before, some patterns may require more complex equations or may not be accurately represented by polynomials at all.

4. How do scientists determine which polynomial equation to use for a given 3D pattern?

Scientists use various mathematical techniques and algorithms to analyze and understand 3D patterns. Based on their findings, they may determine which polynomial equation best represents the pattern.

5. Can 3D patterns be represented using non-polynomial equations?

Yes, 3D patterns can also be represented using non-polynomial equations, such as exponential or trigonometric equations. It ultimately depends on the nature and complexity of the pattern.

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