General function in 2 variables

[Emilijo]

Homework Statement

I need to get a general function in 2 variables f(m,n).
The task is to find a general function f(m,n) with these terms:
The function has to be periodic.
The function has to include those blue and red points in each example.
The value of the function has to be f(m,n) =1 ONLY in blue points, and the value of the function has to be f(m,n)=0 ONLY in red points.

The look of the function isn't important as long as it complies with previous terms.

Homework Equations

You can see a graphicon with charasteristic points:
In the first example m=2 (m is period).

In the next example m=3:

For m=4:

and so on.

The Attempt at a Solution

In first example (for m=2) I used functions: sin and absolute, but for all other m,
it is not possible with only those functions, I also tried use the Fourier series but I don't have so
much knowledge in mathematics to built a such function.
Does somebody know how to do it?

 

[Ray Vickson]

Homework Statement

I need to get a general function in 2 variables f(m,n).
The task is to find a general function f(m,n) with these terms:
The function has to be periodic.
The function has to include those blue and red points in each example.
The value of the function has to be f(m,n) =1 ONLY in blue points, and the value of the function has to be f(m,n)=0 ONLY in red points.

The look of the function isn't important as long as it complies with previous terms.

Homework Equations

You can see a graphicon with charasteristic points:
In the first example m=2 (m is period).

In the next example m=3:

For m=4:

and so on.

The Attempt at a Solution

What have you done so far? You must show some work and exhibit some effort before receiving help in this Forum.

RGV

 

[Emilijo]

What have you done so far? You must show some work and exhibit some effort before receiving help in this Forum.

RGV

I tried and wrote about it above in previous post.

 

[Ray Vickson]

I tried and wrote about it above in previous post.

Your previous post did not show any work; it just said you had tried some things, but did not show exactly what you did.

RGV