Computing and plotting the cantor function

I wanted to implement the cantor function in R and plot it. I only know Python and Java so R is new for me. The cantor function is defined as:

---

Let f0(x) = x.

Then, for every integer n ≥ 0, the next function fn+1(x) will be defined in terms of fn(x) as follows:

Let fn+1(x) = 1/2 × fn(3x), when 0 ≤ x ≤ 1/3 ;

Let fn+1(x) = 1/2, when 1/3 ≤ x ≤ 2/3 ;

Let fn+1(x) = 1/2 + 1/2 × fn(3 x − 2), when 2/3 ≤ x ≤ 1.

---

This is my code:

cantor <- function(x,n){
  if (n==0){
    return(x)
  }else{
    if(0 <= x & x <= 1/3){
      return(1/2*cantor(3*x,n-1))
  }else if(1/3 < x & x < 2/3){
    return(1/2)
  }else{
    return(1/2+1/2*cantor(3*x-2,n-1))
  }
  }
}

which works well as long as it has an single input. But if I try to plot it over x=seq(0,1,0.01) it does not work because my conditions are for single inputs but R gives the whole vector x to my function.

Is there a way to have only an single input over an vector or how do I rewrite my code so it works.