How to apply function over each matrix element's indices

I am wondering if there is a built-in function in R which applies a function to each element of the matrix (of course, the function should be computed based on matrix indices). The equivalent would be something like this:

matrix_apply <- function(m, f) {
  m2 <- m
  for (r in seq(nrow(m2)))
    for (c in seq(ncol(m2)))
      m2[[r, c]] <- f(r, c)
  return(m2)
}

If there is no such built-in function, what is the best way to initialize a matrix to contain values obtained by computing an arbitrary function which has matrix indices as parameters?