Euclidean rhythm

Euclidean rhythm
You are encouraged to solve this task according to the task description, using any language you may know.

The Euclidean rhythm was proposed by Godfried Toussaint in 2004 and is described in a 2005 paper "The Euclidean Algorithm Generates Traditional Musical Rhythms". It generates many forms of rhythm in music around the world. The program takes 2 integers (m, n) and outputs a binary string with m ones and (n-m) zeros.

As an example, here is how it runs on (5, 13):

• Write 5 ones followed by (13-5) zeros, into 13 groups of 1-digit each:
  • 1 1 1 1 1 | 0 0 0 0 0 0 0 0
• Repeatedly append substitute the second group into the first group:
  • 1 1 1 1 1 | 0 0 0 0 0 0 0 0
  • 10 10 10 10 10 | 0 0 0
  • 100 100 100 10 10 |
• If the first group consists of elements of the same form, then output. Otherwise, divide the first group into two groups of the two forms, and repeat the process:
  • 100 100 100 10 10 |
  • 100 100 100 | 10 10
  • 10010 10010 100 |
• At this point, we can continue the algorithm until only one form remains, but notice that one of the groups has only one element [100], so the algorithm can actually terminate right here and output the concatenation 1001010010100.

Javascript

Copied from here and here, under MIT license.

const E = (k, n) => {
    let s = Array(n).fill(0)
        .map((_, i) => (i < k ? [1] : [0]))

    let d = n - k
    n = Math.max(k, d)
    k = Math.min(k, d)
    let z = d

    while (z > 0 || k > 1) {
        for (let i = 0; i < k; i++)
            s[i].push(...s[s.length - 1 - i])
        s.splice(-k)
        z = z - k
        d = n - k
        n = Math.max(k, d)
        k = Math.min(k, d)
    }

    return s.flat()
}

Output:

> E(3,8)
[1, 0, 0, 1, 0, 0, 1, 0]