Medium randomness · simulation · curves

A seeded random walk

A drunk ant that is perfectly repeatable, because you chose its dice.

Write walk(steps, seed). Return the path of a random walk on the integer grid as an array of steps + 1 points [x, y], starting at [0, 0]. Call show(points) after each point is added so the path draws as it wanders.

The walk uses its own dice, not Math.random, so every run is the same. Keep a state s that starts at seed. Before each step, update it with s = (s * 48271) % 2147483647, then pick a direction from s % 4: 0 moves right (x + 1), 1 moves down (y + 1), 2 moves left (x - 1), 3 moves up (y - 1). Here y grows downward, like the screen.

Example: walk(3, 1) updates s to 48271 (48271 % 4 is 3, up), then 182605794 (2, left), then 1291394886 (2, left). It returns [[0, 0], [0, -1], [-1, -1], [-2, -1]].

Tests you can see

walk(3, 1)[[0,0],[0,-1],[-1,-1],[-2,-1]]
walk(40, 2026)[[0,0],[-1,0],[0,0],[-1,0],[0,0],[0,-1],[-1,-1],[-1,0],[0,0],[-1,0],[0,0],[0,-1],[0,0],[0,1],[-1,1],[-1,2],[-2,2],[-3,2],[-2,2],[-2,3],[-1,3],[-1,4],[-1,5],[-2,5],[-1,5],[0,5],[1,5],[1,6],[0,6],[0,5],[0,6],[-1,6],[0,6],[-1,6],[-1,5],[-1,6],[-2,6],[-1,6],[0,6],[-1,6],[-1,5]]

More tests are hidden. The server runs them all before a time counts.

Call show() while your code works and the run plays back here.

javascriptwalk()

function walk(steps, seed) {
  let s = seed;
  const points = [[0, 0]];
  // update s, then move in direction s % 4
  return points;
}

function walk(steps, seed) {
  let s = seed;
  const points = [[0, 0]];
  // update s, then move in direction s % 4
  return points;
}

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