One-dimensional Perlin noise

Above you see a wiggly white line. The white line is generated by joining up the red tangent lines. These tangent lines are regularly spaced with random slopes. This technique, apparently, is the heart of “Perlin noise”. Perlin noise is a way to make “naturalistic” random fluctuation.

const slopeAt = [];
for (let i = 0; i < 10; i++) {
  slopeAt[i] = (Math.random()*2)-1;
}

function samplePerlin(x) {
  const lo = Math.floor(x);
  const hi = lo+1;
  const dist = x-lo;
  loSlope = slopeAt[lo];
  hiSlope = slopeAt[hi];
  loPos = loSlope * dist;
  hiPos = -hiSlope * (1-dist);
  const u = dist * dist * (3.0 - 2.0 * dist);  // cubic curve
  return (loPos*(1-u)) + (hiPos*u);  // interpolate
}

The image above is one “octave” of Perlin noise. More realistic naturalism is generated by summing several octaves. I’ll do that in a future post.

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