Markov Chain

You might want to generate pseudo random data based on a small sample. Markov Chains can allow you to do just that.

Read an input, and calculate the probability of, in this example, a third token following two others. Then generate random numbers and pick from the weighted list of options

Given the input string input = "aaabbbbbaaabbbbbbbbaa" you will notice short clusters of a followed by longer clusters of b.

Result:

Note that I am using a sliding window of size 2 to get a high resemblence of the clustering behavior from the input. So given aa as an input, what is a likely next token?

const createLookup = (input) => {
  const lookup = {}
  let j = 0
  for (let i = 1; i < input.length - 1; i++) {
    const k = input[j] + input[i]
    const result = input[i+1]
    if (!lookup[k]) {
      lookup[k] = {[result]: 1}
    } else {
      lookup[k][result] = 1 + lookup[k][result] || 0
    }
    j = i
  }
  return lookup
}

const nextToken = (k) => {
  const ratio = lookup[k]
  const rnd = Math.random()
  const total = Object.values(ratio).reduce((acc, el) => acc + el)
  let seen = 0
  for (let [k, v] of Object.entries(ratio)) {
     seen += v/total
     if (rnd < seen) {
       return k
     }
  }
}

const lookup = createLookup(input)

// You need something to start with - I am using ab as a seed here
let output = "ab"

for (let i = 0; i < 50; i++) {
  output += nextToken(output.slice(-2))
}

document.getElementById("result").innerHTML = output