Shannon entropy quine generator....

equine.js

//Entropy quine generator....
//of course it all depends on precision...

function display(entropy) {
  return 'Shannon entropy of this text is about ' + entropy; //+', 2X entropy: '+(2*entropy);
}

var precision = 15;
var maxTriesPerIter = 400;
var maxIters = 400;

/////////////////////////////

var bestDiff = Infinity;
var diffNow = 0;
var delta = Math.pow(10, precision - 2);

outer: while (maxIters-->0) {
  var iter = 0,
    cand = Math.random(),
    bestCand = '';

  while (iter++ < maxTriesPerIter) {
    var real = parseFloat(entropy(display(cand)).toFixed(precision));
    if (cand == real) {
      console.log('Exact match!!!', cand);
      console.log(display(cand));
      break outer;
    } else {
      diffNow = Math.abs(cand - real);

      if (diffNow < bestDiff) {
        bestDiff = diffNow;
        bestCand = cand;

        console.log('New best candidate', cand, diffNow);
      }

      cand = parseFloat((real - (Math.random() - 0.5) / delta).toFixed(precision));
    }
  }
}

//entropy function taken from zb3.strefa.pl/tools.html

function entropy(str) {
  var countMap = [],
    c;
  var ret = 0;

  for (var t = 0; t < str.length; t++) {
    c = str.charCodeAt(t);
    countMap[c] = (countMap[c] || 0) + 1;
  }

  var ckeys = Object.keys(countMap),
    p;
  for (var t = 0; t < ckeys.length; t++) {
    p = countMap[ckeys[t]] / str.length;
    ret += p * Math.log(p);
  }

  ret /= Math.log(2);

  return -ret;
}

Shannon entropy of this text is about 4.399250396597324