ツインドラゴンに関する発見と実装 ref: http://qiita.com/butchi_y/items/4f0bd72f4b322d4943b6

twindragon.js

var i, j;
var x = [0];
var y = [0];
var nextX = [];
var nextY = [];
for(j=0; j<4; j++) {
  l = x.length-1;
  for(i=0; i<x.length; i++) {
    nextX[i] = x[i] + 1 - y[l];
    nextY[i] = y[i] + x[l];
  }
  x = x.concat(nextX);
  y = y.concat(nextY);
}
console.log(x);
console.log(y);

twindragon.nb

Graphics[Point[
  Transpose[{Re[#], Im[#]} &[
    Nest[Join[#, # + 1 - Im[Last[#]] + Re[Last[#]] I] &, {0}, 10]
  ]]
]]