yaworsw/euler-manager

---
:id: 220
:name: Heighway Dragon
:url: https://projecteuler.net/problem=220
:content: "Let **_D_** <sub>0</sub> be the two-letter string \"Fa\". For n≥1, derive
  **_D_** <sub>n</sub> from **_D_** <sub>n-1</sub> by the string-rewriting rules:\n\n\"a\"
  → \"aRbFR\"  \n\"b\" → \"LFaLb\"\n\nThus, **_D_** <sub>0</sub> = \"Fa\", **_D_**
  <sub>1</sub> = \"FaRbFR\", **_D_** <sub>2</sub> = \"FaRbFRRLFaLbFR\", and so on.\n\nThese
  strings can be interpreted as instructions to a computer graphics program, with
  \"F\" meaning \"draw forward one unit\", \"L\" meaning \"turn left 90 degrees\",
  \"R\" meaning \"turn right 90 degrees\", and \"a\" and \"b\" being ignored. The
  initial position of the computer cursor is (0,0), pointing up towards (0,1).\n\nThen
  **_D_** <sub>n</sub> is an exotic drawing known as the _Heighway Dragon_ of order
  _n_. For example, **_D_** <sub>10</sub> is shown below; counting each \"F\" as one
  step, the highlighted spot at (18,16) is the position reached after 500 steps.\n\n
  ![]({{ images_dir }}/p220.gif)\n\nWhat is the position of the cursor after 10<sup>12</sup>
  steps in **_D_** <sub>50</sub> ?  \nGive your answer in the form _x_,_y_ with no
  spaces.\n\n"