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id	title	challengeType	forumTopicId	dashedName
5900f4481000cf542c50ff5b	Problem 220: Heighway Dragon	5	301863	problem-220-heighway-dragon

--description--

Let D_0 be the two-letter string "Fa". For n ≥ 1, derive D_n from D_{n - 1} by the string-rewriting rules:

"a" → "aRbFR"
"b" → "LFaLb"

Thus, D_0 = "Fa", D_1 = "FaRbFR", D_2 = "FaRbFRRLFaLbFR", and so on.

These 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).

Then D_n is an exotic drawing known as the Heighway Dragon of order n. For example, D_{10} is shown below; counting each "F" as one step, the highlighted spot at (18,16) is the position reached after 500 steps.

drawing of the Heighway Dragon after 500 steps

What is the position of the cursor after {10}^{12} steps in D_{50}? Give your answer as a string in the form x,y with no spaces.

--hints--

heighwayDragon() should return a string.

assert(typeof heighwayDragon() === 'string');

heighwayDragon() should return the string 139776,963904.

assert.strictEqual(heighwayDragon(), '139776,963904');

--seed--

--seed-contents--

function heighwayDragon() {

  return true;
}

heighwayDragon();

--solutions--

// solution required

1.7 KiB Raw Blame History