Dragon curve in Racket

Question

I got a little problem here. I want to make the dragon curve using Racket. First, I want to make a list with the turns of the given order of the dragon curve.

For example: The order 3 would give me the list: (list 'R 'R 'L 'R 'R 'L 'L). L means a 90 degree turn to the left and R means a 90 degree turn to the right.

The algorithm for generating the list by a given order is:

1. First order is always a right turn (list 'R)
2. the next order is the previous order plus the element (list 'R) plus the previous order, where the middle symbol is been replaced by an 'L.

So, the second order would be (list 'R 'R 'L)

But I don't really know, how to write this 'algorithm' as (recursive) code.

;;number -> list
;; number 'n' is the order of the dragon curve.
;; (dragon-code 3) should make: (list 'R 'R 'L 'R 'R 'L 'L)
(define (dragon-code n)
  (cond
    [(zero? n) empty]
    [else

I would be thankful for every hint! :)

Answer 1

A literal translation of the text gives:

(define (dragon order)
  (if (= order 1)
      (list 'R)
      (append (dragon (- order 1)) 
              (list 'R)
              (replace-middle-with-L (dragon (- order 1))))))

Implement replace-middle-with-L and test with (dragon 3).