dragon curve ascii art

dragon-curve.lisp

(defun f1 (z) (* z #C(1/2 1/2)))
(defun f2 (z) (- 1 (* z #C(1/2 -1/2))))
(defun c2p (z) (list (realpart z) (imagpart z)))

(defun gen (n)
  (let ((b (expt 2 (ash (1+ n) -1))))
    (loop
      for i from 0 to n
      for s = (list (list 0 1))
      then (mapcan (lambda (l) (list (mapcar #'f1 l) (mapcar #'f2 l))) s)
      finally
      (return (mapcar (lambda (l) (mapcar (lambda (z) (c2p (* b z))) l)) s)))))

(defun rng (s)
  (let ((xlb 0) (xub 0) (ylb 0) (yub 0))
    (loop for ((sx sy) (ex ey)) in s
      do (setq xlb (min xlb sx ex)
	       xub (max xub sx ex)
	       ylb (min ylb sy ey)
	       yub (max yub sy ey))
      finally (return (values xlb xub ylb yub)))))

(defun dragon-curve (n)
  (let ((s (gen (1+ (* n 2)))))
    (multiple-value-bind (xlb xub ylb yub) (rng s)
      (let* ((w (- xub xlb))
	     (h (- yub ylb))
	     (a (format nil (format nil "~~V@{~V@{ ~}~~%~~}" w t) h t)))
	(dolist (l s)
	  (let* ((m (sort l #'< :key #'car))
		 (x (caar m))
		 (y (min (cadar m) (cadadr m)))
		 (c (char "/\\" (/ (1+ (- (cadadr m) (cadar m))) 2))))
	    (setf (char a (+ (- x xlb) (* (1+ w) (- y ylb)))) c)))
	(format t "~A" a)))))


#+:sbcl
(let ((n (if #0=(cadr sb-ext:*posix-argv*)
	   (parse-integer #0#)
	   5)))
  (dragon-curve n))

dragon-curve.rb

def dragon_curve(n)
  s = [[0, 1]]
  (n*2+1).times{
    s = s.collect_concat{|l|
      [l.map{|z| z*(1+1i)/2r}, l.map{|z| 1-(z*(1-1i)/2r) }]
    }
  }
  m = 2**(n+1)
  l = r = t = b = 0
  s.map!{|s, e|
    s *= m
    e *= m
    l, r = [l, r, s.real, e.real].minmax
    t, b = [t, b, s.imag, e.imag].minmax
    s.real < e.real ? [s, e] : [e, s]
  }
  w = r - l
  h = b - t
  a = (" " * w + "\n") * h
  s.each{|s, e|
    x = s.real
    y = [s.imag, e.imag].min
    dy = e.imag-s.imag
    a[x-l+(w+1)*(y-t)] = "/\\"[(1+dy)/2]
  }
  a
end

def main(args)
  wide = false
  n = 4
  args.each{|a|
    case a
    when "-w" then wide = true
    when /^\d+$/ then n = a.to_i
    end
  }
  aa = dragon_curve(n)
  if wide
    aa.tr!(" /\\", "　／＼")
  end
  puts aa
end

main($*)

$ sbcl --script dragon-curve.lisp 4
                               /\/\    /\/\    
                               \/\/    \/\/    
                             /\/\    /\/\      
                             \/\/    \/\/      
                               /\/\/\/\/\/\/\/\
    /\  /\                     \/\/\  /\  /\/\/
    \/  \/                   /\/\/\/  \/  \/\  
    /\/\/\/\                 \/\/\/\        /  
    \/\    /           /\/\    /\/\/        \/\
/\  /\/    \           \/\/    \  /\        /\/
\/  \     \/         /\/\    /\/  \/     /  \  
/\/\/                \/\/    \/\         \/\/  
\/\/\/\                /\/\/\/\/               
  /\/\/                \/\/\/\/\/\             
  \/\                /\/\/\/\/\/\/             
    /                \/\/\/\/\/\/\/\           
    \/\/\/\    /\/\    /\/\/\/\/\/\/           
/\  /\/\/\/    \/\/    \/\/\/\/\  /\           
\/  \/\/\    /\/\    /\/\/\/\/\/  \/           
/\/\/\/\/    \/\/    \/\/\/\/\/\               
\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/               
  /\  /\  /\/\/\/\/\  /\  /\/\/\/\             
  \/  \/  \/\/\/\/\/  \/  \/\/\/\/             
            /\/\/\/\        /\/\/\/\           
            \/\/\/\/        \/\/\/\/           
        /\  /\/\  /\    /\  /\/\  /\           
        \/  \/\/  \/    \/  \/\/  \/           
        /\/\/\/\        /\/\/\/\               
        \/\/\/\/        \/\/\/\/               
          /\  /\          /\  /\               
          \/  \/          \/  \/