;; Copyright 2012, 2013 Kevin Ryde
;;
;; This file is part of Math-PlanePath.
;;
;; Math-PlanePath is free software; you can redistribute it and/or modify it
;; under the terms of the GNU General Public License as published by the Free
;; Software Foundation; either version 3, or (at your option) any later
;; version.
;;
;; Math-PlanePath is distributed in the hope that it will be useful, but
;; WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
;; or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
;; for more details.
;;
;; You should have received a copy of the GNU General Public License along
;; with Math-PlanePath. If not, see .
;; Usage: M-x load-file dragon-curve.el
;;
;; And thereafter M-x dragon-picture.
;;
(unless (fboundp 'ignore-errors)
(require 'cl)) ;; Emacs 22 and earlier `ignore-errors'
(defun dragon-ensure-line-above ()
"If point is in the first line of the buffer then insert a new line above."
(when (= (line-beginning-position) (point-min))
(save-excursion
(goto-char (point-min))
(insert "\n"))))
(defun dragon-ensure-column-left ()
"If point is in the first column then insert a new column to the left.
This is designed for use in `picture-mode'."
(when (zerop (current-column))
(save-excursion
(goto-char (point-min))
(insert " ")
(while (= 0 (forward-line 1))
(insert " ")))
(picture-forward-column 1)))
(defun dragon-insert-char (char len)
"Insert CHAR repeated LEN many times.
After each CHAR move point in the current `picture-mode'
direction (per `picture-set-motion' etc).
This is the same as `picture-insert' except in column 0 or row 0
a new row or column is inserted to make room, with existing
buffer contents shifted down or right."
(dotimes (i len)
(dragon-ensure-line-above)
(dragon-ensure-column-left)
(picture-insert char 1)))
(defun dragon-bit-above-lowest-0bit (n)
"Return the bit above the lowest 0-bit in N.
For example N=43 binary \"101011\" has lowest 0-bit at \"...0..\"
and the bit above that is \"..1...\" so return 8 which is that
bit."
(logand n (1+ (logxor n (1+ n)))))
(defun dragon-next-turn-right-p (n)
"Return non-nil if the dragon curve should turn right after segment N.
Segments are numbered from N=0 for the first, so calling with N=0
is whether to turn right at the end of that N=0 segment."
(zerop (dragon-bit-above-lowest-0bit n)))
(defun dragon-picture (len step)
"Draw the dragon curve in a *dragon* buffer.
LEN is the number of segments of the curve to draw.
STEP is the length of each segment, in characters.
Any LEN can be given but a power-of-2 such as 256 shows the
self-similar nature of the curve.
If STEP >= 2 then the segments are lines using \"-\" or \"|\"
characters (`picture-rectangle-h' and `picture-rectangle-v').
If STEP=1 then only \"+\" corners.
There's a `sit-for' delay in the drawing loop to draw the curve
progressively on screen."
(interactive (list (read-number "Length of curve " 256)
(read-number "Each step size " 3)))
(unless (>= step 1)
(error "Step length must be >= 1"))
(switch-to-buffer "*dragon*")
(erase-buffer)
(setq truncate-lines t)
(ignore-errors ;; ignore error if already in picture-mode
(picture-mode))
(dotimes (n len) ;; n=0 to len-1, inclusive
(dragon-insert-char ?+ 1) ;; corner char
(dragon-insert-char (if (zerop picture-vertical-step)
picture-rectangle-h picture-rectangle-v)
(1- step)) ;; line chars
(if (dragon-next-turn-right-p n)
;; turn right
(picture-set-motion (- picture-horizontal-step) picture-vertical-step)
;; turn left
(picture-set-motion picture-horizontal-step (- picture-vertical-step)))
;; delay to display the drawing progressively
(sit-for .01))
(picture-insert ?+ 1) ;; endpoint
(picture-mode-exit)
(goto-char (point-min)))
(dragon-picture 128 2)