``````#!/usr/bin/ucblogo

; Copyright 2012, 2013, 2014 Kevin Ryde
;
; This file is part of Math-PlanePath.
;
; Math-PlanePath is free software; you can redistribute it and/or modify it
; 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 <http://www.gnu.org/licenses/>.

; Usage: ucblogo dragon-curve-turns.logo
;
; Plot the dragon curve using bit-twiddling to turn the turtle left or
; right, as described for example in "Turn" of
; Math::PlanePath::DragonCurve and variously elsewhere.
;
; The commented out "dragon.chamfer 256" is an alternative plot with
; the corners rounded off to help see the shape.
;
;
;
; Mark Horney, "Fractals I: Making Recursion Visible", Logo Exchange,
; Volume 9, number 1, September 1990, pages 23-29.
; Mark Horney, "Fractals II: Representation, Logo Exchange, Volume 9,
; number 2, October 1990, pages 26-29.
; http://el.media.mit.edu/logo-foundation/pubs/nlx.html
; http://el.media.mit.edu/logo-foundation/pubs/nlx/v9/Vol9No1.pdf
; http://el.media.mit.edu/logo-foundation/pubs/nlx/v9/Vol9No2.pdf

; Return the bit above the lowest 1-bit in :n.
; If :n = binary "...z100..00" then the return is "z000..00".
; Eg. n=22 is binary 10110 the lowest 1-bit is the "...1." and the return is
; bit above that "..1.," which is 4.
to bit.above.lowest.1bit :n
output bitand :n (1 + (bitxor :n (:n - 1)))
end

; Return angle +90 or -90 for dragon curve turn at point :n.
; The curve is reckoned as starting from n=0 so the first turn is at n=1.
to dragon.turn.angle :n
output ifelse (bit.above.lowest.1bit :n) = 0  [90] [-90]
end

; Draw :steps many segments of the dragon curve.
to dragon :steps
localmake "step.len 12  ; length of each step
repeat :steps [
forward :step.len
left    dragon.turn.angle repcount  ; repcount = 1 to :steps inclusive
]
end

; Draw :steps many segments of the dragon curve, with corners chamfered
; off with little 45-degree diagonals.
; Done this way the vertices don't touch.
to dragon.chamfer :steps
localmake "step.len       12  ; length of each step
localmake "straight.frac  0.5 ; fraction of the step to go straight

localmake "straight.len   :step.len * :straight.frac
localmake "diagonal.len   (:step.len - :straight.len) * sqrt(1/2)

repeat :steps [
localmake "turn  (dragon.turn.angle repcount)/2   ; +45 or -45
forward :straight.len
left    :turn
forward :diagonal.len
left    :turn
]
end

dragon 256
; dragon.chamfer 256
``````