#!/usr/bin/ucblogo
; Copyright 2014 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: ucblogo fibonacci-word-fractal.logo
;
; Draw the Fibonacci word fractal. fibonacci.word.fractal draws any
; given number of steps. The self-similar nature of the pattern is
; best seen by making it a Fibonacci number, hence 377 below.
;
; The turns are based on the Fibonacci word values which are 0 or 1.
; Those values are calculated by the least significant bit of the
; fibbinary values. Fibbinary values are integers which have no "11"
; adjacent 1-bits. They're iterated by some bit twiddling.
; Return the low 1-bits of :n
; For example if n = binary 10110111 = 183
; then return binary 111 = 7
to low.ones :n
output ashift (bitxor :n (:n+1)) -1
end
; :fibbinary should be a fibbinary value
; return the next larger fibbinary value
to fibbinary.next :fibbinary
localmake "filled bitor :fibbinary (ashift :fibbinary -1)
localmake "mask low.ones :filled
output (bitor :fibbinary :mask) + 1
end
to fibonacci.word.fractal :steps
localmake "step.length 5 ; length of each step
localmake "fibbinary 0
repeat :steps [
forward :step.length
if (bitand 1 :fibbinary) = 0 [
ifelse (bitand repcount 1) = 1 [right 90] [left 90]
]
make "fibbinary fibbinary.next :fibbinary
]
end
setheading 0 ; initial line North
fibonacci.word.fractal 377
;------------------------------------------------------------------------------
; Print the fibbinary values as iterated by fibbinary.next.
;
; make "fibbinary 0
; repeat 20 [
; print :fibbinary
; make "fibbinary fibbinary.next :fibbinary
; ]