limas = [ [ "F", {"F":"F+G","G":"F-G"},10,turtle() ],
[ "F", {"F":"F*F//F*F"},6,turtle() ], # KOCH line
[ "F+F+F+F", {"F":"FF+FF--FF+F"},5,turtle() ],
[ "F+F+F+F", {"F":"FF+F+F-F+FF"},5,turtle() ],
[ "F//F//F", {"F":"F*F//F*F"},5,turtle() ], # KOCH snowflake
[ "F+F+F+F", {"F":"FF+F++F+F"},4,turtle() ],
[ "F+F+F+F", {"F":"FF+F+F+F+F+F-F"},4,turtle() ],
[ "X", {"X":"-YF+XFX+FY-", "Y":"+XF-YFY-FX+"},5,turtle() ], # Hilbert curve
# more plane filling curves
[ "F+XF+F+XF", {"X":"XF-F+F-XF+F+XF-F+F-X"},4,turtle() ],
[ "X", {"X":"XFYFX+F+YFXFY-F-XFYFX", "Y":"YFXFY-F-XFYFX+F+YFXFY"},4,turtle() ],
[ "XF", {"X":"X*YF**YF/FX//FXFX/YF*", "Y":"/FX*YFYF**YF*FX//FX/Y"},4,turtle() ], # GOSPER line
[ "F**F**F", {"F":"F*J++F**F", "J":"JJ"},6,turtle() ],
[ "F*F*F*F*F*F", {"F":"+F/F*F-"},5,turtle({'+':'ro(20);','-':'ro(-20);'}) ],
[ "F*F*F*F*F*F/F/F/F/F/F*F*F*F*F*F", {"F":"+F/F*F-"},4,turtle({'+':'ro(20);','-':'ro(-20);'}) ],
# some examples of plants
[ "+F", {"F":"F[*F]F[/F]F"},5,turtle({'*':'ro(25);','/':'ro(-25);'}) ],
[ "+Y", {"Y":"YFX[*Y][/Y]", "X":"[/F][*F]FX"},7,turtle({'*':'ro(25);','/':'ro(-25);'}) ],
[ "+F", {"F":"FF/[/F*F*F]*[*F/F/F]"},4,turtle({'*':'ro(22.5);','/':'ro(-22.5);'}) ],
# hexagones
[ "F*F*F*F*F*F", {"F":"[//J*G*F*G]J", "G":"[//K*G*F*G]J"},5,turtle() ],
[ "F+F", {"F":"F*FF**F**FF*F"},4,turtle() ]
]
for a,r,g,t in limas:
S = [ lima(a,r,i,t) for i in range(g) ]
# and display them in series
for s in S:
if len(s): # avoid error when list is empty
clear()
draw(Formex(s))
#!/usr/bin/env pyformex
# $Id$
##
## This file is part of pyFormex 0.3 Release Mon Feb 20 21:04:03 2006
## pyFormex is a python implementation of Formex algebra
## Homepage: http://pyformex.berlios.de/
## Distributed under the GNU General Public License, see file COPYING
## Copyright (C) Benedict Verhegghe except where stated otherwise
##
"""Koch line"""
from lima import *
import math
# We use the lima module to create six generations of the Koch line
F = [ Formex(lima("F",{"F":"F*F//F*F"},i,{ 'F' : 'fd();', '*' : 'ro(60);', '/' : 'ro(-60);' })) for i in range(6) ]
# and display them in series
clear()
draw(Formex.concatenate([F[i].scale(math.pow(3,5-i)).translate([0,i*60,0]) for i in range(6)]))
# a variant which dispays the lines as radii of a six-pointed star
#clear()
#draw(Formex.concatenate([F[i].rotate(60*i).scale(math.pow(3,5-i)) for i in range(6)]))