lsys/lib/penrose.l

        // Generation of Penrose aperiodic tilings

        // Thanks to Herb Savage, who showed it was possible to generate those tilings
        // with L-systems and Fractint.

        // Based on decomposition of tilings described in Tilings and Pattern, by
        // Branko Grunbaum and G.C. Shepard, W.H. Freeman and Company, chapter 10

        // Philippe Hurbain
        // 49 rue Jules Fossier
        // 95380 LOUVRES
        // FRANCE


ruleset (
        // by Herb Savage
        // based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
        // Roger Penrose's rhombuses

        Penrose(n)      => attr (delta, 360/10) +WF--XF---YF--ZF, n;
        W       => YF++ZF----XF[-YF----WF]++;
        X       => +YF--ZF[---WF--XF]+;
        Y       => -WF++XF[+++YF++ZF]-;
        Z       => --YF++++WF[+ZF++++XF]--XF;
        F       => ;
)

ruleset (
        // by Philippe Hurbain
        // Penrose's rhombuses, generated by decomposition rules
        // x generate the fat rhombus, y the thin one
        // Individualization of rhombuses allows easy coloring
        // 0.618034 is ({5-1)/2

        Losanges(n)     => attr (delta, 360/10) x, n;
        x       =>  attr (distance, distance*0.618034) +F[|y]--F[|x][|+ attr (distance, distance*0.618034) f attr (distance, distance/0.618034) x]---[x]F--[y]F;
        y       =>  attr (distance, distance*0.618034) ++[x]F|+F[|y]-[y]F|+F[|x];
        F       => f;
)

ruleset (
        // by Philippe Hurbain
        // Simple coloring of Penrose's rhombuses, showing pentagons

        Penta_color(n)  => attr (delta, 360/20) [x]++++[x]++++[x]++++[x]++++[x], n;
        x       =>  attr (distance, distance*0.618034) ++F[ attr (distance, distance*01.1755) -------F][|y]----F[|x];
        x       => [|++ attr (distance, distance*0.618034) f attr (distance, distance/0.618034) x]------[x]F----[y]F;
        y       =>  attr (distance, distance*0.618034) ++++[x]F|++F[|y]--[y]F|++F[|x];
        F       => f;
)

ruleset (
        // by Philippe Hurbain
        // Same as PentaColor, but showing only the coloring

        Penta(n)        => attr (delta, 360/20) [x]++++[x]++++[x]++++[x]++++[x], n;
        x       =>  attr (distance, distance*0.618034) ++f[ attr (distance, distance*01.1755) -------F][|y]----f[|x];
        x       => [|++ attr (distance, distance*0.618034) f attr (distance, distance/0.618034) x]------[x]f----[y]f;
        y       =>  attr (distance, distance*0.618034) ++++[x]f|++f[|y]--[y]f|++f[|x];
        F       => f;
)


ruleset (
        // by Philippe Hurbain
        // Penrose's kites and darts
        // k generates the kite, a generates the dart

        Kites_darts(n)  => attr (delta, 360/10) k, n;
        k       => +[ attr (distance, distance*0.618034) a]F attr (distance, distance*0.618034) ---[-k]F-F---[-k] attr (distance, distance/0.618034) F[ attr (distance, distance*0.618034) |a];
        a       => [ attr (distance, distance*0.618034) k]+F attr (distance, distance*0.618034) [|a]----F+F----[a] attr (distance, distance/0.618034) F;
        F       => f;
)

ruleset (
        // by Philippe Hurbain
        // Penrose's kites and darts, with kites seed

        Kites_darts1(n) => attr (delta, 360/10) [k]++[k]++[k]++[k]++[k], n;
        k       => +[ attr (distance, distance*0.618034) a]F attr (distance, distance*0.618034) ---[-k]F-F---[-k] attr (distance, distance/0.618034) F[ attr (distance, distance*0.618034) |a];
        a       => [ attr (distance, distance*0.618034) k]+F attr (distance, distance*0.618034) [|a]----F+F----[a] attr (distance, distance/0.618034) F;
        F       => f;
)

ruleset (
        // by Philippe Hurbain
        // Penrose's kites and darts, with darts seed

        Kites_darts2(n) => attr (delta, 360/10) [a]++[a]++[a]++[a]++[a], n;
        k       => +[ attr (distance, distance*0.618034) a]F attr (distance, distance*0.618034) ---[-k]F-F---[-k] attr (distance, distance/0.618034) F[ attr (distance, distance*0.618034) |a];
        a       => [ attr (distance, distance*0.618034) k]+F attr (distance, distance*0.618034) [|a]----F+F----[a] attr (distance, distance/0.618034) F;
        F       => f;
)

ruleset (
        // by Philippe Hurbain
        // Penrose's kites and darts, with serpentine coloring

        Kites_darts_color(n)    => attr (delta, 360/10) [k]++[k]++[k]++[k]++[k], n;
        k       => +[ attr (distance, distance*0.618034) a[f--- attr (distance, distance*0.618) F][--f+++ attr (distance, distance*0.618) F]];
        k       => F attr (distance, distance*0.618034) ---[-k]F-F---[-k] attr (distance, distance/0.618034) F[ attr (distance, distance*0.618034) |a];
        a       => [ attr (distance, distance*0.618034) k]+F attr (distance, distance*0.618034) [|a][|f++ attr (distance, distance*0.382) F]----F+;
        a       => F----[a][f-- attr (distance, distance*0.382) F] attr (distance, distance/0.618034) F;
        F       => f;
)


ruleset (
        // by Philippe Hurbain
        // Ammann's coloring of Penrose's rhombuses, giving an
        // aperiodic tiling of 2 pentagons and 1 hexagon

        Ammann_poly_color(n)    => attr (delta, 360/10) x, n;
        x       =>  attr (distance, distance*0.618034) +(36) [ -(9) attr (distance, distance*0.66) F]F[ +(196.5) attr (distance, distance*0.363) F][ +(180) y] -(72) F[ +(180) x];
        x       => [ -(144) attr (distance, distance*0.618034) f attr (distance, distance/0.618034) x] -(108) [ -(36) attr (distance, distance*0.509) F attr (distance, distance*01.18) -(30) F][x]F[ -(153) attr (distance, distance*0.66) F] -(72) [y]F;
        y       =>  attr (distance, distance*0.618034) +(72) [x][ -(36) attr (distance, distance*0.509) F]F -(144) [ -(9) attr (distance, distance*0.66) F]F[ +(180) y][ +(196.5) attr (distance, distance*0.363) F];
        y       =>  -(36) [y]F -(144) F[ +(180) x];
        F       => f;
)

ruleset (
        // by Philippe Hurbain
        // Same as AmmanPolyColor, showing only the
        // pentagon/hexagon tiling

        Ammann_poly(n)  => attr (delta, 360/10) x, n;
        x       =>  attr (distance, distance*0.618034) +(36) [ -(9) attr (distance, distance*0.66) F]f[ +(196.5) attr (distance, distance*0.363) F][ +(180) y] -(72) f[ +(180) x];
        x       => [ -(144) attr (distance, distance*0.618034) f attr (distance, distance/0.618034) x] -(108) [ -(36) attr (distance, distance*0.509) F attr (distance, distance*01.18) -(30) F][x]f[ -(153) attr (distance, distance*0.66) F] -(72) [y]f;
        y       =>  attr (distance, distance*0.618034) +(72) [x][ -(36) attr (distance, distance*0.509) F]f -(144) [ -(9) attr (distance, distance*0.66) F]f[ +(180) y][ +(196.5) attr (distance, distance*0.363) F];
        y       =>  -(36) [y]f -(144) f[ +(180) x];
        F       => f;
)

ruleset (
        // by Philippe Hurbain
        // Penrose's stars and pentagon tiling, generated as
        // a coloring of kites and darts

        Stars_pentas_color(n)   => attr (delta, 360/20) k, n;
        k       => ++[ attr (distance, distance*0.618034) [f- attr (distance, distance*0.5878) [F]------F F++++F]a]F attr (distance, distance*0.618034) ------;
        k       => [--k]F--F------[--k] attr (distance, distance/0.618034) F[ attr (distance, distance*0.618034) |a];
        a       => [ attr (distance, distance*0.618034) k]++F attr (distance, distance*0.618034) [|[f attr (distance, distance*0.5878) +++++++F]a]--------F;
        a       => ++F--------[f attr (distance, distance*0.5878) -------F][a] attr (distance, distance/0.618034) F;
        F       => f;
)

ruleset (
        // by Philippe Hurbain
        // Same as Stars&PentasColor, showing only coloring

        Stars_pentas(n) => attr (delta, 360/20) [k]++++[k]++++[k]++++[k]++++[k], n;
        k       => ++[ attr (distance, distance*0.618034) [f- attr (distance, distance*0.5878) [F]------F F++++F]a]f attr (distance, distance*0.618034) ------;
        k       => [--k]f--f------[--k] attr (distance, distance/0.618034) f[ attr (distance, distance*0.618034) |a];
        a       => [ attr (distance, distance*0.618034) k]++f attr (distance, distance*0.618034) [|[f attr (distance, distance*0.5878) +++++++F]a]--------f;
        a       => ++f--------[f attr (distance, distance*0.5878) -------F][a] attr (distance, distance/0.618034) f;
        F       => f;
)


ruleset (
        // by Philippe Hurbain
        // Penrose's stars and pentagons, generated from
        // decomposition rules
        // u is the star, v is the boat, w is the thin rhombus
        // x, y and z are the pentagons

        Stars_pentas1(n)        => attr (delta, 360/10) u, n;
        u       =>  attr (distance, distance*0.381966) [v]F[|y][-u]++F|+[v]F[|y]++F|+[v]F[|y]++F|+;
        u       => [v]F[|y]++F|+[v]F[|y]++F;
        v       =>  attr (distance, distance*0.381966) [v]F[|y]++F|+[v]F[|y]-[u]F-F|+[v]F[|y]++F;
        w       =>  attr (distance, distance*0.381966) f++[u]F|+F-F|+[v]F[|y];
        y       =>  attr (distance, distance*0.381966) [x][y][w]F[|!y]++F++[y][w]F[|!y]++F++[z]F;
        x       =>  attr (distance, distance*0.381966) f++f++[!x][!z]F--[!z]F--[!z]F--[!z]F--[!z]F;
        z       =>  attr (distance, distance*0.381966) [z][x]F++[z]F++[w][y]F[|!y]++F++[z]F;
        F       => f;
)

Revision:	1.1
Committed:	Thu Nov 6 14:31:25 2008 UTC (15 years, 7 months ago) by root
Branch:	MAIN
CVS Tags:	HEAD
Log Message:	* empty log message *
#	User	Rev	Content
1	root	1.1	// Generation of Penrose aperiodic tilings
2
3			// Thanks to Herb Savage, who showed it was possible to generate those tilings
4			// with L-systems and Fractint.
5
6			// Based on decomposition of tilings described in Tilings and Pattern, by
7			// Branko Grunbaum and G.C. Shepard, W.H. Freeman and Company, chapter 10
8
9			// Philippe Hurbain
10			// 49 rue Jules Fossier
11			// 95380 LOUVRES
12			// FRANCE
13
14
15			ruleset (
16			// by Herb Savage
17			// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
18			// Roger Penrose's rhombuses
19
20			Penrose(n) => attr (delta, 360/10) +WF--XF---YF--ZF, n;
21			W => YF++ZF----XF[-YF----WF]++;
22			X => +YF--ZF[---WF--XF]+;
23			Y => -WF++XF[+++YF++ZF]-;
24			Z => --YF++++WF[+ZF++++XF]--XF;
25			F => ;
26			)
27
28			ruleset (
29			// by Philippe Hurbain
30			// Penrose's rhombuses, generated by decomposition rules
31			// x generate the fat rhombus, y the thin one
32			// Individualization of rhombuses allows easy coloring
33			// 0.618034 is ({5-1)/2
34
35			Losanges(n) => attr (delta, 360/10) x, n;
36			x => attr (distance, distance0.618034) +F[\|y]--F[\|x][\|+ attr (distance, distance0.618034) f attr (distance, distance/0.618034) x]---[x]F--[y]F;
37			y => attr (distance, distance*0.618034) ++[x]F\|+F[\|y]-[y]F\|+F[\|x];
38			F => f;
39			)
40
41			ruleset (
42			// by Philippe Hurbain
43			// Simple coloring of Penrose's rhombuses, showing pentagons
44
45			Penta_color(n) => attr (delta, 360/20) [x]++++[x]++++[x]++++[x]++++[x], n;
46			x => attr (distance, distance0.618034) ++F[ attr (distance, distance01.1755) -------F][\|y]----F[\|x];
47			x => [\|++ attr (distance, distance*0.618034) f attr (distance, distance/0.618034) x]------[x]F----[y]F;
48			y => attr (distance, distance*0.618034) ++++[x]F\|++F[\|y]--[y]F\|++F[\|x];
49			F => f;
50			)
51
52			ruleset (
53			// by Philippe Hurbain
54			// Same as PentaColor, but showing only the coloring
55
56			Penta(n) => attr (delta, 360/20) [x]++++[x]++++[x]++++[x]++++[x], n;
57			x => attr (distance, distance0.618034) ++f[ attr (distance, distance01.1755) -------F][\|y]----f[\|x];
58			x => [\|++ attr (distance, distance*0.618034) f attr (distance, distance/0.618034) x]------[x]f----[y]f;
59			y => attr (distance, distance*0.618034) ++++[x]f\|++f[\|y]--[y]f\|++f[\|x];
60			F => f;
61			)
62
63
64			ruleset (
65			// by Philippe Hurbain
66			// Penrose's kites and darts
67			// k generates the kite, a generates the dart
68
69			Kites_darts(n) => attr (delta, 360/10) k, n;
70			k => +[ attr (distance, distance0.618034) a]F attr (distance, distance0.618034) ---[-k]F-F---[-k] attr (distance, distance/0.618034) F[ attr (distance, distance*0.618034) \|a];
71			a => [ attr (distance, distance0.618034) k]+F attr (distance, distance0.618034) [\|a]----F+F----[a] attr (distance, distance/0.618034) F;
72			F => f;
73			)
74
75			ruleset (
76			// by Philippe Hurbain
77			// Penrose's kites and darts, with kites seed
78
79			Kites_darts1(n) => attr (delta, 360/10) [k]++[k]++[k]++[k]++[k], n;
80			k => +[ attr (distance, distance0.618034) a]F attr (distance, distance0.618034) ---[-k]F-F---[-k] attr (distance, distance/0.618034) F[ attr (distance, distance*0.618034) \|a];
81			a => [ attr (distance, distance0.618034) k]+F attr (distance, distance0.618034) [\|a]----F+F----[a] attr (distance, distance/0.618034) F;
82			F => f;
83			)
84
85			ruleset (
86			// by Philippe Hurbain
87			// Penrose's kites and darts, with darts seed
88
89			Kites_darts2(n) => attr (delta, 360/10) [a]++[a]++[a]++[a]++[a], n;
90			k => +[ attr (distance, distance0.618034) a]F attr (distance, distance0.618034) ---[-k]F-F---[-k] attr (distance, distance/0.618034) F[ attr (distance, distance*0.618034) \|a];
91			a => [ attr (distance, distance0.618034) k]+F attr (distance, distance0.618034) [\|a]----F+F----[a] attr (distance, distance/0.618034) F;
92			F => f;
93			)
94
95			ruleset (
96			// by Philippe Hurbain
97			// Penrose's kites and darts, with serpentine coloring
98
99			Kites_darts_color(n) => attr (delta, 360/10) [k]++[k]++[k]++[k]++[k], n;
100			k => +[ attr (distance, distance0.618034) a[f--- attr (distance, distance0.618) F][--f+++ attr (distance, distance*0.618) F]];
101			k => F attr (distance, distance0.618034) ---[-k]F-F---[-k] attr (distance, distance/0.618034) F[ attr (distance, distance0.618034) \|a];
102			a => [ attr (distance, distance0.618034) k]+F attr (distance, distance0.618034) [\|a][\|f++ attr (distance, distance*0.382) F]----F+;
103			a => F----[a][f-- attr (distance, distance*0.382) F] attr (distance, distance/0.618034) F;
104			F => f;
105			)
106
107
108			ruleset (
109			// by Philippe Hurbain
110			// Ammann's coloring of Penrose's rhombuses, giving an
111			// aperiodic tiling of 2 pentagons and 1 hexagon
112
113			Ammann_poly_color(n) => attr (delta, 360/10) x, n;
114			x => attr (distance, distance0.618034) +(36) [ -(9) attr (distance, distance0.66) F]F[ +(196.5) attr (distance, distance*0.363) F][ +(180) y] -(72) F[ +(180) x];
115			x => [ -(144) attr (distance, distance0.618034) f attr (distance, distance/0.618034) x] -(108) [ -(36) attr (distance, distance0.509) F attr (distance, distance01.18) -(30) F][x]F[ -(153) attr (distance, distance0.66) F] -(72) [y]F;
116			y => attr (distance, distance0.618034) +(72) [x][ -(36) attr (distance, distance0.509) F]F -(144) [ -(9) attr (distance, distance0.66) F]F[ +(180) y][ +(196.5) attr (distance, distance0.363) F];
117			y => -(36) [y]F -(144) F[ +(180) x];
118			F => f;
119			)
120
121			ruleset (
122			// by Philippe Hurbain
123			// Same as AmmanPolyColor, showing only the
124			// pentagon/hexagon tiling
125
126			Ammann_poly(n) => attr (delta, 360/10) x, n;
127			x => attr (distance, distance0.618034) +(36) [ -(9) attr (distance, distance0.66) F]f[ +(196.5) attr (distance, distance*0.363) F][ +(180) y] -(72) f[ +(180) x];
128			x => [ -(144) attr (distance, distance0.618034) f attr (distance, distance/0.618034) x] -(108) [ -(36) attr (distance, distance0.509) F attr (distance, distance01.18) -(30) F][x]f[ -(153) attr (distance, distance0.66) F] -(72) [y]f;
129			y => attr (distance, distance0.618034) +(72) [x][ -(36) attr (distance, distance0.509) F]f -(144) [ -(9) attr (distance, distance0.66) F]f[ +(180) y][ +(196.5) attr (distance, distance0.363) F];
130			y => -(36) [y]f -(144) f[ +(180) x];
131			F => f;
132			)
133
134			ruleset (
135			// by Philippe Hurbain
136			// Penrose's stars and pentagon tiling, generated as
137			// a coloring of kites and darts
138
139			Stars_pentas_color(n) => attr (delta, 360/20) k, n;
140			k => ++[ attr (distance, distance0.618034) [f- attr (distance, distance0.5878) [F]------F F++++F]a]F attr (distance, distance*0.618034) ------;
141			k => [--k]F--F------[--k] attr (distance, distance/0.618034) F[ attr (distance, distance*0.618034) \|a];
142			a => [ attr (distance, distance0.618034) k]++F attr (distance, distance0.618034) [\|[f attr (distance, distance*0.5878) +++++++F]a]--------F;
143			a => ++F--------[f attr (distance, distance*0.5878) -------F][a] attr (distance, distance/0.618034) F;
144			F => f;
145			)
146
147			ruleset (
148			// by Philippe Hurbain
149			// Same as Stars&PentasColor, showing only coloring
150
151			Stars_pentas(n) => attr (delta, 360/20) [k]++++[k]++++[k]++++[k]++++[k], n;
152			k => ++[ attr (distance, distance0.618034) [f- attr (distance, distance0.5878) [F]------F F++++F]a]f attr (distance, distance*0.618034) ------;
153			k => [--k]f--f------[--k] attr (distance, distance/0.618034) f[ attr (distance, distance*0.618034) \|a];
154			a => [ attr (distance, distance0.618034) k]++f attr (distance, distance0.618034) [\|[f attr (distance, distance*0.5878) +++++++F]a]--------f;
155			a => ++f--------[f attr (distance, distance*0.5878) -------F][a] attr (distance, distance/0.618034) f;
156			F => f;
157			)
158
159
160			ruleset (
161			// by Philippe Hurbain
162			// Penrose's stars and pentagons, generated from
163			// decomposition rules
164			// u is the star, v is the boat, w is the thin rhombus
165			// x, y and z are the pentagons
166
167			Stars_pentas1(n) => attr (delta, 360/10) u, n;
168			u => attr (distance, distance*0.381966) [v]F[\|y][-u]++F\|+[v]F[\|y]++F\|+[v]F[\|y]++F\|+;
169			u => [v]F[\|y]++F\|+[v]F[\|y]++F;
170			v => attr (distance, distance*0.381966) [v]F[\|y]++F\|+[v]F[\|y]-[u]F-F\|+[v]F[\|y]++F;
171			w => attr (distance, distance*0.381966) f++[u]F\|+F-F\|+[v]F[\|y];
172			y => attr (distance, distance*0.381966) [x][y][w]F[\|!y]++F++[y][w]F[\|!y]++F++[z]F;
173			x => attr (distance, distance*0.381966) f++f++[!x][!z]F--[!z]F--[!z]F--[!z]F--[!z]F;
174			z => attr (distance, distance*0.381966) [z][x]F++[z]F++[w][y]F[\|!y]++F++[z]F;
175			F => f;
176			)
177