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 (17 years, 11 months ago) by root
Branch:	MAIN
CVS Tags:	HEAD
Log Message:	* empty log message *
#	Content
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