| 1 |
|
| 2 |
ruleset ( // by Herb Savage |
| 3 |
// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", |
| 4 |
// Roger Penrose's kites and darts |
| 5 |
|
| 6 |
Kites_and_darts(n) => attr (delta, 360/10) Wf+Xf+Wf+Xf+Wf+Xf+Wf+Xf+Wf+X, n; |
| 7 |
W => [F][++ attr (distance, distance*01.618033989) F][++f--- attr (distance, distance*0.618033989) f|X-Y|f|W]; |
| 8 |
X => [F+++ attr (distance, distance*01.618033989) F][++ attr (distance, distance*0.618033989) fZ|X|-f|W]; |
| 9 |
Y => [+F][ attr (distance, distance*01.618033989) F][+f attr (distance, distance*0.618033989) |Y+X]; |
| 10 |
Z => [-F][ attr (distance, distance*01.618033989) F][ attr (distance, distance*0.618033989) f--Wf|+Z]; |
| 11 |
F => ; |
| 12 |
) |
| 13 |
|
| 14 |
ruleset ( // by Herb Savage |
| 15 |
// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", |
| 16 |
// Roger Penrose's kites and darts |
| 17 |
|
| 18 |
Kites_and_darts_color(n) => attr (delta, 360/10) Wf+Xf+Wf+Xf+Wf+Xf+Wf+Xf+Wf+X, n; |
| 19 |
W => [F][++ attr (distance, distance*01.618033989) F][++f--- attr (distance, distance*0.618033989) f|X-Y|f|W]; |
| 20 |
X => [F+++ attr (distance, distance*01.618033989) F][++ attr (distance, distance*0.618033989) fZ|X|-f|W]; |
| 21 |
Y => [+F][ attr (distance, distance*01.618033989) F][+f attr (distance, distance*0.618033989) |Y+X]; |
| 22 |
Z => [-F][ attr (distance, distance*01.618033989) F][ attr (distance, distance*0.618033989) f--Wf|+Z]; |
| 23 |
F => ; |
| 24 |
) |
| 25 |
|
| 26 |
ruleset ( // by Herb Savage |
| 27 |
// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", |
| 28 |
// Roger Penrose's rhombuses |
| 29 |
|
| 30 |
Penrose(n) => attr (delta, 360/10) +WF--XF---YF--ZF, n; |
| 31 |
W => YF++ZF----XF[-YF----WF]++; |
| 32 |
X => +YF--ZF[---WF--XF]+; |
| 33 |
Y => -WF++XF[+++YF++ZF]-; |
| 34 |
Z => --YF++++WF[+ZF++++XF]--XF; |
| 35 |
F => ; |
| 36 |
) |
| 37 |
|
| 38 |
ruleset ( // by Herb Savage |
| 39 |
// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", |
| 40 |
// Roger Penrose's rhombuses |
| 41 |
// Uses color to show similar lines |
| 42 |
|
| 43 |
Penrose_color(n) => attr (delta, 360/10) +WF--XF---YF--ZF, n; |
| 44 |
W => YF++ZF----XF[-YF----WF]++; |
| 45 |
X => +YF--ZF[---WF--XF]+; |
| 46 |
Y => -WF++XF[+++YF++ZF]-; |
| 47 |
Z => --YF++++WF[+ZF++++XF]--XF; |
| 48 |
F => ; |
| 49 |
) |
| 50 |
|
| 51 |
ruleset ( // by Herb Savage |
| 52 |
// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", |
| 53 |
// Roger Penrose's rhombuses |
| 54 |
// Uses color to show the edge matching rules to force nonperiodicy |
| 55 |
|
| 56 |
Penrose_forced(n) => attr (delta, 360/10) +WFF--XFF---YFF--ZFF, n; |
| 57 |
W => YFF++ZFF----XFF[-YFF----WFF]++; |
| 58 |
X => +YFF--ZFF[---WFF--XFF]+; |
| 59 |
Y => -WFF++XFF[+++YFF++ZFF]-; |
| 60 |
Z => --YFF++++WFF[+ZFF++++XFF]--XFF; |
| 61 |
F => ; |
| 62 |
C => ; |
| 63 |
) |
| 64 |
|
| 65 |
ruleset ( // by Herb Savage |
| 66 |
// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", |
| 67 |
// Roger Penrose's rhombuses |
| 68 |
|
| 69 |
Penrose1(n) => attr (delta, 360/10) ++ZF----XF-YF----WF, n; |
| 70 |
W => YF++ZF----XF[-YF----WF]++; |
| 71 |
X => +YF--ZF[---WF--XF]+; |
| 72 |
Y => -WF++XF[+++YF++ZF]-; |
| 73 |
Z => --YF++++WF[+ZF++++XF]--XF; |
| 74 |
F => ; |
| 75 |
) |
| 76 |
|
| 77 |
ruleset ( // by Herb Savage |
| 78 |
// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", |
| 79 |
// Roger Penrose's rhombuses |
| 80 |
|
| 81 |
Penrose2(n) => attr (delta, 360/10) [X]++[X]++[X]++[X]++[X], n; |
| 82 |
W => YF++ZF----XF[-YF----WF]++; |
| 83 |
X => +YF--ZF[---WF--XF]+; |
| 84 |
Y => -WF++XF[+++YF++ZF]-; |
| 85 |
Z => --YF++++WF[+ZF++++XF]--XF; |
| 86 |
F => ; |
| 87 |
) |
| 88 |
|
| 89 |
ruleset ( // by Herb Savage |
| 90 |
// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", |
| 91 |
// Roger Penrose's rhombuses |
| 92 |
|
| 93 |
Penrose3(n) => attr (delta, 360/10) [Y]++[Y]++[Y]++[Y]++[Y], n; |
| 94 |
W => YF++ZF----XF[-YF----WF]++; |
| 95 |
X => +YF--ZF[---WF--XF]+; |
| 96 |
Y => -WF++XF[+++YF++ZF]-; |
| 97 |
Z => --YF++++WF[+ZF++++XF]--XF; |
| 98 |
F => ; |
| 99 |
) |
| 100 |
|
| 101 |
ruleset ( // by Herb Savage |
| 102 |
// This is Penrose3 and Penrose4 superimposed |
| 103 |
|
| 104 |
Penrose_double(n) => attr (delta, 360/10) [X][Y]++[X][Y]++[X][Y]++[X][Y]++[X][Y], n; |
| 105 |
W => YF++ZF----XF[-YF----WF]++; |
| 106 |
X => +YF--ZF[---WF--XF]+; |
| 107 |
Y => -WF++XF[+++YF++ZF]-; |
| 108 |
Z => --YF++++WF[+ZF++++XF]--XF; |
| 109 |
F => ; |
| 110 |
) |
| 111 |
|
| 112 |
ruleset ( |
| 113 |
// Manual construction by Roger Penrose as a prelude to his development of |
| 114 |
// the famous Penrose tiles (the kites and darts) that tile the plane |
| 115 |
// only non-periodically. |
| 116 |
// Translated first to a "dragon curve" and finally to an L-system |
| 117 |
// by Joe Saverino. |
| 118 |
|
| 119 |
Penta_plexity(n) => attr (delta, 360/10) F++F++F++F++F, n; |
| 120 |
F => F++F++F|F-F++F; |
| 121 |
) |
| 122 |
|
| 123 |
// old PentaPlexity: |
| 124 |
// Angle 10 |
| 125 |
// Axiom F++F++F++F++Fabxjeabxykabxyelbxyeahxyeabiye |
| 126 |
// F= |
| 127 |
// a=Fabxjea |
| 128 |
// b=++F--bxykab |
| 129 |
// x=++++F----xyelbx |
| 130 |
// y=----F++++yeahxy |
| 131 |
// e=--F++eabiye |
| 132 |
// h=+++++F-----hijxlh |
| 133 |
// i=---F+++ijkyhi |
| 134 |
// j=-F+jkleij |
| 135 |
// k=+F-klhajk |
| 136 |
// l=+++F---lhibkl |
| 137 |
|
| 138 |
|
| 139 |
|
| 140 |
|
| 141 |
|
| 142 |
|
| 143 |
|
| 144 |
|
| 145 |
|
| 146 |
|
| 147 |
|
| 148 |
|
| 149 |
|
| 150 |
) |
| 151 |
|
| 152 |
ruleset ( |
| 153 |
// by Philippe Hurbain |
| 154 |
// Penrose's rhombuses, generated by decomposition rules |
| 155 |
// x generate the fat rhombus, y the thin one |
| 156 |
// Individualization of rhombuses allows easy coloring |
| 157 |
// 0.618034 is (SQRT(5)-1)/2 |
| 158 |
|
| 159 |
Losanges(n) => attr (delta, 360/10) x, n; |
| 160 |
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; |
| 161 |
y => attr (distance, distance*0.618034) ++[x]F|+F[|y]-[y]F|+F[|x]; |
| 162 |
F => f; |
| 163 |
) |
| 164 |
|
| 165 |
ruleset ( |
| 166 |
// by Philippe Hurbain |
| 167 |
// Simple coloring of Penrose's rhombuses, showing pentagons |
| 168 |
|
| 169 |
Penta_color(n) => attr (delta, 360/20) [x]++++[x]++++[x]++++[x]++++[x], n; |
| 170 |
x => attr (distance, distance*0.618034) ++F[ attr (distance, distance*01.1755) -------F][|y]----F[|x]; |
| 171 |
x => [|++ attr (distance, distance*0.618034) f attr (distance, distance/0.618034) x]------[x]F----[y]F; |
| 172 |
y => attr (distance, distance*0.618034) ++++[x]F|++F[|y]--[y]F|++F[|x]; |
| 173 |
F => f; |
| 174 |
) |
| 175 |
|
| 176 |
ruleset ( |
| 177 |
// by Philippe Hurbain |
| 178 |
// Same as PentaColor, but showing only the coloring |
| 179 |
|
| 180 |
Penta(n) => attr (delta, 360/20) [x]++++[x]++++[x]++++[x]++++[x], n; |
| 181 |
x => attr (distance, distance*0.618034) ++f[ attr (distance, distance*01.1755) -------F][|y]----f[|x]; |
| 182 |
x => [|++ attr (distance, distance*0.618034) f attr (distance, distance/0.618034) x]------[x]f----[y]f; |
| 183 |
y => attr (distance, distance*0.618034) ++++[x]f|++f[|y]--[y]f|++f[|x]; |
| 184 |
F => f; |
| 185 |
) |
| 186 |
|
| 187 |
ruleset ( |
| 188 |
// by Philippe Hurbain |
| 189 |
// Penrose's kites and darts |
| 190 |
// k generates the kite, a generates the dart |
| 191 |
|
| 192 |
Kites_darts(n) => attr (delta, 360/10) k, n; |
| 193 |
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]; |
| 194 |
a => [ attr (distance, distance*0.618034) k]+F attr (distance, distance*0.618034) [|a]----F+F----[a] attr (distance, distance/0.618034) F; |
| 195 |
F => f; |
| 196 |
) |
| 197 |
|
| 198 |
ruleset ( |
| 199 |
// by Philippe Hurbain |
| 200 |
// Penrose's kites and darts, with kites seed |
| 201 |
|
| 202 |
Kites_darts1(n) => attr (delta, 360/10) [k]++[k]++[k]++[k]++[k], n; |
| 203 |
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]; |
| 204 |
a => [ attr (distance, distance*0.618034) k]+F attr (distance, distance*0.618034) [|a]----F+F----[a] attr (distance, distance/0.618034) F; |
| 205 |
F => f; |
| 206 |
) |
| 207 |
|
| 208 |
ruleset ( |
| 209 |
// by Philippe Hurbain |
| 210 |
// Penrose's kites and darts, with darts seed |
| 211 |
|
| 212 |
Kites_darts2(n) => attr (delta, 360/10) [a]++[a]++[a]++[a]++[a], n; |
| 213 |
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]; |
| 214 |
a => [ attr (distance, distance*0.618034) k]+F attr (distance, distance*0.618034) [|a]----F+F----[a] attr (distance, distance/0.618034) F; |
| 215 |
F => f; |
| 216 |
) |
| 217 |
|
| 218 |
ruleset ( |
| 219 |
// by Philippe Hurbain |
| 220 |
// Penrose's kites and darts, with serpentine coloring |
| 221 |
|
| 222 |
Kites_darts_color(n) => attr (delta, 360/10) [k]++[k]++[k]++[k]++[k], n; |
| 223 |
k => +[ attr (distance, distance*0.618034) a[f--- attr (distance, distance*0.618) F][--f+++ attr (distance, distance*0.618) F]]; |
| 224 |
k => F attr (distance, distance*0.618034) ---[-k]F-F---[-k] attr (distance, distance/0.618034) F[ attr (distance, distance*0.618034) |a]; |
| 225 |
a => [ attr (distance, distance*0.618034) k]+F attr (distance, distance*0.618034) [|a][|f++ attr (distance, distance*0.382) F]----F+; |
| 226 |
a => F----[a][f-- attr (distance, distance*0.382) F] attr (distance, distance/0.618034) F; |
| 227 |
F => f; |
| 228 |
) |
| 229 |
|
| 230 |
ruleset ( |
| 231 |
// by Philippe Hurbain |
| 232 |
// Ammann's coloring of Penrose's rhombuses, giving an |
| 233 |
// aperiodic tiling of 2 pentagons and 1 hexagon |
| 234 |
|
| 235 |
Ammann_poly_color(n) => attr (delta, 360/10) x, n; |
| 236 |
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]; |
| 237 |
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; |
| 238 |
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]; |
| 239 |
y => -(36) [y]F -(144) F[ +(180) x]; |
| 240 |
F => f; |
| 241 |
) |
| 242 |
|
| 243 |
ruleset ( |
| 244 |
// by Philippe Hurbain |
| 245 |
// Same as AmmanPolyColor, showing only the |
| 246 |
// pentagon/hexagon tiling |
| 247 |
|
| 248 |
Ammann_poly(n) => attr (delta, 360/10) x, n; |
| 249 |
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]; |
| 250 |
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; |
| 251 |
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]; |
| 252 |
y => -(36) [y]f -(144) f[ +(180) x]; |
| 253 |
F => f; |
| 254 |
) |
| 255 |
|
| 256 |
ruleset ( |
| 257 |
// by Philippe Hurbain |
| 258 |
// Penrose's stars and pentagon tiling, generated as |
| 259 |
// a coloring of kites and darts |
| 260 |
|
| 261 |
Stars_pentas_color(n) => attr (delta, 360/20) k, n; |
| 262 |
k => ++[ attr (distance, distance*0.618034) [f- attr (distance, distance*0.5878) [F]------F F++++F]a]F attr (distance, distance*0.618034) ------; |
| 263 |
k => [--k]F--F------[--k] attr (distance, distance/0.618034) F[ attr (distance, distance*0.618034) |a]; |
| 264 |
a => [ attr (distance, distance*0.618034) k]++F attr (distance, distance*0.618034) [|[f attr (distance, distance*0.5878) +++++++F]a]--------F; |
| 265 |
a => ++F--------[f attr (distance, distance*0.5878) -------F][a] attr (distance, distance/0.618034) F; |
| 266 |
F => f; |
| 267 |
) |
| 268 |
|
| 269 |
ruleset ( |
| 270 |
// by Philippe Hurbain |
| 271 |
// Same as Stars&PentasColor, showing only coloring |
| 272 |
|
| 273 |
Stars_pentas(n) => attr (delta, 360/20) [k]++++[k]++++[k]++++[k]++++[k], n; |
| 274 |
k => ++[ attr (distance, distance*0.618034) [f- attr (distance, distance*0.5878) [F]------F F++++F]a]f attr (distance, distance*0.618034) ------; |
| 275 |
k => [--k]f--f------[--k] attr (distance, distance/0.618034) f[ attr (distance, distance*0.618034) |a]; |
| 276 |
a => [ attr (distance, distance*0.618034) k]++f attr (distance, distance*0.618034) [|[f attr (distance, distance*0.5878) +++++++F]a]--------f; |
| 277 |
a => ++f--------[f attr (distance, distance*0.5878) -------F][a] attr (distance, distance/0.618034) f; |
| 278 |
F => f; |
| 279 |
) |
| 280 |
|
| 281 |
ruleset ( |
| 282 |
// by Philippe Hurbain |
| 283 |
// Penrose's stars and pentagons, generated from |
| 284 |
// decomposition rules |
| 285 |
// u is the star, v is the boat, w is the thin rhombus |
| 286 |
// x, y and z are the pentagons |
| 287 |
|
| 288 |
Stars_pentas1(n) => attr (delta, 360/10) u, n; |
| 289 |
u => attr (distance, distance*0.381966) [v]F[|y][-u]++F|+[v]F[|y]++F|+[v]F[|y]++F|+; |
| 290 |
u => [v]F[|y]++F|+[v]F[|y]++F; |
| 291 |
v => attr (distance, distance*0.381966) [v]F[|y]++F|+[v]F[|y]-[u]F-F|+[v]F[|y]++F; |
| 292 |
w => attr (distance, distance*0.381966) f++[u]F|+F-F|+[v]F[|y]; |
| 293 |
y => attr (distance, distance*0.381966) [x][y][w]F[|!y]++F++[y][w]F[|!y]++F++[z]F; |
| 294 |
x => attr (distance, distance*0.381966) f++f++[!x][!z]F--[!z]F--[!z]F--[!z]F--[!z]F; |
| 295 |
z => attr (distance, distance*0.381966) [z][x]F++[z]F++[w][y]F[|!y]++F++[z]F; |
| 296 |
F => f; |
| 297 |
) |
| 298 |
|
