1 Koch1 { ; Adrian Mariano 2 ; from The Fractal Geometry of Nature by Mandelbrot 3 Angle 6 4 Axiom F--F--F 5 F=F+F--F+F 6 } 7 8 Koch2 { ; Adrian Mariano 9 ; from The Fractal Geometry of Nature by Mandelbrot 10 Angle 12 11 Axiom F---F---F---F 12 F=-F+++F---F+ 13 } 14 15 Koch3 { ; Adrian Mariano 16 ; from The Fractal Geometry of Nature by Mandelbrot 17 Angle 4 18 Axiom F-F-F-F 19 F=F-F+F+FF-F-F+F 20 } 21 22 Koch6 { ; Adrian Mariano 23 axiom f+f+f+f 24 f=f-ff+ff+f+f-f-ff+f+f-f-ff-ff+f 25 angle 4 26 } 27 28 Dragon { ; Adrian Mariano 29 ; from The Fractal Geometry of Nature by Mandelbrot 30 Angle 8 31 Axiom FX 32 F= 33 y=+FX--FY+ 34 x=-FX++FY- 35 } 36 37 Peano1 { ; Adrian Mariano 38 ; from The Fractal Geometry of Nature by Mandelbrot 39 Angle 4 40 Axiom F-F-F-F 41 F=F-F+F+F+F-F-F-F+F 42 } 43 44 Cesaro { ; Adrian Mariano 45 ; from The Fractal Geometry of Nature by Mandelbrot 46 Angle 34 47 Axiom FX 48 F= 49 X=----F!X!++++++++F!X!---- 50 } 51 52 DoubleCesaro { ; Adrian Mariano 53 ; from The Fractal Geometry of Nature by Mandelbrot 54 Angle 4 55 axiom D\90D\90D\90D\90 56 D=\42!D!/84!D!\42 57 } 58 59 FlowSnake { ; Adrian Mariano 60 ; from The Fractal Geometry of Nature by Mandelbrot 61 angle=6; 62 axiom FL 63 L=FL-FR--FR+FL++FLFL+FR-", 64 R=+FL-FRFR--FR-FL++FL+FR", 65 F= 66 } 67 68 CantorDust { ; Adrian Mariano 69 ; from The Fractal Geometry of Nature by Mandelbrot 70 Angle 6 71 Axiom F 72 F=FGF 73 G=GGG 74 } 75 76 Snowflake2 { ; Adrian Mariano 77 ; from The Fractal Geometry of Nature by Mandelbrot 78 angle 12 79 axiom F 80 F=++!F!F--F--F@IQ3|+F!F-- 81 F=F--F!+++@Q3F@QI3|+F!F@Q3|+F!F 82 } 83 84 SnowflakeColor { ; Adrian Mariano 85 ; from The Fractal Geometry of Nature by Mandelbrot 86 angle 12 87 axiom F 88 F=--!F<1!F<1++F<1++F<1@IQ3|-F<1!F<1++ 89 F=F<1++F<1!---@Q3F<1@QI3|-F<1!F<1@Q3|-F<1!F<1 90 F= 91 } 92 93 Island1 { ; Adrian Mariano 94 ; from The Fractal Geometry of Nature by Mandelbrot 95 angle 4 96 axiom F+F+F+F 97 F=FFFF-F+F+F-F[-GFF+F+FF+F]FF 98 G=@8G@I8 99 } 100 101 Island2 { ; Adrian Mariano 102 ; from The Fractal Geometry of Nature by Mandelbrot 103 angle 4 104 axiom f+f+f+f 105 f=f+gf-ff-f-ff+g+ff-gf+ff+f+ff-g-fff 106 g=@6G@I6 107 } 108 109 Quartet { ; Adrian Mariano 110 ; from The Fractal Geometry of Nature by Mandelbrot 111 angle 4 112 axiom fb 113 A=FBFA+HFA+FB-FA 114 B=FB+FA-FB-JFBFA 115 F= 116 H=- 117 J=+ 118 } 119 120 SnowFlake1 { ; Adrian Mariano 121 ; from The Fractal Geometry of Nature by Mandelbrot 122 Angle 12 123 Axiom FR 124 R=++!FRFU++FU++FU!---@Q3FU|-@IQ3!FRFU! 125 U=!FRFU!|+@Q3FR@IQ3+++!FR--FR--FRFU!-- 126 F= 127 } 128 129 SnowFlake3 { ; Adrian Mariano 130 ; from The Fractal Geometry of Nature by Mandelbrot 131 angle 12 132 axiom fx 133 x=++f!x!fy--fx--fy|+@iq3fyf!x!++f!y!++f!y!fx@q3+++f!y!fx 134 y=fyf!x!+++@iq3fyf!x!++f!x!++f!y!fx@q3|+fx--fy--fxf!y!++ 135 f= 136 } 137 138 Tree1 { ; Adrian Mariano 139 ; from The Fractal Geometry of Nature by Mandelbrot 140 angle=12; 141 axiom +++FX 142 X=@.6[-FX]+FX 143 } 144 145 Peano2 { ; Adrian Mariano 146 ; from The Fractal Geometry of Nature by Mandelbrot 147 Angle 8 148 Axiom FXY++F++FXY++F 149 X=XY@Q2-F@IQ2-FXY++F++FXY 150 Y=-@Q2F-@IQ2FXY 151 } 152 153 Sierpinski1 { ; Adrian Mariano 154 ; from The Fractal Geometry of Nature by Mandelbrot 155 angle 3 156 axiom F 157 F=FXF 158 X=+FXF-FXF-FXF+ 159 } 160 161 Koch4 { ; Adrian Mariano 162 ; from The Fractal Geometry of Nature by Mandelbrot 163 angle 12 164 axiom f++++f++++f 165 f=+f--f++f- 166 } 167 168 169 Plant07 { ; Ken Philip, from The Science of Fractal Images p.285b 170 axiom Z 171 z=zFX[+Z][-Z] 172 x=x[-FFF][+FFF]FX 173 angle 14 174 } 175 176 Plant08 { ; Ken Philip, from The Science of Fractal Images, p.286 177 axiom SLFFF 178 s=[+++Z][---Z]TS 179 z=+H[-Z]L 180 h=-Z[+H]L 181 t=TL 182 l=[-FFF][+FFF]F 183 angle 20 184 } 185 186 Hilbert { ; Ken Philip, from The Science of Fractal Images 187 axiom x 188 x=-YF+XFX+FY- 189 y=+XF-YFY-FX+ 190 angle 4 191 } 192 193 Sierpinski3 { ; From Jim Hanan via Corbit 194 axiom F-F-F 195 f=F[-F]F 196 angle 3 197 } 198 199 200 Peano3 { 201 axiom x 202 x=XFYFX+F+YFXFY-F-XFYFX 203 y=YFXFY-F-XFYFX+F+YFXFY 204 angle 4 205 } 206 207 Koch5 { 208 axiom f+F+F+F 209 f=F+F-F-FFF+F+F-F 210 angle 4 211 } 212 213 Sierpinski2 { ; from The Science of Fractal Images 214 axiom FXF--FF--FF 215 f=FF 216 x=--FXF++FXF++FXF-- 217 angle 6 218 } 219 220 SierpinskiSquare { 221 axiom F+F+F+F 222 f=FF+F+F+F+FF 223 angle 4 224 } 225 226 227 Pentagram { ; created by Adrian Mariano 228 angle 10 229 axiom fx++fx++fx++fx++fx 230 ; f=f[++++@1.618033989f] 231 x=[++++@i1.618033989f@.618033989f!x!@i.618033989f] 232 } 233 234 235 QuadKoch { ; Adrian Mariano, from the Algorithmic Beauty of Plants 236 ; Quadratic Koch island, Figure 1.7a p.9 237 angle 4 238 AXIOM F-F-F-F- 239 F=F+FF-FF-F-F+F+FF-F-F+F+FF+FF-F 240 } 241 242 Fass1 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 243 ; FASS curve (3x3 tiles form macrotile), Figure 1.16a p.17 244 axiom -l 245 angle 4 246 L=LF+RFR+FL-F-LFLFL-FRFR+ 247 R=-LFLF+RFRFR+F+RF-LFL-FR 248 } 249 250 Fass2 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 251 ; FASS curve (4x4 tiles form macrotile), Figure 1.16b p.17 252 angle 4 253 axiom -l 254 L=LFLF+RFR+FLFL-FRF-LFL-FR+F+RF-LFL-FRFRFR+ 255 R=-LFLFLF+RFR+FL-F-LF+RFR+FLF+RFRF-LFL-FRFR 256 } 257 258 QuadGosper { ; Adrian Mariano, from the Algorithmic Beauty of Plants 259 ; Quadratic Gosper curve, Figure 1.11b p.12 260 angle 4 261 axiom -Fr 262 l=FlFl-Fr-Fr+Fl+Fl-Fr-FrFl+Fr+FlFlFr-Fl+Fr+FlFl+Fr-FlFr-Fr-Fl+Fl+FrFr- 263 r=+FlFl-Fr-Fr+Fl+FlFr+Fl-FrFr-Fl-Fr+FlFrFr-Fl-FrFl+Fl+Fr-Fr-Fl+Fl+FrFr 264 f= 265 } 266 267 Plant01 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 268 ; Plant-like structure, figure 1.24a p.25 269 ; also p.285a The Science of Fractal Images 270 angle 14 271 axiom f 272 f=F[+F]F[-F]F 273 } 274 275 Plant02 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 276 ; Plant-like structure, figure 1.24b p.25 277 angle 18 278 axiom f 279 f=F[+F]F[-F][F] 280 } 281 282 Plant03 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 283 ; Plant-like structure, figure 1.24c p.25 284 angle 16 285 axiom f 286 f=FF-[-F+F+F]+[+F-F-F] 287 } 288 289 Plant04 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 290 ; Plant-like structure, figure 1.24d p.25 291 angle 18 292 axiom x 293 X=F[+X]F[-X]+X 294 F=FF 295 } 296 297 Plant05 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 298 ; Plant-like structure, figure 1.24e p.25 299 angle 14 300 axiom x 301 X=f[+X][-X]FX 302 F=FF 303 } 304 305 Plant06 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 306 ; Plant-like structure, figure 1.24f p.25 307 angle 16 308 axiom x 309 X=F-[[X]+X]+F[+FX]-X 310 F=FF 311 } 312 313 Plant09 { ; Adrian Mariano 314 axiom y 315 x=X[-FFF][+FFF]FX 316 y=YFX[+Y][-Y] 317 angle 14 318 } 319 320 Plant10 { ; Adrian Mariano 321 axiom f 322 f=f[+ff][-ff]f[+ff][-ff]f 323 angle 10 324 } 325 326 327 Plant11 { ; Adrian Mariano 328 axiom f 329 f=F[+F[+F][-F]F][-F[+F][-F]F]F[+F][-F]F 330 angle 12 331 } 332 333 Curve1 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 334 ; curve from figure 1.9a p.10 335 angle 4 336 axiom F-F-F-F- 337 f=FF-F-F-F-F-F+F 338 } 339 340 Curve2 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 341 angle 4 342 axiom F-F-F-F- 343 f=FF-F+F-F-FF 344 } 345 346 Curve3 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 347 ; curve from figure 1.9e p.10 348 axiom F-F-F-F- 349 angle 4 350 F=F-FF--F-F 351 } 352 353 Curve4 { ; Adrian Mariano 354 axiom yf 355 x=YF+XF+Y 356 y=XF-YF-X 357 angle 6 358 } 359 360 Leaf1 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 361 ; Compound leaf with alternating branches, Figure 5.12b p.130 362 angle 8 363 axiom x 364 a=n 365 n=o 366 o=p 367 p=x 368 b=e 369 e=h 370 h=j 371 j=y 372 x=F[+A(4)]Fy 373 y=F[-B(4)]Fx 374 F=@1.18F@i1.18 375 } 376 377 Leaf2 { ; Adrian Mariano, from the Algorithmic Beauty of Plants 378 ; Compound leaf with alternating branches, Figure 5.12a p.130 379 angle 8 380 axiom a 381 a=f[+x]fb 382 b=f[-y]fa 383 x=a 384 y=b 385 f=@1.36f@i1.36 386 } 387 388 Bush { ; Adrian Mariano 389 Angle 16 390 Axiom ++++F 391 F=FF-[-F+F+F]+[+F-F-F] 392 } 393 394 MyTree { ; Adrian Mariano 395 Angle 16 396 Axiom ++++F 397 F=FF-[XY]+[XY] 398 X=+FY 399 Y=-FX 400 } 401 402 ColorTriangGasket { ; Adrian Mariano 403 Angle 6 404 Axiom --X 405 X=++FXF++FXF++FXF>1 406 F=FF 407 } 408 409 SquareGasket { ; Adrian Mariano 410 Angle 4 411 Axiom X 412 X=+FXF+FXF+FXF+FXF 413 F=FF 414 } 415 416 DragonCurve { ; Adrian Mariano 417 Angle 4 418 Axiom X 419 X=X-YF- 420 Y=+FX+Y 421 } 422 423 Square { ; Adrian Mariano 424 Angle 4 425 Axiom F+F+F+F 426 F=FF+F+F+F+FF 427 } 428 429 KochCurve { ; Adrian Mariano 430 Angle 6 431 Axiom F 432 F=F+F--F+F 433 } 434 435 436 Penrose1 { ; by Herb Savage 437 ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", 438 ; Roger Penrose's rhombuses 439 Angle 10 440 Axiom +WF--XF---YF--ZF 441 W=YF++ZF----XF[-YF----WF]++ 442 X=+YF--ZF[---WF--XF]+ 443 Y=-WF++XF[+++YF++ZF]- 444 Z=--YF++++WF[+ZF++++XF]--XF 445 F= 446 } 447 448 ColorPenrose1 { ; by Herb Savage 449 ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", 450 ; Roger Penrose's rhombuses 451 ; Uses color to show the edge matching rules to force nonperiodicy 452 Angle 10 453 Axiom +WC02F--XC04F---YC04F--ZC02F 454 W=YC04F++ZC02F----XC04F[-YC04F----WC02F]++ 455 X=+YC04F--ZC02F[---WC02F--XC04F]+ 456 Y=-WC02F++XC04F[+++YC04F++ZC02F]- 457 Z=--YC04F++++WC02F[+ZC02F++++XC04F]--XC04F 458 F= 459 } 460 461 Penrose2 { ; by Herb Savage 462 ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", 463 ; Roger Penrose's rhombuses 464 Angle 10 465 Axiom ++ZF----XF-YF----WF 466 W=YF++ZF----XF[-YF----WF]++ 467 X=+YF--ZF[---WF--XF]+ 468 Y=-WF++XF[+++YF++ZF]- 469 Z=--YF++++WF[+ZF++++XF]--XF 470 F= 471 } 472 473 Penrose3 { ; by Herb Savage 474 ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", 475 ; Roger Penrose's rhombuses 476 Angle 10 477 Axiom [X]++[X]++[X]++[X]++[X] 478 W=YF++ZF----XF[-YF----WF]++ 479 X=+YF--ZF[---WF--XF]+ 480 Y=-WF++XF[+++YF++ZF]- 481 Z=--YF++++WF[+ZF++++XF]--XF 482 F= 483 } 484 485 Penrose4 { ; by Herb Savage 486 ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", 487 ; Roger Penrose's rhombuses 488 Angle 10 489 Axiom [Y]++[Y]++[Y]++[Y]++[Y] 490 W=YF++ZF----XF[-YF----WF]++ 491 X=+YF--ZF[---WF--XF]+ 492 Y=-WF++XF[+++YF++ZF]- 493 Z=--YF++++WF[+ZF++++XF]--XF 494 F= 495 } 496 497 DoublePenrose { ; by Herb Savage 498 ; This is Penrose3 and Penrose4 superimposed 499 Angle 10 500 Axiom [X][Y]++[X][Y]++[X][Y]++[X][Y]++[X][Y] 501 W=YF++ZF----XF[-YF----WF]++ 502 X=+YF--ZF[---WF--XF]+ 503 Y=-WF++XF[+++YF++ZF]- 504 Z=--YF++++WF[+ZF++++XF]--XF 505 F= 506 } 507 508 Sphinx { ; by Herb Savage 509 ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers" 510 ; This is an example of a "reptile" 511 Angle 6 512 Axiom X 513 X=+FF-YFF+FF--FFF|X|F--YFFFYFFF| 514 Y=-FF+XFF-FF++FFF|Y|F++XFFFXFFF| 515 F=GG 516 G=GG 517 } 518 519 PentaPlexity { 520 ; Manual construction by Roger Penrose as a prelude to his development of 521 ; the famous Penrose tiles (the kites and darts) that tile the plane 522 ; only non-periodically. 523 ; Translated first to a "dragon curve" and finally to an L-system 524 ; by Joe Saverino. 525 Angle 10 526 Axiom F++F++F++F++F 527 F=F++F++F|F-F++F 528 } 529 530 ; old PentaPlexity: 531 ; Angle 10 532 ; Axiom F++F++F++F++Fabxjeabxykabxyelbxyeahxyeabiye 533 ; F= 534 ; a=Fabxjea 535 ; b=++F--bxykab 536 ; x=++++F----xyelbx 537 ; y=----F++++yeahxy 538 ; e=--F++eabiye 539 ; h=+++++F-----hijxlh 540 ; i=---F+++ijkyhi 541 ; j=-F+jkleij 542 ; k=+F-klhajk 543 ; l=+++F---lhibkl 544 545 CircularTile { ; Adrian Mariano 546 axiom X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X 547 x=[F+F+F+F[---X-Y]+++++F++++++++F-F-F-F] 548 y=[F+F+F+F[---Y]+++++F++++++++F-F-F-F] 549 angle 24 550 } 551 552 Lars1{ ; By Jonathan Osuch [73277,1432] 553 ; Based on a suggestion by Lars Vangsgaard 554 Angle 8 ; angle increment/decrement is 45 555 axiom [F]++[F]++[F]++F 556 F=F[+F][-F] 557 } 558 559 Lars2{ ; By Jonathan Osuch [73277,1432] 560 ; Based on a suggestion by Lars Vangsgaard 561 Angle 8 ; angle increment/decrement is 45 562 axiom +[F]++[F]++[F]++F 563 F=F[+F][-F] 564 } 565 566 Lars1Color{ ; By Jonathan Osuch [73277,1432] 567 ; Based on a suggestion by Lars Vangsgaard 568 Angle 8 ; angle increment/decrement is 45 569 axiom C1[F]++[F]++[F]++F 570 F=F<1[+F][-F]>1 571 } 572 573 Lars2Color{ ; By Jonathan Osuch [73277,1432] 574 ; Based on a suggestion by Lars Vangsgaard 575 Angle 8 ; angle increment/decrement is 45 576 axiom C1+[F]++[F]++[F]++F 577 F=F<1[+F][-F]>1 578 } 579 580 Man { ; From Ivan Daunis daunis@teleline.es 581 ; looks like man with an odd number of iterations 582 Angle 8 583 Axiom F++F++F++F 584 F=-F-FF+++F+FF-F 585 } 586 587 Lace { ; From Ivan Daunis daunis@teleline.es 588 Angle 8 589 Axiom F++F++F++F 590 F=F+++F---F+F---F++F--F++F 591 } 592