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Fractal curve

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167: 31: 1110: 537: 532: 460: 475: 1128: 160: 385: 574: 607: 452: 1134: 360: 17: 990: 947: 194:. Self-similarity occurs, and analysis of these patterns has found fractal curves in such diverse fields as 863: 1068: 1188: 1150: 634: 445: 400: 140: 128: 50: 800: 132: 656: 1183: 1142: 1093: 701: 567: 313: 267: 293: 927: 619: 324: 418: 1088: 1083: 873: 805: 496: 298: 8: 846: 823: 706: 691: 624: 152: 46: 758: 1073: 1053: 1017: 1012: 775: 136: 124: 120: 1116: 1078: 1002: 910: 815: 721: 696: 686: 629: 612: 602: 597: 560: 329: 252: 191: 183: 156: 58: 517: 1033: 900: 883: 711: 461:"Fractal patterns in nature and art are aesthetically pleasing and stress-reducing" 339: 247: 234: 230: 218: 207: 113: 70: 1048: 985: 646: 410: 319: 226: 199: 187: 74: 53:, regardless of how high it is magnified, that is, its graph takes the form of a 743: 1063: 995: 966: 922: 905: 888: 841: 785: 770: 738: 676: 344: 278: 272: 171: 155:
one, but as a general rule, fractal curves have different dimensions, also see
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of fractal curves, and have applied theory of fractals to modelling
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Fractal curves and fractal patterns are widespread, in
151:Most of us are used to mathematical curves having 1175: 419:"Earth's Most Stunning Natural Fractal Patterns" 146: 49:whose shape retains the same general pattern of 178:Relationships of fractal curves to other fields 568: 392: 538:Area of a Koch Snowflake, from Khan Academy 443: 87: 27:Mathematical curve whose shape is a fractal 575: 561: 533:Making a Kock Snowflake, from Khan Academy 57:. In general, fractal curves are nowhere 458: 398: 165: 80:A famous example is the boundary of the 29: 1129:List of fractals by Hausdorff dimension 473: 386:"Geometric and topological recreations" 161:list of fractals by Hausdorff dimension 14: 1176: 217:As examples, "landscapes" revealed by 556: 494: 476:"14 amazing fractals found in nature" 446:"8 Stunning Fractals Found in Nature" 459:LaMonica, Martin (March 30, 2017). 444:Tennenhouse, Erica (July 5, 2016). 416: 61:— that is, they do not have finite 24: 25: 1200: 1111:How Long Is the Coast of Britain? 523:The Fractal Foundation's homepage 511: 474:Gunther, Shea (April 24, 2013). 543:Youtube on space-filling curves 1135:The Fractal Geometry of Nature 518:Wolfram math on fractal curves 497:"Fractal Curves and Dimension" 361:The Fractal Geometry of Nature 237:all relate to fractal curves. 13: 1: 368: 147:Dimensions of a fractal curve 582: 45:is, loosely, a mathematical 7: 1151:Chaos: Making a New Science 548:Youtube on the Dragon Curve 305: 240: 10: 1205: 141:self-organized criticality 96:, found in such places as 1102: 1026: 975: 946: 862: 832: 814: 655: 590: 186:and others have studied 88:Fractal curves in nature 1143:The Beauty of Fractals 495:Bogomolny, Alexander. 399:Ritzenthaler, Chella. 314:The Beauty of Fractals 268:Fibonacci word fractal 182:Starting in the 1950s 174: 133:Hofstadter's butterfly 38: 325:Fractal expressionism 169: 69:longer than a single 33: 1089:Lewis Fry Richardson 1084:Hamid Naderi Yeganeh 874:Burning Ship fractal 806:Weierstrass function 299:Weierstrass function 34:Construction of the 847:Space-filling curve 824:Multifractal system 707:Space-filling curve 692:Sierpinski triangle 294:Sierpiński triangle 225:in connection with 1189:Types of functions 1074:Aleksandr Lyapunov 1054:Desmond Paul Henry 1018:Self-avoiding walk 1013:Percolation theory 657:Iterated function 598:Fractal dimensions 175: 170:Zooming in on the 137:Lichtenberg figure 121:Romanesco broccoli 59:rectifiable curves 39: 1171: 1170: 1117:Coastline paradox 1094:Wacław Sierpiński 1079:Benoit Mandelbrot 1003:Fractal landscape 911:Misiurewicz point 816:Strange attractor 697:Apollonian gasket 687:Sierpinski carpet 528:fractalcurves.com 330:Fractal landscape 253:Coastline paradox 235:polymer molecules 231:vascular networks 219:microscopic views 192:natural phenomena 184:Benoit Mandelbrot 157:fractal dimension 16:(Redirected from 1196: 1034:Michael Barnsley 901:Lyapunov fractal 759:Sierpiński curve 712:Blancmange curve 577: 570: 563: 554: 553: 505: 504: 492: 486: 485: 483: 482: 471: 465: 464: 456: 450: 449: 441: 435: 434: 432: 430: 414: 408: 407: 405: 401:"Fractal Curves" 396: 390: 389: 382: 340:Mosely snowflake 277:Boundary of the 248:Blancmange curve 233:, and shapes of 208:human physiology 125:dendrite crystal 21: 1204: 1203: 1199: 1198: 1197: 1195: 1194: 1193: 1174: 1173: 1172: 1167: 1098: 1049:Felix Hausdorff 1022: 986:Brownian motion 971: 942: 865: 858: 828: 810: 801:Pythagoras tree 658: 651: 647:Self-similarity 591:Characteristics 586: 581: 514: 509: 508: 493: 489: 480: 478: 472: 468: 457: 453: 442: 438: 428: 426: 417:McNally, Jess. 415: 411: 403: 397: 393: 384: 383: 376: 371: 366: 320:Fractal antenna 308: 303: 243: 227:Brownian motion 200:fluid mechanics 188:self-similarity 180: 149: 129:trees, fractals 114:lightning bolts 90: 75:infinite length 28: 23: 22: 15: 12: 11: 5: 1202: 1192: 1191: 1186: 1184:Fractal curves 1169: 1168: 1166: 1165: 1160: 1155: 1147: 1139: 1131: 1126: 1121: 1120: 1119: 1106: 1104: 1100: 1099: 1097: 1096: 1091: 1086: 1081: 1076: 1071: 1066: 1064:Helge von Koch 1061: 1056: 1051: 1046: 1041: 1036: 1030: 1028: 1024: 1023: 1021: 1020: 1015: 1010: 1005: 1000: 999: 998: 996:Brownian motor 993: 982: 980: 973: 972: 970: 969: 967:Pickover stalk 964: 959: 953: 951: 944: 943: 941: 940: 935: 930: 925: 923:Newton fractal 920: 915: 914: 913: 906:Mandelbrot set 903: 898: 897: 896: 891: 889:Newton fractal 886: 876: 870: 868: 860: 859: 857: 856: 855: 854: 844: 842:Fractal canopy 838: 836: 830: 829: 827: 826: 820: 818: 812: 811: 809: 808: 803: 798: 793: 788: 786:Vicsek fractal 783: 778: 773: 768: 767: 766: 761: 756: 751: 746: 741: 736: 731: 726: 725: 724: 714: 704: 702:Fibonacci word 699: 694: 689: 684: 679: 677:Koch snowflake 674: 669: 663: 661: 653: 652: 650: 649: 644: 639: 638: 637: 632: 627: 622: 617: 616: 615: 605: 594: 592: 588: 587: 580: 579: 572: 565: 557: 551: 550: 545: 540: 535: 530: 525: 520: 513: 512:External links 510: 507: 506: 487: 466: 451: 436: 409: 391: 373: 372: 370: 367: 365: 364: 357: 352: 347: 345:Newton fractal 342: 337: 332: 327: 322: 317: 309: 307: 304: 302: 301: 296: 291: 286: 281: 279:Mandelbrot set 275: 273:Koch snowflake 270: 265: 260: 255: 250: 244: 242: 239: 179: 176: 172:Mandelbrot set 148: 145: 110:frost crystals 89: 86: 82:Mandelbrot set 26: 18:Fractal Curves 9: 6: 4: 3: 2: 1201: 1190: 1187: 1185: 1182: 1181: 1179: 1164: 1161: 1159: 1156: 1153: 1152: 1148: 1145: 1144: 1140: 1137: 1136: 1132: 1130: 1127: 1125: 1122: 1118: 1115: 1114: 1112: 1108: 1107: 1105: 1101: 1095: 1092: 1090: 1087: 1085: 1082: 1080: 1077: 1075: 1072: 1070: 1067: 1065: 1062: 1060: 1057: 1055: 1052: 1050: 1047: 1045: 1042: 1040: 1037: 1035: 1032: 1031: 1029: 1025: 1019: 1016: 1014: 1011: 1009: 1006: 1004: 1001: 997: 994: 992: 991:Brownian tree 989: 988: 987: 984: 983: 981: 978: 974: 968: 965: 963: 960: 958: 955: 954: 952: 949: 945: 939: 936: 934: 931: 929: 926: 924: 921: 919: 918:Multibrot set 916: 912: 909: 908: 907: 904: 902: 899: 895: 894:Douady rabbit 892: 890: 887: 885: 882: 881: 880: 877: 875: 872: 871: 869: 867: 861: 853: 850: 849: 848: 845: 843: 840: 839: 837: 835: 831: 825: 822: 821: 819: 817: 813: 807: 804: 802: 799: 797: 794: 792: 789: 787: 784: 782: 779: 777: 774: 772: 769: 765: 764:Z-order curve 762: 760: 757: 755: 752: 750: 747: 745: 742: 740: 737: 735: 734:Hilbert curve 732: 730: 727: 723: 720: 719: 718: 717:De Rham curve 715: 713: 710: 709: 708: 705: 703: 700: 698: 695: 693: 690: 688: 685: 683: 682:Menger sponge 680: 678: 675: 673: 670: 668: 667:Barnsley fern 665: 664: 662: 660: 654: 648: 645: 643: 640: 636: 633: 631: 628: 626: 623: 621: 618: 614: 611: 610: 609: 606: 604: 601: 600: 599: 596: 595: 593: 589: 585: 578: 573: 571: 566: 564: 559: 558: 555: 549: 546: 544: 541: 539: 536: 534: 531: 529: 526: 524: 521: 519: 516: 515: 502: 498: 491: 477: 470: 462: 455: 447: 440: 424: 420: 413: 402: 395: 387: 381: 379: 374: 363: 362: 358: 356: 353: 351: 348: 346: 343: 341: 338: 336: 333: 331: 328: 326: 323: 321: 318: 316: 315: 311: 310: 300: 297: 295: 292: 290: 287: 285: 284:Menger sponge 282: 280: 276: 274: 271: 269: 266: 264: 261: 259: 258:De Rham curve 256: 254: 251: 249: 246: 245: 238: 236: 232: 228: 224: 220: 215: 213: 209: 205: 204:geomorphology 201: 197: 193: 189: 185: 173: 168: 164: 162: 158: 154: 144: 142: 138: 134: 130: 126: 122: 117: 115: 111: 107: 103: 99: 95: 85: 83: 78: 76: 72: 68: 64: 60: 56: 52: 48: 44: 43:fractal curve 37: 32: 19: 1163:Chaos theory 1158:Kaleidoscope 1149: 1141: 1133: 1059:Gaston Julia 1039:Georg Cantor 864:Escape-time 796:Gosper curve 744:Lévy C curve 729:Dragon curve 608:Box-counting 501:cut-the-knot 500: 490: 479:. Retrieved 469: 454: 439: 427:. Retrieved 422: 412: 394: 359: 312: 263:Dragon curve 216: 181: 150: 118: 91: 79: 65:— and every 51:irregularity 42: 40: 36:Gosper curve 1154:(1987 book) 1146:(1986 book) 1138:(1982 book) 1124:Fractal art 1044:Bill Gosper 1008:Lévy flight 754:Peano curve 749:Moore curve 635:Topological 620:Correlation 425:. wired.com 355:Quasicircle 289:Peano curve 212:linguistics 1178:Categories 962:Orbit trap 957:Buddhabrot 950:techniques 938:Mandelbulb 739:Koch curve 672:Cantor set 481:2020-05-17 369:References 350:Orbit trap 104:, feet of 102:snowflakes 1069:Paul Lévy 948:Rendering 933:Mandelbox 879:Julia set 791:Hexaflake 722:Minkowski 642:Recursion 625:Hausdorff 335:Hexaflake 196:economics 153:dimension 119:See also 979:fractals 866:fractals 834:L-system 776:T-square 584:Fractals 306:See also 241:Examples 223:surfaces 98:broccoli 928:Tricorn 781:n-flake 630:Packing 613:Higuchi 603:Assouad 139:, and 55:fractal 1027:People 977:Random 884:Filled 852:H tree 771:String 659:system 429:17 May 112:, and 106:geckos 94:nature 67:subarc 63:length 1103:Other 423:Wired 404:(PDF) 71:point 47:curve 431:2020 210:and 159:and 73:has 221:of 1180:: 1113:" 499:. 421:. 377:^ 229:, 214:. 206:, 202:, 198:, 163:. 143:. 135:, 131:, 127:, 123:, 116:. 108:, 100:, 84:. 77:. 41:A 1109:" 576:e 569:t 562:v 503:. 484:. 463:. 448:. 433:. 406:. 388:. 20:)

Index

Fractal Curves

Gosper curve
curve
irregularity
fractal
rectifiable curves
length
subarc
point
infinite length
Mandelbrot set
nature
broccoli
snowflakes
geckos
frost crystals
lightning bolts
Romanesco broccoli
dendrite crystal
trees, fractals
Hofstadter's butterfly
Lichtenberg figure
self-organized criticality
dimension
fractal dimension
list of fractals by Hausdorff dimension

Mandelbrot set
Benoit Mandelbrot

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