1816:
1010:
998:
1828:
1804:
1747:
1778:
1766:
1790:
950:
312:
1932:
A. Douady, “Algorithms for computing angles in the
Mandelbrot set,” in Chaotic Dynamics and Fractals, M. Barnsley and S. G. Demko, Eds., vol. 2 of Notes and Reports in Mathematics in Science and Engineering, pp. 155–168, Academic Press, Atlanta, Georgia, USA,
817:
2551:
189:
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783:
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337:
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1356:
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1213:
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1187:
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1143:
1096:
118:
46:
1645:
1619:
1596:
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1309:
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1163:
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980:
811:
451:
428:
404:
185:
158:
138:
66:
1503:
1895:
1777:
1746:
680:
476:
1380:
1189:
945:{\displaystyle A_{f}(\infty )\ {\overset {\underset {\mathrm {def} }{}}{=}}\ \{z\in \mathbb {C} :f^{(k)}(z)\to \infty \ as\ k\to \infty \}.}
307:{\displaystyle K(f){\overset {\mathrm {def} }{{}={}}}\left\{z\in \mathbb {C} :f^{(k)}(z)\not \to \infty ~{\text{as}}~k\to \infty \right\}}
1815:
2569:
1765:
549:
1977:
1972:
Peitgen Heinz-Otto, Richter, P.H. : The beauty of fractals: Images of
Complex Dynamical Systems. Springer-Verlag 1986.
1987:
608:
1803:
1911:
John Milnor : Pasting
Together Julia Sets: A Worked Out Example of Mating. Experimental Mathematics Volume 13 (2004)
1893:
Douglas C. Ravenel : External angles in the
Mandelbrot set: the work of Douady and Hubbard. University of Rochester
2015:
1986: : Holomorphic dynamical systems in the complex plane. Department of Mathematics Technical University of Denmark,
1827:
602:
543:
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1390:
2304:
1320:
1021:
2509:
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2075:
1947:
Topics from One-Dimensional
Dynamics Series: London Mathematical Society Student Texts (No. 62) page 257
1946:
2634:
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752:
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320:
598:
462:
347:
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2008:
657:
1325:
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1428:
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1957:
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1363:
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2314:
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1789:
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407:
94:
22:
8:
2629:
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2264:
2147:
2132:
2065:
955:
786:
671:
667:
535:
466:
73:
2199:
2514:
2494:
2458:
2453:
2216:
1783:
Filled Julia set for c=−1+0.1*i. Here Julia set is the boundary of filled-in Julia set.
1630:
1604:
1581:
1558:
1294:
1274:
1148:
1101:
965:
796:
436:
413:
389:
170:
143:
123:
51:
2624:
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2519:
2443:
2351:
2256:
2162:
2137:
2127:
2070:
2053:
2043:
2038:
2001:
1973:
983:
962:
coincides with the filled-in Julia set. This happens when all the critical points of
790:
675:
539:
470:
431:
1922:
Saaed Zakeri: Biaccessiblility in quadratic Julia sets I: The locally-connected case
1868:
1856:
2474:
2341:
2152:
164:
161:
2489:
2426:
2087:
1899:
2184:
2504:
2436:
2407:
2363:
2346:
2329:
2282:
2226:
2211:
2179:
2117:
340:
2448:
1728:{\displaystyle R{\overset {\mathrm {def} }{{}={}}}R_{1/2}\cup S_{c}\cup R_{0}}
2618:
2358:
2334:
2204:
2174:
2157:
2122:
2107:
1983:
1847:
1795:
658:
Relation between Julia, filled-in Julia set and attractive basin of infinity
2603:
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2169:
1942:
1757:
1449:
1384:
77:
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2194:
2189:
1873:
1860:
2417:
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2397:
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2112:
2373:
2319:
2231:
2082:
1921:
959:
663:
89:
69:
2274:
1958:
The
Mandelbrot Set And Its Associated Julia Sets by Hermann Karcher
2221:
2024:
2292:
793:= exterior of filled-in Julia set = set of escaping points for
1993:
742:{\displaystyle J(f)=\partial K(f)=\partial A_{f}(\infty )}
1771:
Filled Julia with no interior = Julia set. It is for c=i.
525:{\displaystyle K(f)=\mathbb {C} \setminus A_{f}(\infty )}
982:
are pre-periodic. Such critical points are often called
1653:
1633:
1607:
1584:
1561:
1541:
1518:
1457:
1431:
1393:
1366:
1328:
1297:
1277:
1221:
1198:
1175:
1151:
1124:
1104:
1077:
1029:
968:
820:
799:
755:
683:
611:
552:
479:
439:
416:
392:
350:
323:
192:
173:
146:
126:
97:
54:
25:
1727:
1639:
1613:
1590:
1567:
1547:
1527:
1487:
1440:
1415:
1372:
1350:
1303:
1283:
1259:
1207:
1181:
1157:
1137:
1110:
1090:
1063:
974:
944:
805:
777:
741:
647:
587:
524:
445:
422:
398:
378:
331:
306:
179:
152:
132:
112:
60:
40:
2616:
1118:is any complex number. In this case, the spine
597:In other words, the filled-in Julia set is the
1601:otherwise take the shortest way that contains
2009:
1735:divides dynamical plane into two components.
1314:spine is invariant under 180 degree rotation,
936:
867:
456:
2016:
2002:
1020:The most studied polynomials are probably
588:{\displaystyle A_{f}(\infty )=F_{\infty }}
1756:, c=1−φ=−0.618033988749…, where φ is the
877:
496:
325:
241:
1488:{\displaystyle {\mathcal {R}}_{1/2}^{K}}
2570:List of fractals by Hausdorff dimension
1821:Filled Julia set for c = 0.285 + 0.01i.
1809:Filled Julia set for c = −0.8 + 0.156i.
1499:Algorithms for constructing the spine:
2617:
1598:has empty interior then arc is unique,
1416:{\displaystyle {\mathcal {R}}_{0}^{K}}
1997:
648:{\displaystyle K(f)=F_{\infty }^{C}.}
140:is defined as the set of all points
83:
1317:spine is a finite topological tree,
670:of the filled-in Julia set and the
13:
1675:
1672:
1669:
1461:
1397:
954:If the filled-in Julia set has no
933:
912:
857:
854:
851:
834:
769:
733:
717:
699:
632:
580:
566:
516:
296:
276:
223:
220:
217:
14:
2646:
2552:How Long Is the Coast of Britain?
1509:Simplified version of algorithm:
500:
160:of the dynamical plane that have
1833:Filled Julia set for c = −1.476.
1826:
1814:
1802:
1788:
1776:
1764:
1745:
1008:
996:
461:The filled-in Julia set is the
2576:The Fractal Geometry of Nature
1951:
1936:
1926:
1915:
1904:
1886:
1039:
1033:
930:
909:
906:
900:
895:
889:
837:
831:
778:{\displaystyle A_{f}(\infty )}
772:
766:
736:
730:
711:
705:
693:
687:
621:
615:
569:
563:
519:
513:
489:
483:
373:
367:
362:
356:
293:
270:
264:
259:
253:
202:
196:
107:
101:
35:
29:
1:
1966:
1071:, which are often denoted by
1015:Basilica Julia set with spine
2023:
1358:always belongs to the spine.
1064:{\displaystyle f(z)=z^{2}+c}
332:{\displaystyle \mathbb {C} }
7:
2592:Chaos: Making a New Science
1260:{\displaystyle S_{c}=\left}
1003:Rabbit Julia set with spine
544:components of the Fatou set
10:
2651:
379:{\displaystyle f^{(k)}(z)}
2543:
2467:
2416:
2387:
2303:
2273:
2255:
2096:
2031:
1738:
1506:is described by A. Douady
457:Relation to the Fatou set
1879:
1838:
1351:{\displaystyle z_{cr}=0}
1291:. This makes sense when
1145:of the filled Julia set
989:
1528:{\displaystyle -\beta }
1441:{\displaystyle -\beta }
1208:{\displaystyle -\beta }
2584:The Beauty of Fractals
1988:MAT-Report no. 1996-42
1752:Filled Julia set for f
1729:
1641:
1615:
1592:
1569:
1549:
1548:{\displaystyle \beta }
1529:
1489:
1442:
1417:
1383:is a landing point of
1374:
1373:{\displaystyle \beta }
1352:
1305:
1285:
1267:with such properties:
1261:
1209:
1183:
1182:{\displaystyle \beta }
1159:
1139:
1112:
1092:
1065:
976:
946:
807:
779:
743:
649:
589:
526:
447:
424:
400:
380:
341:set of complex numbers
333:
308:
181:
154:
134:
114:
62:
42:
1730:
1642:
1616:
1593:
1570:
1550:
1530:
1490:
1443:
1418:
1375:
1353:
1311:is connected and full
1306:
1286:
1262:
1210:
1184:
1160:
1140:
1138:{\displaystyle S_{c}}
1113:
1093:
1091:{\displaystyle f_{c}}
1066:
977:
947:
808:
780:
744:
650:
590:
527:
463:(absolute) complement
448:
432:iteration of function
425:
401:
381:
334:
309:
182:
155:
135:
115:
63:
43:
2530:Lewis Fry Richardson
2525:Hamid Naderi Yeganeh
2315:Burning Ship fractal
2247:Weierstrass function
1651:
1631:
1605:
1582:
1559:
1539:
1516:
1455:
1448:is landing point of
1429:
1391:
1364:
1326:
1295:
1275:
1219:
1196:
1173:
1149:
1122:
1102:
1075:
1027:
966:
818:
797:
753:
681:
609:
550:
477:
437:
414:
390:
348:
321:
190:
171:
144:
124:
113:{\displaystyle K(f)}
95:
52:
41:{\displaystyle K(f)}
23:
2288:Space-filling curve
2265:Multifractal system
2148:Space-filling curve
2133:Sierpinski triangle
1484:
1412:
641:
18:filled-in Julia set
2515:Aleksandr Lyapunov
2495:Desmond Paul Henry
2459:Self-avoiding walk
2454:Percolation theory
2098:Iterated function
2039:Fractal dimensions
1898:2012-02-08 at the
1725:
1637:
1611:
1588:
1565:
1545:
1525:
1485:
1458:
1438:
1413:
1394:
1370:
1348:
1301:
1281:
1271:spine lies inside
1257:
1205:
1179:
1155:
1135:
1108:
1088:
1061:
984:Misiurewicz points
972:
942:
861:
803:
775:
739:
645:
627:
585:
522:
443:
420:
396:
376:
329:
304:
177:
150:
130:
110:
58:
38:
2612:
2611:
2558:Coastline paradox
2535:Wacław Sierpiński
2520:Benoit Mandelbrot
2444:Fractal landscape
2352:Misiurewicz point
2257:Strange attractor
2138:Apollonian gasket
2128:Sierpinski carpet
1978:978-0-387-15851-8
1945:, H Bruin :
1857:San Marco fractal
1679:
1640:{\displaystyle R}
1614:{\displaystyle 0}
1591:{\displaystyle K}
1568:{\displaystyle K}
1304:{\displaystyle K}
1284:{\displaystyle K}
1158:{\displaystyle K}
1111:{\displaystyle c}
1022:those of the form
975:{\displaystyle f}
926:
917:
866:
862:
849:
848:
842:
806:{\displaystyle f}
601:of the unbounded
446:{\displaystyle f}
423:{\displaystyle f}
399:{\displaystyle k}
289:
285:
281:
227:
180:{\displaystyle f}
153:{\displaystyle z}
133:{\displaystyle f}
84:Formal definition
61:{\displaystyle f}
2642:
2635:Complex dynamics
2475:Michael Barnsley
2342:Lyapunov fractal
2200:Sierpiński curve
2153:Blancmange curve
2018:
2011:
2004:
1995:
1994:
1960:
1955:
1949:
1940:
1934:
1930:
1924:
1919:
1913:
1908:
1902:
1890:
1861:San Marco dragon
1830:
1818:
1806:
1792:
1780:
1768:
1749:
1734:
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1572:
1571:
1566:
1554:
1552:
1551:
1546:
1534:
1532:
1531:
1526:
1504:detailed version
1494:
1492:
1491:
1486:
1483:
1478:
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1464:
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1439:
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973:
951:
949:
948:
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924:
915:
899:
898:
880:
864:
863:
860:
844:
840:
830:
829:
812:
810:
809:
804:
787:attractive basin
784:
782:
781:
776:
765:
764:
748:
746:
745:
740:
729:
728:
672:attractive basin
654:
652:
651:
646:
640:
635:
594:
592:
591:
586:
584:
583:
562:
561:
536:attractive basin
531:
529:
528:
523:
512:
511:
499:
467:attractive basin
452:
450:
449:
444:
429:
427:
426:
421:
405:
403:
402:
397:
385:
383:
382:
377:
366:
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279:
263:
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244:
228:
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215:
214:
209:
206:
186:
184:
183:
178:
167:with respect to
159:
157:
156:
151:
139:
137:
136:
131:
120:of a polynomial
119:
117:
116:
111:
78:non-escaping set
67:
65:
64:
59:
48:of a polynomial
47:
45:
44:
39:
2650:
2649:
2645:
2644:
2643:
2641:
2640:
2639:
2615:
2614:
2613:
2608:
2539:
2490:Felix Hausdorff
2463:
2427:Brownian motion
2412:
2383:
2306:
2299:
2269:
2251:
2242:Pythagoras tree
2099:
2092:
2088:Self-similarity
2032:Characteristics
2027:
2022:
1969:
1964:
1963:
1956:
1952:
1941:
1937:
1931:
1927:
1920:
1916:
1909:
1905:
1900:Wayback Machine
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964:
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754:
751:
750:
724:
720:
682:
679:
678:
660:
636:
631:
610:
607:
606:
603:Fatou component
579:
575:
557:
553:
551:
548:
547:
507:
503:
495:
478:
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459:
438:
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96:
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86:
53:
50:
49:
24:
21:
20:
12:
11:
5:
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2601:
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2560:
2547:
2545:
2541:
2540:
2538:
2537:
2532:
2527:
2522:
2517:
2512:
2507:
2505:Helge von Koch
2502:
2497:
2492:
2487:
2482:
2477:
2471:
2469:
2465:
2464:
2462:
2461:
2456:
2451:
2446:
2441:
2440:
2439:
2437:Brownian motor
2434:
2423:
2421:
2414:
2413:
2411:
2410:
2408:Pickover stalk
2405:
2400:
2394:
2392:
2385:
2384:
2382:
2381:
2376:
2371:
2366:
2364:Newton fractal
2361:
2356:
2355:
2354:
2347:Mandelbrot set
2344:
2339:
2338:
2337:
2332:
2330:Newton fractal
2327:
2317:
2311:
2309:
2301:
2300:
2298:
2297:
2296:
2295:
2285:
2283:Fractal canopy
2279:
2277:
2271:
2270:
2268:
2267:
2261:
2259:
2253:
2252:
2250:
2249:
2244:
2239:
2234:
2229:
2227:Vicsek fractal
2224:
2219:
2214:
2209:
2208:
2207:
2202:
2197:
2192:
2187:
2182:
2177:
2172:
2167:
2166:
2165:
2155:
2145:
2143:Fibonacci word
2140:
2135:
2130:
2125:
2120:
2118:Koch snowflake
2115:
2110:
2104:
2102:
2094:
2093:
2091:
2090:
2085:
2080:
2079:
2078:
2073:
2068:
2063:
2058:
2057:
2056:
2046:
2035:
2033:
2029:
2028:
2021:
2020:
2013:
2006:
1998:
1992:
1991:
1981:
1968:
1965:
1962:
1961:
1950:
1935:
1925:
1914:
1903:
1884:
1883:
1881:
1878:
1877:
1876:
1871:
1866:
1863:
1853:
1850:
1845:
1840:
1837:
1836:
1835:
1832:
1825:
1823:
1820:
1813:
1811:
1808:
1801:
1799:
1794:
1787:
1785:
1782:
1775:
1773:
1770:
1763:
1761:
1753:
1751:
1744:
1740:
1737:
1722:
1718:
1714:
1709:
1705:
1701:
1696:
1692:
1688:
1684:
1677:
1674:
1671:
1664:
1656:
1636:
1625:
1624:
1623:
1622:
1610:
1599:
1587:
1576:
1564:
1544:
1524:
1521:
1507:
1497:
1496:
1482:
1477:
1473:
1469:
1463:
1437:
1434:
1424:
1410:
1405:
1399:
1387:of angle zero
1369:
1359:
1347:
1344:
1339:
1336:
1332:
1321:Critical point
1318:
1315:
1312:
1300:
1280:
1255:
1251:
1248:
1245:
1242:
1238:
1234:
1229:
1225:
1204:
1201:
1178:
1165:is defined as
1154:
1132:
1128:
1107:
1085:
1081:
1060:
1057:
1052:
1048:
1044:
1041:
1038:
1035:
1032:
1018:
1017:
1014:
1007:
1005:
1002:
995:
991:
988:
971:
941:
938:
935:
932:
929:
923:
920:
914:
911:
908:
905:
902:
897:
894:
891:
887:
883:
879:
875:
872:
869:
859:
856:
853:
847:
839:
836:
833:
828:
824:
802:
774:
771:
768:
763:
759:
738:
735:
732:
727:
723:
719:
716:
713:
710:
707:
704:
701:
698:
695:
692:
689:
686:
666:is the common
659:
656:
644:
639:
634:
630:
626:
623:
620:
617:
614:
582:
578:
574:
571:
568:
565:
560:
556:
542:is one of the
521:
518:
515:
510:
506:
502:
498:
494:
491:
488:
485:
482:
458:
455:
454:
453:
442:
430:with itself =
419:
395:
375:
372:
369:
364:
361:
358:
354:
343:
327:
302:
298:
295:
292:
278:
275:
272:
269:
266:
261:
258:
255:
251:
247:
243:
239:
236:
232:
225:
222:
219:
212:
204:
201:
198:
195:
176:
149:
129:
109:
106:
103:
100:
88:The filled-in
85:
82:
57:
37:
34:
31:
28:
9:
6:
4:
3:
2:
2647:
2636:
2633:
2631:
2628:
2626:
2623:
2622:
2620:
2605:
2602:
2600:
2597:
2594:
2593:
2589:
2586:
2585:
2581:
2578:
2577:
2573:
2571:
2568:
2566:
2563:
2559:
2556:
2555:
2553:
2549:
2548:
2546:
2542:
2536:
2533:
2531:
2528:
2526:
2523:
2521:
2518:
2516:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2493:
2491:
2488:
2486:
2483:
2481:
2478:
2476:
2473:
2472:
2470:
2466:
2460:
2457:
2455:
2452:
2450:
2447:
2445:
2442:
2438:
2435:
2433:
2432:Brownian tree
2430:
2429:
2428:
2425:
2424:
2422:
2419:
2415:
2409:
2406:
2404:
2401:
2399:
2396:
2395:
2393:
2390:
2386:
2380:
2377:
2375:
2372:
2370:
2367:
2365:
2362:
2360:
2359:Multibrot set
2357:
2353:
2350:
2349:
2348:
2345:
2343:
2340:
2336:
2335:Douady rabbit
2333:
2331:
2328:
2326:
2323:
2322:
2321:
2318:
2316:
2313:
2312:
2310:
2308:
2302:
2294:
2291:
2290:
2289:
2286:
2284:
2281:
2280:
2278:
2276:
2272:
2266:
2263:
2262:
2260:
2258:
2254:
2248:
2245:
2243:
2240:
2238:
2235:
2233:
2230:
2228:
2225:
2223:
2220:
2218:
2215:
2213:
2210:
2206:
2205:Z-order curve
2203:
2201:
2198:
2196:
2193:
2191:
2188:
2186:
2183:
2181:
2178:
2176:
2175:Hilbert curve
2173:
2171:
2168:
2164:
2161:
2160:
2159:
2158:De Rham curve
2156:
2154:
2151:
2150:
2149:
2146:
2144:
2141:
2139:
2136:
2134:
2131:
2129:
2126:
2124:
2123:Menger sponge
2121:
2119:
2116:
2114:
2111:
2109:
2108:Barnsley fern
2106:
2105:
2103:
2101:
2095:
2089:
2086:
2084:
2081:
2077:
2074:
2072:
2069:
2067:
2064:
2062:
2059:
2055:
2052:
2051:
2050:
2047:
2045:
2042:
2041:
2040:
2037:
2036:
2034:
2030:
2026:
2019:
2014:
2012:
2007:
2005:
2000:
1999:
1996:
1989:
1985:
1984:Bodil Branner
1982:
1979:
1975:
1971:
1970:
1959:
1954:
1948:
1944:
1939:
1929:
1923:
1918:
1912:
1907:
1901:
1897:
1894:
1889:
1885:
1875:
1872:
1870:
1867:
1864:
1862:
1858:
1854:
1851:
1849:
1848:Douady rabbit
1846:
1843:
1842:
1829:
1824:
1817:
1812:
1805:
1800:
1797:
1796:Douady rabbit
1791:
1786:
1779:
1774:
1767:
1762:
1759:
1748:
1743:
1742:
1736:
1720:
1716:
1712:
1707:
1703:
1699:
1694:
1690:
1686:
1682:
1662:
1654:
1634:
1608:
1600:
1585:
1577:
1562:
1542:
1522:
1519:
1511:
1510:
1508:
1505:
1502:
1501:
1500:
1480:
1475:
1471:
1467:
1451:
1435:
1432:
1425:
1408:
1403:
1386:
1382:
1367:
1360:
1345:
1342:
1337:
1334:
1330:
1322:
1319:
1316:
1313:
1298:
1278:
1270:
1269:
1268:
1253:
1249:
1246:
1243:
1240:
1236:
1232:
1227:
1223:
1202:
1199:
1191:
1176:
1168:
1152:
1130:
1126:
1105:
1083:
1079:
1058:
1055:
1050:
1046:
1042:
1036:
1030:
1023:
1011:
1006:
999:
994:
993:
987:
985:
969:
961:
957:
952:
939:
927:
921:
918:
903:
892:
885:
881:
873:
870:
845:
826:
822:
813:
800:
792:
788:
761:
757:
725:
721:
714:
708:
702:
696:
690:
684:
677:
673:
669:
665:
655:
642:
637:
628:
624:
618:
612:
604:
600:
595:
576:
572:
558:
554:
545:
541:
537:
532:
508:
504:
492:
486:
480:
472:
468:
464:
440:
433:
417:
409:
393:
370:
359:
352:
344:
342:
317:
316:
315:
300:
290:
273:
267:
256:
249:
245:
237:
234:
230:
210:
199:
193:
174:
166:
163:
147:
127:
104:
98:
91:
81:
79:
75:
71:
55:
32:
26:
19:
2604:Chaos theory
2599:Kaleidoscope
2590:
2582:
2574:
2500:Gaston Julia
2480:Georg Cantor
2324:
2305:Escape-time
2237:Gosper curve
2185:Lévy C curve
2170:Dragon curve
2049:Box-counting
1953:
1938:
1928:
1917:
1906:
1888:
1855:basilica or
1758:Golden ratio
1626:
1498:
1450:external ray
1385:external ray
1381:-fixed point
1190:-fixed point
1019:
953:
814:
785:denotes the
661:
596:
533:
460:
87:
17:
15:
2595:(1987 book)
2587:(1986 book)
2579:(1982 book)
2565:Fractal art
2485:Bill Gosper
2449:Lévy flight
2195:Peano curve
2190:Moore curve
2076:Topological
2061:Correlation
1943:K M. Brucks
1874:Siegel disc
1865:cauliflower
408:composition
2630:Limit sets
2619:Categories
2403:Orbit trap
2398:Buddhabrot
2391:techniques
2379:Mandelbulb
2180:Koch curve
2113:Cantor set
1967:References
1575:by an arc,
599:complement
2510:Paul Lévy
2389:Rendering
2374:Mandelbox
2320:Julia set
2232:Hexaflake
2163:Minkowski
2083:Recursion
2066:Hausdorff
1713:∪
1700:∪
1543:β
1523:β
1520:−
1436:β
1433:−
1368:β
1250:β
1244:β
1241:−
1203:β
1200:−
1177:β
960:Julia set
958:then the
934:∞
931:→
913:∞
910:→
874:∈
835:∞
770:∞
734:∞
718:∂
700:∂
664:Julia set
633:∞
581:∞
567:∞
517:∞
501:∖
297:∞
294:→
277:∞
238:∈
90:Julia set
70:Julia set
2625:Fractals
2420:fractals
2307:fractals
2275:L-system
2217:T-square
2025:Fractals
1896:Archived
1869:dendrite
1844:airplane
1512:connect
1169:between
1098:, where
956:interior
791:infinity
676:infinity
668:boundary
540:infinity
471:infinity
274:↛
74:interior
72:and its
2369:Tricorn
2222:n-flake
2071:Packing
2054:Higuchi
2044:Assouad
1555:within
749:where:
465:of the
386:is the
339:is the
314:where:
162:bounded
2468:People
2418:Random
2325:Filled
2293:H tree
2212:String
2100:system
1976:
1852:dragon
1739:Images
1627:Curve
925:
916:
865:
841:
406:-fold
288:
280:
2544:Other
1933:1986.
1880:Notes
1839:Names
1578:when
1192:and
990:Spine
165:orbit
68:is a
1974:ISBN
1535:and
662:The
534:The
16:The
1859:or
1167:arc
789:of
674:of
538:of
469:of
410:of
2621::
2554:"
1647::
1215:,
986:.
605::
546:.
473:.
284:as
80:.
76:,
2550:"
2017:e
2010:t
2003:v
1990:.
1980:.
1754:c
1721:0
1717:R
1708:c
1704:S
1695:2
1691:/
1687:1
1683:R
1676:f
1673:e
1670:d
1663:=
1655:R
1635:R
1621:.
1609:0
1586:K
1563:K
1495:.
1481:K
1476:2
1472:/
1468:1
1462:R
1423:,
1409:K
1404:0
1398:R
1346:0
1343:=
1338:r
1335:c
1331:z
1299:K
1279:K
1254:]
1247:,
1237:[
1233:=
1228:c
1224:S
1153:K
1131:c
1127:S
1106:c
1084:c
1080:f
1059:c
1056:+
1051:2
1047:z
1043:=
1040:)
1037:z
1034:(
1031:f
970:f
940:.
937:}
928:k
922:s
919:a
907:)
904:z
901:(
896:)
893:k
890:(
886:f
882::
878:C
871:z
868:{
858:f
855:e
852:d
846:=
838:)
832:(
827:f
823:A
801:f
773:)
767:(
762:f
758:A
737:)
731:(
726:f
722:A
715:=
712:)
709:f
706:(
703:K
697:=
694:)
691:f
688:(
685:J
643:.
638:C
629:F
625:=
622:)
619:f
616:(
613:K
577:F
573:=
570:)
564:(
559:f
555:A
520:)
514:(
509:f
505:A
497:C
493:=
490:)
487:f
484:(
481:K
441:f
418:f
394:k
374:)
371:z
368:(
363:)
360:k
357:(
353:f
326:C
301:}
291:k
271:)
268:z
265:(
260:)
257:k
254:(
250:f
246::
242:C
235:z
231:{
224:f
221:e
218:d
211:=
203:)
200:f
197:(
194:K
175:f
148:z
128:f
108:)
105:f
102:(
99:K
56:f
36:)
33:f
30:(
27:K
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