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multiplicities) onto the 3-sphere. In the 1920s
Alexander and Briggs used this technique to compute the homology of cyclic branched covers of knots with 8 or fewer crossings, successfully distinguishing them all from each other (and the unknot). By 1932 Reidemeister extended this to 9 crossings, relying on linking numbers between branch curves of non-cyclic knot covers. The fact that these imaginary objects have no "real" existence does not stand in the way of their usefulness for proving knots distinct. It was the key to Perko's 1973 discovery of the duplicate knot type in Little's 1899 table of 10-crossing knots.
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Permutation groups have nice visualizations of their elements that assist in explaining their structureâe.g., the rotated and flipped regular p-gons that comprise the dihedral group of order 2p. They may be used to "see" the relationships among linking numbers between branch curves of dihedral
510:
Many people have a vivid âmindâs eye,â but a team of
British scientists has found that tens of millions of people cannot conjure images. The lack of a mental camera is known as aphantasia, and millions more experience extraordinarily strong mental imagery, called hyperphantasia. Researchers are
519:
used to classify all closed orientable 2-manifolds, Heegaard's 1898 thesis "looked at" similar structures for functions of two complex variables, taking an imaginary 4-dimensional surface in
Euclidean 6-space (corresponding to the function f=x^2-y^3) and projecting it stereographically (with
828:â that a sphere can be turned inside out in 3 dimension if allowed to pass through itself, but without kinks â was a startling and counter-intuitive result, originally proven via abstract means, later demonstrated graphically, first in drawings, later in computer animation.
328:, functions of the complex plane are inherently 4-dimensional, but there is no natural geometric projection into lower dimensional visual representations. Instead, colour vision is exploited to capture dimensional information using techniques such as
514:
Visualization played an important role at the beginning of topological knot theory, when polyhedral decompositions were used to compute the homology of covering spaces of knots. Extending to 3 dimensions the physically impossible
188:, these three planes represent solutions of linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations.
42:. Classically, this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century). In contrast, today it most frequently consists of
721:"Inelegant" is a translation of Knuth's version of the algorithm with a subtraction-based remainder-loop replacing his use of division (or a "modulus" instruction). Derived from Knuth 1973:2â4.
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to make static two- or three-dimensional drawings, animations, or interactive programs. Writing programs to visualize mathematics is an aspect of
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705:(2002), is one of the most intensely visual books published in the field of mathematics. It has been criticized for being
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Geometry can be defined as the study of shapes their size, angles, dimensions and proportions
123:
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heavily visual, with much information conveyed by pictures that do not have formal meaning.
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Mathematical visualization is used throughout mathematics, particularly in the fields of
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studying how these two conditions arise through changes in the wiring of the brain.
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have existed since antiquity, as in the
Pythagorean theorem proof found in the
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1051:"The Visualization of Mathematics: Towards a Mathematical Exploratorium"
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1020:"A Revolution or self indulgent hype? How top scientists view Wolfram"
340:
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31:, one of the most famous examples of mathematical visualization.
1287:
16:
For mathematical visualization in the context of science, see
1589:
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588:(with six bells), one of the earliest nontrivial results in
1207:
1197:
842:
1465:
1018:
Berry, Michael; Ellis, John; Deutch, David (15 May 2002).
1614:
885:"What is Geometry? - Definition, Facts and Examples"
839:regularly features a mathematical visualization.
3349:
1017:
793:Chinese text which dates from 1046 BC to 256 BC.
18:scientific_visualization § In_mathematics
2367:Note: This template roughly follows the 2012
2343:
1451:
1099:
38:phenomena can be understood and explored via
1059:Notices of the American Mathematical Society
836:Notices of the American Mathematical Society
2350:
2336:
1458:
1444:
1106:
1092:
908:
86:(particularly numerical solutions, as in
841:
807:
764:
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635:
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404:
339:
231:
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117:
22:
471:or fewer (not including mirror images).
3350:
3067:Knowledge representation and reasoning
1048:
948:"On dihedral covering spaces of knots"
3092:Philosophy of artificial intelligence
2331:
1439:
1087:
1049:Palais, Richard S. (JuneâJuly 1999),
945:
2411:Energy consumption (Green computing)
2357:
1113:
1011:
724:
656:
631:
595:
572:covering spaces of knots and links.
535:
532:A force-based network visualization.
474:
418:
368:
288:
191:
139:
3097:Distributed artificial intelligence
2369:ACM Computing Classification System
227:
13:
2602:Integrated development environment
14:
3374:
3077:Automated planning and scheduling
2607:Software configuration management
1072:
760:
175:
3331:
3321:
3312:
3311:
728:
660:
599:
575:
539:
478:
422:
372:
292:
195:
143:
3322:
2725:Computational complexity theory
911:"La connaissance est un réseau"
523:
335:
80:ordinary differential equations
53:
2509:Network performance evaluation
978:
939:
901:
877:
712:
84:partial differential equations
1:
2880:Multimedia information system
2865:Geographic information system
2855:Enterprise information system
2444:Computer systems organization
1482:Biological data visualization
870:
3239:Computational social science
2827:Theoretical computer science
2640:Software development process
2416:Electronic design automation
2401:Very Large Scale Integration
650:" in the cellular automaton
7:
3062:Natural language processing
2850:Information storage systems
853:
818:turning a sphere inside out
802:27 lines on a cubic surface
454:
113:
66:. Notable examples include
10:
3379:
2978:Humanâcomputer interaction
2948:Intrusion detection system
2860:Social information systems
2845:Database management system
1522:Mathematical visualization
1407:Mathematical visualization
1382:Computer-generated imagery
946:Perko, K. A. (June 1976).
909:Grandjean, Martin (2014).
15:
3307:
3244:Computational engineering
3219:Computational mathematics
3196:
3143:
3105:
3052:
3014:
2976:
2918:
2835:
2781:
2743:
2688:
2625:
2558:
2522:
2479:
2443:
2376:
2365:
2200:
2070:
1934:
1888:
1812:
1711:
1680:
1673:
1580:
1517:Information visualization
1502:Educational visualization
1474:
1420:
1374:
1333:
1300:
1280:
1244:
1237:
1216:
1185:
1144:
1121:
993:, Penguin Books, London,
832:The cover of the journal
126:, an important result in
3363:Visualization (graphics)
3254:Computational healthcare
3249:Differentiable computing
3168:Graphics processing unit
2587:Domain-specific language
2456:Computational complexity
1693:Charles-René de Fourcroy
1542:Scientific visualization
1469:of technical information
1402:Iterated function system
952:Inventiones mathematicae
915:Les Cahiers du Numérique
816:, the half-way stage in
798:Clebsch diagonal surface
3229:Computational chemistry
3163:Photograph manipulation
3054:Artificial intelligence
2870:Decision support system
990:Darwin's Dangerous Idea
414:Costa's Minimal Surface
3294:Educational technology
3125:Reinforcement learning
2875:Process control system
2773:Computational geometry
2763:Algorithmic efficiency
2758:Analysis of algorithms
2406:Systems on Chip (SoCs)
2113:Christopher R. Johnson
1665:Technical illustration
1552:Software visualization
927:10.3166/lcn.10.3.37-54
850:
821:
782:
722:
654:
593:
533:
472:
416:
366:
286:
189:
134:
48:computational geometry
32:
3264:Electronic publishing
3234:Computational biology
3224:Computational physics
3120:Unsupervised learning
3034:Distributed computing
2910:Information retrieval
2817:Mathematical analysis
2807:Mathematical software
2690:Theory of computation
2655:Software construction
2645:Requirements analysis
2523:Software organization
2451:Computer architecture
2421:Hardware acceleration
2386:Printed circuit board
2007:Lawrence J. Rosenblum
1820:Edward Walter Maunder
1744:Charles Joseph Minard
1562:User interface design
1537:Product visualization
845:
811:
768:
720:
702:A New Kind of Science
652:Conway's Game of Life
639:
583:
531:
462:
412:
405:Differential geometry
343:
235:
184:In three-dimensional
183:
121:
26:
3024:Concurrent computing
2996:Ubiquitous computing
2968:Application security
2963:Information security
2792:Discrete mathematics
2768:Randomized algorithm
2720:Computability theory
2698:Model of computation
2670:Software maintenance
2665:Software engineering
2627:Software development
2577:Programming language
2572:Programming paradigm
2489:Network architecture
2287:Scientific modelling
2262:Information graphics
2002:Clifford A. Pickover
1952:William S. Cleveland
1860:Henry Norris Russell
1845:Howard G. Funkhouser
1789:Florence Nightingale
1754:Francis Amasa Walker
1650:Statistical graphics
1572:Volume visualization
1547:Social visualization
1341:Burning Ship fractal
860:Mathematical diagram
787:Proofs without words
3299:Document management
3289:Operations research
3214:Enterprise software
3130:Multi-task learning
3115:Supervised learning
2837:Information systems
2660:Software deployment
2617:Software repository
2471:Real-time computing
2267:Information science
2230:in computer science
2022:Sheelagh Carpendale
1957:George G. Robertson
1794:Karl Wilhelm Pohlke
1729:André-Michel Guerry
1605:Graph of a function
1600:Engineering drawing
1387:Fractal compression
1310:MojoWorld Generator
1272:Wolfram Mathematica
1079:Virtual Math Museum
1028:The Daily Telegraph
889:www.splashlearn.com
775:Pythagorean theorem
771:proof without words
132:projective geometry
122:An illustration of
3082:Search methodology
3029:Parallel computing
2986:Interaction design
2895:Computing platform
2822:Numerical analysis
2812:Information theory
2597:Software framework
2560:Software notations
2499:Network components
2396:Integrated circuit
2307:Volume cartography
2071:Early 21st century
1967:Catherine Plaisant
1962:Bruce H. McCormick
1916:Mary Eleanor Spear
1906:Arthur H. Robinson
1840:Arthur Lyon Bowley
1813:Early 20th century
1660:Technical drawings
1532:Molecular graphics
1507:Flow visualization
1497:Data visualization
964:10.1007/bf01425475
851:
822:
783:
740:. You can help by
723:
672:. You can help by
655:
611:. You can help by
594:
551:. You can help by
534:
490:. You can help by
473:
434:. You can help by
417:
384:. You can help by
367:
304:. You can help by
287:
207:. You can help by
190:
155:. You can help by
135:
124:Desargues' theorem
33:
3345:
3344:
3274:Electronic voting
3204:Quantum Computing
3197:Applied computing
3183:Image compression
2953:Hardware security
2943:Security services
2900:Digital marketing
2680:Open-source model
2592:Modeling language
2504:Network scheduler
2325:
2324:
2302:Visual perception
2252:Graphic organizer
2225:Computer graphics
2196:
2195:
2178:Martin Wattenberg
2153:Hanspeter Pfister
2108:Martin Krzywinski
2032:Jock D. Mackinlay
2012:Thomas A. DeFanti
1935:Late 20th century
1855:Ejnar Hertzsprung
1557:Technical drawing
1433:
1432:
1392:Fractal landscape
1302:Scenery generator
1296:
1295:
1131:Graphics software
999:978-0-14-016734-4
800:demonstrates the
758:
757:
697:cellular automata
690:
689:
632:Cellular automata
629:
628:
569:
568:
508:
507:
452:
451:
402:
401:
322:
321:
225:
224:
173:
172:
3370:
3335:
3334:
3325:
3324:
3315:
3314:
3135:Cross-validation
3107:Machine learning
2991:Social computing
2958:Network security
2753:Algorithm design
2675:Programming team
2635:Control variable
2612:Software library
2550:Software quality
2545:Operating system
2494:Network protocol
2359:Computer science
2352:
2345:
2338:
2329:
2328:
2312:Volume rendering
2297:Visual analytics
2292:Spatial analysis
2272:Misleading graph
2123:David McCandless
2098:Gordon Kindlmann
2062:Alfred Inselberg
2057:Leland Wilkinson
1992:Michael Friendly
1926:Howard T. Fisher
1889:Mid 20th century
1830:W. E. B. Du Bois
1734:William Playfair
1724:Adolphe Quetelet
1698:Joseph Priestley
1681:Pre-19th century
1678:
1677:
1645:Skeletal formula
1512:Geovisualization
1487:Chemical imaging
1460:
1453:
1446:
1437:
1436:
1242:
1241:
1167:Kalles Fraktaler
1115:Fractal software
1108:
1101:
1094:
1085:
1084:
1067:
1055:
1040:
1039:
1037:
1035:
1024:
1015:
1009:
982:
976:
975:
943:
937:
936:
934:
933:
905:
899:
898:
896:
895:
881:
753:
750:
732:
725:
685:
682:
664:
657:
624:
621:
603:
596:
564:
561:
543:
536:
517:Riemann surfaces
503:
500:
482:
475:
447:
444:
426:
419:
397:
394:
376:
369:
365:
358:
354:
346:Lorenz attractor
326:complex analysis
317:
314:
296:
289:
284:
283:
281:
280:
271:
268:
228:Complex analysis
220:
217:
199:
192:
168:
165:
147:
140:
92:minimal surfaces
3378:
3377:
3373:
3372:
3371:
3369:
3368:
3367:
3348:
3347:
3346:
3341:
3332:
3303:
3284:Word processing
3192:
3178:Virtual reality
3139:
3101:
3072:Computer vision
3048:
3044:Multiprocessing
3010:
2972:
2938:Security hacker
2914:
2890:Digital library
2831:
2782:Mathematics of
2777:
2739:
2715:Automata theory
2710:Formal language
2684:
2650:Software design
2621:
2554:
2540:Virtual machine
2518:
2514:Network service
2475:
2466:Embedded system
2439:
2372:
2361:
2356:
2326:
2321:
2317:Information art
2257:Imaging science
2202:
2192:
2173:Fernanda Viégas
2168:Moritz Stefaner
2093:Jessica Hullman
2066:
2037:Alan MacEachren
1987:Ben Shneiderman
1930:
1884:
1808:
1707:
1669:
1582:
1576:
1527:Medical imaging
1470:
1464:
1434:
1429:
1416:
1370:
1329:
1292:
1276:
1233:
1212:
1181:
1140:
1117:
1112:
1075:
1070:
1053:
1044:
1043:
1033:
1031:
1022:
1016:
1012:
983:
979:
944:
940:
931:
929:
906:
902:
893:
891:
883:
882:
878:
873:
865:Geometry Center
856:
826:Sphere eversion
791:Zhoubi Suanjing
779:Zhoubi Suanjing
763:
754:
748:
745:
738:needs expansion
715:
693:Stephen Wolfram
686:
680:
677:
670:needs expansion
634:
625:
619:
616:
609:needs expansion
578:
565:
559:
556:
549:needs expansion
526:
504:
498:
495:
488:needs expansion
463:A table of all
457:
448:
442:
439:
432:needs expansion
407:
398:
392:
389:
382:needs expansion
360:
356:
349:
338:
330:domain coloring
318:
312:
309:
302:needs expansion
285:
272:
269:
254:
253:
251:
242:
240:
237:Domain coloring
230:
221:
215:
212:
205:needs expansion
186:Euclidean space
178:
169:
163:
160:
153:needs expansion
116:
56:
44:using computers
21:
12:
11:
5:
3376:
3366:
3365:
3360:
3343:
3342:
3340:
3339:
3329:
3319:
3308:
3305:
3304:
3302:
3301:
3296:
3291:
3286:
3281:
3276:
3271:
3266:
3261:
3256:
3251:
3246:
3241:
3236:
3231:
3226:
3221:
3216:
3211:
3206:
3200:
3198:
3194:
3193:
3191:
3190:
3188:Solid modeling
3185:
3180:
3175:
3170:
3165:
3160:
3155:
3149:
3147:
3141:
3140:
3138:
3137:
3132:
3127:
3122:
3117:
3111:
3109:
3103:
3102:
3100:
3099:
3094:
3089:
3087:Control method
3084:
3079:
3074:
3069:
3064:
3058:
3056:
3050:
3049:
3047:
3046:
3041:
3039:Multithreading
3036:
3031:
3026:
3020:
3018:
3012:
3011:
3009:
3008:
3003:
2998:
2993:
2988:
2982:
2980:
2974:
2973:
2971:
2970:
2965:
2960:
2955:
2950:
2945:
2940:
2935:
2933:Formal methods
2930:
2924:
2922:
2916:
2915:
2913:
2912:
2907:
2905:World Wide Web
2902:
2897:
2892:
2887:
2882:
2877:
2872:
2867:
2862:
2857:
2852:
2847:
2841:
2839:
2833:
2832:
2830:
2829:
2824:
2819:
2814:
2809:
2804:
2799:
2794:
2788:
2786:
2779:
2778:
2776:
2775:
2770:
2765:
2760:
2755:
2749:
2747:
2741:
2740:
2738:
2737:
2732:
2727:
2722:
2717:
2712:
2707:
2706:
2705:
2694:
2692:
2686:
2685:
2683:
2682:
2677:
2672:
2667:
2662:
2657:
2652:
2647:
2642:
2637:
2631:
2629:
2623:
2622:
2620:
2619:
2614:
2609:
2604:
2599:
2594:
2589:
2584:
2579:
2574:
2568:
2566:
2556:
2555:
2553:
2552:
2547:
2542:
2537:
2532:
2526:
2524:
2520:
2519:
2517:
2516:
2511:
2506:
2501:
2496:
2491:
2485:
2483:
2477:
2476:
2474:
2473:
2468:
2463:
2458:
2453:
2447:
2445:
2441:
2440:
2438:
2437:
2428:
2423:
2418:
2413:
2408:
2403:
2398:
2393:
2388:
2382:
2380:
2374:
2373:
2366:
2363:
2362:
2355:
2354:
2347:
2340:
2332:
2323:
2322:
2320:
2319:
2314:
2309:
2304:
2299:
2294:
2289:
2284:
2282:Patent drawing
2279:
2274:
2269:
2264:
2259:
2254:
2249:
2247:Graphic design
2244:
2239:
2234:
2233:
2232:
2222:
2217:
2212:
2206:
2204:
2198:
2197:
2194:
2193:
2191:
2190:
2188:Hadley Wickham
2185:
2180:
2175:
2170:
2165:
2160:
2155:
2150:
2145:
2143:Tamara Munzner
2140:
2135:
2130:
2125:
2120:
2115:
2110:
2105:
2100:
2095:
2090:
2085:
2080:
2074:
2072:
2068:
2067:
2065:
2064:
2059:
2054:
2049:
2044:
2042:David Goodsell
2039:
2034:
2029:
2027:Cynthia Brewer
2024:
2019:
2014:
2009:
2004:
1999:
1994:
1989:
1984:
1979:
1974:
1969:
1964:
1959:
1954:
1949:
1944:
1938:
1936:
1932:
1931:
1929:
1928:
1923:
1921:Edgar Anderson
1918:
1913:
1908:
1903:
1898:
1896:Jacques Bertin
1892:
1890:
1886:
1885:
1883:
1882:
1877:
1872:
1867:
1862:
1857:
1852:
1850:John B. Peddle
1847:
1842:
1837:
1832:
1827:
1822:
1816:
1814:
1810:
1809:
1807:
1806:
1804:Francis Galton
1801:
1799:Toussaint Loua
1796:
1791:
1786:
1781:
1779:Georg von Mayr
1776:
1771:
1769:Matthew Sankey
1766:
1761:
1756:
1751:
1746:
1741:
1736:
1731:
1726:
1721:
1715:
1713:
1709:
1708:
1706:
1705:
1700:
1695:
1690:
1684:
1682:
1675:
1671:
1670:
1668:
1667:
1662:
1657:
1652:
1647:
1642:
1637:
1635:Sankey diagram
1632:
1627:
1622:
1617:
1612:
1607:
1602:
1597:
1592:
1586:
1584:
1578:
1577:
1575:
1574:
1569:
1567:Visual culture
1564:
1559:
1554:
1549:
1544:
1539:
1534:
1529:
1524:
1519:
1514:
1509:
1504:
1499:
1494:
1489:
1484:
1478:
1476:
1472:
1471:
1463:
1462:
1455:
1448:
1440:
1431:
1430:
1428:
1427:
1421:
1418:
1417:
1415:
1414:
1409:
1404:
1399:
1394:
1389:
1384:
1378:
1376:
1372:
1371:
1369:
1368:
1363:
1361:Mandelbrot set
1358:
1353:
1348:
1346:Jerusalem cube
1343:
1337:
1335:
1331:
1330:
1328:
1327:
1322:
1317:
1312:
1306:
1304:
1298:
1297:
1294:
1293:
1291:
1290:
1284:
1282:
1278:
1277:
1275:
1274:
1269:
1264:
1259:
1254:
1248:
1246:
1245:Cross-platform
1239:
1235:
1234:
1232:
1231:
1226:
1220:
1218:
1214:
1213:
1211:
1210:
1205:
1200:
1195:
1193:Electric Sheep
1189:
1187:
1183:
1182:
1180:
1179:
1174:
1169:
1164:
1159:
1154:
1148:
1146:
1142:
1141:
1139:
1138:
1133:
1128:
1122:
1119:
1118:
1111:
1110:
1103:
1096:
1088:
1082:
1081:
1074:
1073:External links
1071:
1069:
1068:
1045:
1042:
1041:
1010:
985:Daniel Dennett
977:
938:
900:
875:
874:
872:
869:
868:
867:
862:
855:
852:
830:
829:
806:
805:
794:
762:
761:Other examples
759:
756:
755:
735:
733:
714:
711:
688:
687:
667:
665:
633:
630:
627:
626:
606:
604:
586:change ringing
584:An example of
577:
574:
567:
566:
546:
544:
525:
522:
506:
505:
485:
483:
456:
453:
450:
449:
429:
427:
406:
403:
400:
399:
379:
377:
344:A plot of the
337:
334:
320:
319:
299:
297:
241:
229:
226:
223:
222:
202:
200:
177:
176:Linear algebra
174:
171:
170:
150:
148:
115:
112:
100:conformal maps
88:fluid dynamics
55:
52:
29:Mandelbrot set
9:
6:
4:
3:
2:
3375:
3364:
3361:
3359:
3356:
3355:
3353:
3338:
3330:
3328:
3320:
3318:
3310:
3309:
3306:
3300:
3297:
3295:
3292:
3290:
3287:
3285:
3282:
3280:
3277:
3275:
3272:
3270:
3267:
3265:
3262:
3260:
3257:
3255:
3252:
3250:
3247:
3245:
3242:
3240:
3237:
3235:
3232:
3230:
3227:
3225:
3222:
3220:
3217:
3215:
3212:
3210:
3207:
3205:
3202:
3201:
3199:
3195:
3189:
3186:
3184:
3181:
3179:
3176:
3174:
3173:Mixed reality
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3150:
3148:
3146:
3142:
3136:
3133:
3131:
3128:
3126:
3123:
3121:
3118:
3116:
3113:
3112:
3110:
3108:
3104:
3098:
3095:
3093:
3090:
3088:
3085:
3083:
3080:
3078:
3075:
3073:
3070:
3068:
3065:
3063:
3060:
3059:
3057:
3055:
3051:
3045:
3042:
3040:
3037:
3035:
3032:
3030:
3027:
3025:
3022:
3021:
3019:
3017:
3013:
3007:
3006:Accessibility
3004:
3002:
3001:Visualization
2999:
2997:
2994:
2992:
2989:
2987:
2984:
2983:
2981:
2979:
2975:
2969:
2966:
2964:
2961:
2959:
2956:
2954:
2951:
2949:
2946:
2944:
2941:
2939:
2936:
2934:
2931:
2929:
2926:
2925:
2923:
2921:
2917:
2911:
2908:
2906:
2903:
2901:
2898:
2896:
2893:
2891:
2888:
2886:
2883:
2881:
2878:
2876:
2873:
2871:
2868:
2866:
2863:
2861:
2858:
2856:
2853:
2851:
2848:
2846:
2843:
2842:
2840:
2838:
2834:
2828:
2825:
2823:
2820:
2818:
2815:
2813:
2810:
2808:
2805:
2803:
2800:
2798:
2795:
2793:
2790:
2789:
2787:
2785:
2780:
2774:
2771:
2769:
2766:
2764:
2761:
2759:
2756:
2754:
2751:
2750:
2748:
2746:
2742:
2736:
2733:
2731:
2728:
2726:
2723:
2721:
2718:
2716:
2713:
2711:
2708:
2704:
2701:
2700:
2699:
2696:
2695:
2693:
2691:
2687:
2681:
2678:
2676:
2673:
2671:
2668:
2666:
2663:
2661:
2658:
2656:
2653:
2651:
2648:
2646:
2643:
2641:
2638:
2636:
2633:
2632:
2630:
2628:
2624:
2618:
2615:
2613:
2610:
2608:
2605:
2603:
2600:
2598:
2595:
2593:
2590:
2588:
2585:
2583:
2580:
2578:
2575:
2573:
2570:
2569:
2567:
2565:
2561:
2557:
2551:
2548:
2546:
2543:
2541:
2538:
2536:
2533:
2531:
2528:
2527:
2525:
2521:
2515:
2512:
2510:
2507:
2505:
2502:
2500:
2497:
2495:
2492:
2490:
2487:
2486:
2484:
2482:
2478:
2472:
2469:
2467:
2464:
2462:
2461:Dependability
2459:
2457:
2454:
2452:
2449:
2448:
2446:
2442:
2436:
2432:
2429:
2427:
2424:
2422:
2419:
2417:
2414:
2412:
2409:
2407:
2404:
2402:
2399:
2397:
2394:
2392:
2389:
2387:
2384:
2383:
2381:
2379:
2375:
2370:
2364:
2360:
2353:
2348:
2346:
2341:
2339:
2334:
2333:
2330:
2318:
2315:
2313:
2310:
2308:
2305:
2303:
2300:
2298:
2295:
2293:
2290:
2288:
2285:
2283:
2280:
2278:
2275:
2273:
2270:
2268:
2265:
2263:
2260:
2258:
2255:
2253:
2250:
2248:
2245:
2243:
2242:Graph drawing
2240:
2238:
2235:
2231:
2228:
2227:
2226:
2223:
2221:
2218:
2216:
2213:
2211:
2208:
2207:
2205:
2199:
2189:
2186:
2184:
2181:
2179:
2176:
2174:
2171:
2169:
2166:
2164:
2163:Claudio Silva
2161:
2159:
2156:
2154:
2151:
2149:
2146:
2144:
2141:
2139:
2136:
2134:
2131:
2129:
2128:Mauro Martino
2126:
2124:
2121:
2119:
2116:
2114:
2111:
2109:
2106:
2104:
2101:
2099:
2096:
2094:
2091:
2089:
2086:
2084:
2081:
2079:
2076:
2075:
2073:
2069:
2063:
2060:
2058:
2055:
2053:
2052:Michael Maltz
2050:
2048:
2045:
2043:
2040:
2038:
2035:
2033:
2030:
2028:
2025:
2023:
2020:
2018:
2017:George Furnas
2015:
2013:
2010:
2008:
2005:
2003:
2000:
1998:
1997:Howard Wainer
1995:
1993:
1990:
1988:
1985:
1983:
1980:
1978:
1975:
1973:
1970:
1968:
1965:
1963:
1960:
1958:
1955:
1953:
1950:
1948:
1945:
1943:
1940:
1939:
1937:
1933:
1927:
1924:
1922:
1919:
1917:
1914:
1912:
1909:
1907:
1904:
1902:
1901:Rudolf Modley
1899:
1897:
1894:
1893:
1891:
1887:
1881:
1878:
1876:
1873:
1871:
1868:
1866:
1865:Max O. Lorenz
1863:
1861:
1858:
1856:
1853:
1851:
1848:
1846:
1843:
1841:
1838:
1836:
1833:
1831:
1828:
1826:
1823:
1821:
1818:
1817:
1815:
1811:
1805:
1802:
1800:
1797:
1795:
1792:
1790:
1787:
1785:
1782:
1780:
1777:
1775:
1774:Charles Booth
1772:
1770:
1767:
1765:
1762:
1760:
1757:
1755:
1752:
1750:
1749:Luigi Perozzo
1747:
1745:
1742:
1740:
1739:August Kekulé
1737:
1735:
1732:
1730:
1727:
1725:
1722:
1720:
1719:Charles Dupin
1717:
1716:
1714:
1710:
1704:
1703:Gaspard Monge
1701:
1699:
1696:
1694:
1691:
1689:
1688:Edmond Halley
1686:
1685:
1683:
1679:
1676:
1672:
1666:
1663:
1661:
1658:
1656:
1653:
1651:
1648:
1646:
1643:
1641:
1638:
1636:
1633:
1631:
1628:
1626:
1623:
1621:
1618:
1616:
1613:
1611:
1608:
1606:
1603:
1601:
1598:
1596:
1593:
1591:
1588:
1587:
1585:
1579:
1573:
1570:
1568:
1565:
1563:
1560:
1558:
1555:
1553:
1550:
1548:
1545:
1543:
1540:
1538:
1535:
1533:
1530:
1528:
1525:
1523:
1520:
1518:
1515:
1513:
1510:
1508:
1505:
1503:
1500:
1498:
1495:
1493:
1492:Crime mapping
1490:
1488:
1485:
1483:
1480:
1479:
1477:
1473:
1468:
1467:Visualization
1461:
1456:
1454:
1449:
1447:
1442:
1441:
1438:
1426:
1423:
1422:
1419:
1413:
1410:
1408:
1405:
1403:
1400:
1398:
1397:Fractal flame
1395:
1393:
1390:
1388:
1385:
1383:
1380:
1379:
1377:
1373:
1367:
1364:
1362:
1359:
1357:
1354:
1352:
1349:
1347:
1344:
1342:
1339:
1338:
1336:
1334:Found objects
1332:
1326:
1323:
1321:
1318:
1316:
1313:
1311:
1308:
1307:
1305:
1303:
1299:
1289:
1286:
1285:
1283:
1279:
1273:
1270:
1268:
1267:Ultra Fractal
1265:
1263:
1260:
1258:
1255:
1253:
1250:
1249:
1247:
1243:
1240:
1236:
1230:
1227:
1225:
1222:
1221:
1219:
1215:
1209:
1206:
1204:
1201:
1199:
1196:
1194:
1191:
1190:
1188:
1184:
1178:
1175:
1173:
1170:
1168:
1165:
1163:
1160:
1158:
1155:
1153:
1150:
1149:
1147:
1143:
1137:
1134:
1132:
1129:
1127:
1124:
1123:
1120:
1116:
1109:
1104:
1102:
1097:
1095:
1090:
1089:
1086:
1080:
1077:
1076:
1065:
1061:
1060:
1052:
1047:
1046:
1030:
1029:
1021:
1014:
1008:
1007:0-14-016734-X
1004:
1000:
996:
992:
991:
986:
981:
973:
969:
965:
961:
957:
953:
949:
942:
928:
924:
920:
916:
912:
907:Published in
904:
890:
886:
880:
876:
866:
863:
861:
858:
857:
849:
844:
840:
838:
837:
827:
824:
823:
819:
815:
814:Morin surface
810:
803:
799:
795:
792:
788:
785:
784:
780:
776:
772:
767:
752:
743:
739:
736:This section
734:
731:
727:
726:
719:
710:
708:
704:
703:
698:
694:
684:
675:
671:
668:This section
666:
663:
659:
658:
653:
649:
645:
642:
638:
623:
614:
610:
607:This section
605:
602:
598:
597:
591:
587:
582:
576:Combinatorics
573:
563:
554:
550:
547:This section
545:
542:
538:
537:
530:
521:
518:
512:
502:
493:
489:
486:This section
484:
481:
477:
476:
470:
466:
461:
446:
437:
433:
430:This section
428:
425:
421:
420:
415:
411:
396:
387:
383:
380:This section
378:
375:
371:
370:
363:
352:
347:
342:
333:
331:
327:
316:
307:
303:
300:This section
298:
295:
291:
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40:visualization
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3269:Cyberwarfare
2928:Cryptography
2277:Neuroimaging
2237:CPK coloring
2220:Color coding
2158:Hans Rosling
2138:Miriah Meyer
2103:Aaron Koblin
2088:Jeffrey Heer
1982:Edward Tufte
1977:Pat Hanrahan
1947:Nigel Holmes
1825:Otto Neurath
1764:Oliver Byrne
1712:19th century
1406:
1281:Windows only
1066:(6): 647â658
1063:
1057:
1032:. Retrieved
1026:
1013:
988:
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958:(2): 77â82.
955:
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941:
930:. Retrieved
921:(3): 37â54.
918:
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892:. Retrieved
888:
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848:random walks
833:
831:
790:
746:
742:adding to it
737:
706:
700:
691:
678:
674:adding to it
669:
617:
613:adding to it
608:
590:graph theory
570:
557:
553:adding to it
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524:Graph theory
513:
509:
496:
492:adding to it
487:
440:
436:adding to it
431:
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381:
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336:Chaos theory
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157:adding to it
152:
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72:space curves
68:plane curves
57:
54:Applications
36:Mathematical
34:
3279:Video games
3259:Digital art
3016:Concurrency
2885:Data mining
2797:Probability
2530:Interpreter
2210:Cartography
2148:Ade Olufeko
2118:Manuel Lima
2047:Kwan-Liu Ma
1972:Stuart Card
1942:Borden Dent
1880:Erwin Raisz
1835:Henry Gantt
1145:Open-source
1136:Fractal art
1126:Digital art
749:August 2020
713:Computation
695:'s book on
681:August 2020
620:August 2020
560:August 2020
499:August 2020
467:with seven
465:prime knots
443:August 2020
393:August 2020
348:for values
313:August 2020
216:August 2020
164:August 2020
3352:Categories
3337:Glossaries
3209:E-commerce
2802:Statistics
2745:Algorithms
2703:Stochastic
2535:Middleware
2391:Peripheral
2133:John Maeda
1911:John Tukey
1875:Harry Beck
1870:Fritz Kahn
1620:Photograph
1412:Orbit trap
1366:Mandelbulb
932:2014-10-15
894:2021-09-07
871:References
646:creating "
644:Glider Gun
96:soap films
3158:Rendering
3153:Animation
2784:computing
2735:Semantics
2426:Processor
2215:Chartjunk
2183:Bang Wong
2078:Polo Chau
1784:John Snow
1759:John Venn
1640:Schematic
1625:Pictogram
1356:Mandelbox
1351:Julia set
1152:Apophysis
1034:14 August
972:0020-9910
469:crossings
128:Euclidean
76:polyhedra
3358:Geometry
3317:Category
3145:Graphics
2920:Security
2582:Compiler
2481:Networks
2378:Hardware
2201:Related
1610:Ideogram
1425:Category
1325:VistaPro
1320:Terragen
1257:Chaotica
1224:Fractint
1217:Freeware
1203:openPlaG
1177:Sterling
1172:MilkDrop
987:(1995),
854:See also
641:Gosper's
455:Topology
114:Geometry
104:fractals
94:such as
64:analysis
60:geometry
3327:Outline
2083:Ben Fry
1595:Diagram
1375:Related
1315:Picogen
1229:IFStile
1157:Blender
773:of the
648:gliders
282:
252:
2203:topics
1674:People
1581:Image
1475:Fields
1288:VisSim
1238:Retail
1005:
997:
970:
846:Three
357:Ï = 10
106:, and
2730:Logic
2564:tools
1655:Table
1590:Chart
1583:types
1262:Maple
1252:Bryce
1054:(PDF)
1023:(PDF)
364:= 8/3
108:chaos
2562:and
2435:Form
2431:Size
1630:Plot
1208:XaoS
1198:GIMP
1162:Fyre
1036:2012
1003:ISBN
995:ISBN
968:ISSN
834:The
796:The
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