Fun with chaos

By Thomas Stig Jacobsen


Graphical display of the 100 first values:


Based on: Formel
k: 2.9
fk(x0): 0.2
Duplicate values: 769

Here comes the data:
x0: 0.2
x1: 0.464
x2: 0.7212416
x3: 0.583051247845
x4: 0.704997221671
x5: 0.603130803411
x6: 0.694155708425
x7: 0.61568032657
x8: 0.68619237993
x9: 0.624463953203
x10: 0.680075300624
x11: 0.630961369705
x12: 0.675262446971
x13: 0.635920916578
x14: 0.671423962867
x15: 0.63978009237
x16: 0.668338424753
x17: 0.642820306779
x18: 0.665846843917
x19: 0.645234990652
x20: 0.663829712722
x21: 0.647163493165
x22: 0.66219442821
x23: 0.648709605627
x24: 0.660867814263
x25: 0.649952484369
x26: 0.659791332052
x27: 0.650953517583
x28: 0.658917803035
x29: 0.651760882448
x30: 0.65820904022
x31: 0.652412708819
x32: 0.657634061952
x33: 0.652939357286
x34: 0.65716770368
x35: 0.653365107468
x36: 0.656789517053
x37: 0.653709437293
x38: 0.656482885773
x39: 0.653988008735
x40: 0.656234310181
x41: 0.654213436935
x42: 0.65603282602
x43: 0.654395895893
x44: 0.655869531261
x45: 0.654543598751
x46: 0.655737200647
x47: 0.65466318057
x48: 0.65562997167
x49: 0.654760004562
x50: 0.655543088865
x51: 0.654838407768
x52: 0.655472695691
x53: 0.654901898594
x54: 0.655415665255
x55: 0.654953315881
x56: 0.655369462703
x57: 0.654994957172
x58: 0.655332033428
x59: 0.655028682234
x60: 0.655301712286
x61: 0.655055996667
x62: 0.655277149903
x63: 0.655078119482
x64: 0.655257252888
x65: 0.655096037735
x66: 0.655241135329
x67: 0.655110550715
x68: 0.655228079465
x69: 0.655122305702
x70: 0.655217503793
x71: 0.655131826897
x72: 0.655208937223
x73: 0.655139538838
x74: 0.655201998118
x75: 0.655145785362
x76: 0.655196377325
x77: 0.655150844949
x78: 0.655191824403
x79: 0.655154943151
x80: 0.655188136486
x81: 0.655158262653
x82: 0.655185149239
x83: 0.655160951422
x84: 0.655182729546
x85: 0.655163129307
x86: 0.655180769581
x87: 0.655164893382
x88: 0.655179181999
x89: 0.655166322275
x90: 0.655177896052
x91: 0.655167479673
x92: 0.655176854431
x93: 0.655168417162
x94: 0.655176010715
x95: 0.655169176526
x96: 0.655175327303
x97: 0.65516979161
x98: 0.655174773738
x99: 0.655170289826
x100: 0.65517432535
x101: 0.655170693381
x102: 0.655173962155
x103: 0.65517102026
x104: 0.655173667967
x105: 0.655171285032
x106: 0.655173429674
x107: 0.655171499497
x108: 0.655173236657
x109: 0.655171673213
x110: 0.655173080313
x111: 0.655171813924
x112: 0.655172953675
x113: 0.655171927899
x114: 0.655172851097
x115: 0.655172020219
x116: 0.655172768009
x117: 0.655172094998
x118: 0.655172700708
x119: 0.655172155569
x120: 0.655172646194
x121: 0.655172204632
x122: 0.655172602038
x123: 0.655172244372
x124: 0.655172566272
x125: 0.655172276562
x126: 0.655172537301
x127: 0.655172302636
x128: 0.655172513834
x129: 0.655172323756
x130: 0.655172494826
x131: 0.655172340863
x132: 0.65517247943
x133: 0.65517235472
x134: 0.655172466959
x135: 0.655172365944
x136: 0.655172456858
x137: 0.655172375035
x138: 0.655172448675
x139: 0.655172382399
x140: 0.655172442048
x141: 0.655172388364
x142: 0.655172436679
x143: 0.655172393196
x144: 0.655172432331
x145: 0.655172397109
x146: 0.655172428809
x147: 0.655172400279
x148: 0.655172425956
x149: 0.655172402847
x150: 0.655172423645
x151: 0.655172404927
x152: 0.655172421773
x153: 0.655172406611
x154: 0.655172420257
x155: 0.655172407976
x156: 0.655172419029
x157: 0.655172409081
x158: 0.655172418034
x159: 0.655172409976
x160: 0.655172417228
x161: 0.655172410702
x162: 0.655172416576
x163: 0.655172411289
x164: 0.655172416047
x165: 0.655172411765
x166: 0.655172415619
x167: 0.65517241215
x168: 0.655172415272
x169: 0.655172412462
x170: 0.655172414991
x171: 0.655172412715
x172: 0.655172414763
x173: 0.65517241292
x174: 0.655172414579
x175: 0.655172413086
x176: 0.65517241443
x177: 0.65517241322
x178: 0.655172414309
x179: 0.655172413329
x180: 0.655172414211
x181: 0.655172413417
x182: 0.655172414131
x183: 0.655172413489
x184: 0.655172414067
x185: 0.655172413546
x186: 0.655172414015
x187: 0.655172413593
x188: 0.655172413973
x189: 0.655172413631
x190: 0.655172413939
x191: 0.655172413662
x192: 0.655172413911
x193: 0.655172413687
x194: 0.655172413889
x195: 0.655172413707
x196: 0.65517241387
x197: 0.655172413723
x198: 0.655172413856
x199: 0.655172413737
x200: 0.655172413844
x201: 0.655172413747
x202: 0.655172413834
x203: 0.655172413756
x204: 0.655172413826
x205: 0.655172413763
x206: 0.65517241382
x207: 0.655172413769
x208: 0.655172413815
x209: 0.655172413773
x210: 0.655172413811
x211: 0.655172413777
x212: 0.655172413807
x213: 0.65517241378
x214: 0.655172413805
x215: 0.655172413783
x216: 0.655172413803
x217: 0.655172413785
x218: 0.655172413801
x219: 0.655172413786
x220: 0.655172413799
x221: 0.655172413788
x222: 0.655172413798
x223: 0.655172413789
x224: 0.655172413797
x225: 0.655172413789
x226: 0.655172413796
x227: 0.65517241379
x228: 0.655172413796
x229: 0.655172413791
x230: 0.655172413795
x231: 0.655172413791
x232: 0.655172413795
x233: 0.655172413792
x234: 0.655172413795
x235: 0.655172413792
x236: 0.655172413794
x237: 0.655172413792
x238: 0.655172413794
x239: 0.655172413792
x240: 0.655172413794
x241: 0.655172413792
x242: 0.655172413794
x243: 0.655172413793
x244: 0.655172413794
x245: 0.655172413793
x246: 0.655172413794
x247: 0.655172413793
x248: 0.655172413793
x249: 0.655172413793
x250: 0.655172413793
x251: 0.655172413793
x252: 0.655172413793
x253: 0.655172413793
x254: 0.655172413793
x255: 0.655172413793
x256: 0.655172413793
x257: 0.655172413793
x258: 0.655172413793
x259: 0.655172413793
x260: 0.655172413793
x261: 0.655172413793
x262: 0.655172413793
x263: 0.655172413793
x264: 0.655172413793
x265: 0.655172413793
x266: 0.655172413793
x267: 0.655172413793
x268: 0.655172413793
x269: 0.655172413793
x270: 0.655172413793
x271: 0.655172413793
x272: 0.655172413793
x273: 0.655172413793
x274: 0.655172413793
x275: 0.655172413793
x276: 0.655172413793
x277: 0.655172413793
x278: 0.655172413793
x279: 0.655172413793
x280: 0.655172413793
x281: 0.655172413793
x282: 0.655172413793
x283: 0.655172413793
x284: 0.655172413793
x285: 0.655172413793
x286: 0.655172413793
x287: 0.655172413793
x288: 0.655172413793
x289: 0.655172413793
x290: 0.655172413793
x291: 0.655172413793
x292: 0.655172413793
x293: 0.655172413793
x294: 0.655172413793
x295: 0.655172413793
x296: 0.655172413793
x297: 0.655172413793
x298: 0.655172413793
x299: 0.655172413793
x300: 0.655172413793
x301: 0.655172413793
x302: 0.655172413793
x303: 0.655172413793
x304: 0.655172413793
x305: 0.655172413793
x306: 0.655172413793
x307: 0.655172413793
x308: 0.655172413793
x309: 0.655172413793
x310: 0.655172413793
x311: 0.655172413793
x312: 0.655172413793
x313: 0.655172413793
x314: 0.655172413793
x315: 0.655172413793
x316: 0.655172413793
x317: 0.655172413793
x318: 0.655172413793
x319: 0.655172413793
x320: 0.655172413793
x321: 0.655172413793
x322: 0.655172413793
x323: 0.655172413793
x324: 0.655172413793
x325: 0.655172413793
x326: 0.655172413793
x327: 0.655172413793
x328: 0.655172413793
x329: 0.655172413793
x330: 0.655172413793
x331: 0.655172413793
x332: 0.655172413793
x333: 0.655172413793
x334: 0.655172413793
x335: 0.655172413793
x336: 0.655172413793
x337: 0.655172413793
x338: 0.655172413793
x339: 0.655172413793
x340: 0.655172413793
x341: 0.655172413793
x342: 0.655172413793
x343: 0.655172413793
x344: 0.655172413793
x345: 0.655172413793
x346: 0.655172413793
x347: 0.655172413793
x348: 0.655172413793
x349: 0.655172413793
x350: 0.655172413793
x351: 0.655172413793
x352: 0.655172413793
x353: 0.655172413793
x354: 0.655172413793
x355: 0.655172413793
x356: 0.655172413793
x357: 0.655172413793
x358: 0.655172413793
x359: 0.655172413793
x360: 0.655172413793
x361: 0.655172413793
x362: 0.655172413793
x363: 0.655172413793
x364: 0.655172413793
x365: 0.655172413793
x366: 0.655172413793
x367: 0.655172413793
x368: 0.655172413793
x369: 0.655172413793
x370: 0.655172413793
x371: 0.655172413793
x372: 0.655172413793
x373: 0.655172413793
x374: 0.655172413793
x375: 0.655172413793
x376: 0.655172413793
x377: 0.655172413793
x378: 0.655172413793
x379: 0.655172413793
x380: 0.655172413793
x381: 0.655172413793
x382: 0.655172413793
x383: 0.655172413793
x384: 0.655172413793
x385: 0.655172413793
x386: 0.655172413793
x387: 0.655172413793
x388: 0.655172413793
x389: 0.655172413793
x390: 0.655172413793
x391: 0.655172413793
x392: 0.655172413793
x393: 0.655172413793
x394: 0.655172413793
x395: 0.655172413793
x396: 0.655172413793
x397: 0.655172413793
x398: 0.655172413793
x399: 0.655172413793
x400: 0.655172413793
x401: 0.655172413793
x402: 0.655172413793
x403: 0.655172413793
x404: 0.655172413793
x405: 0.655172413793
x406: 0.655172413793
x407: 0.655172413793
x408: 0.655172413793
x409: 0.655172413793
x410: 0.655172413793
x411: 0.655172413793
x412: 0.655172413793
x413: 0.655172413793
x414: 0.655172413793
x415: 0.655172413793
x416: 0.655172413793
x417: 0.655172413793
x418: 0.655172413793
x419: 0.655172413793
x420: 0.655172413793
x421: 0.655172413793
x422: 0.655172413793
x423: 0.655172413793
x424: 0.655172413793
x425: 0.655172413793
x426: 0.655172413793
x427: 0.655172413793
x428: 0.655172413793
x429: 0.655172413793
x430: 0.655172413793
x431: 0.655172413793
x432: 0.655172413793
x433: 0.655172413793
x434: 0.655172413793
x435: 0.655172413793
x436: 0.655172413793
x437: 0.655172413793
x438: 0.655172413793
x439: 0.655172413793
x440: 0.655172413793
x441: 0.655172413793
x442: 0.655172413793
x443: 0.655172413793
x444: 0.655172413793
x445: 0.655172413793
x446: 0.655172413793
x447: 0.655172413793
x448: 0.655172413793
x449: 0.655172413793
x450: 0.655172413793
x451: 0.655172413793
x452: 0.655172413793
x453: 0.655172413793
x454: 0.655172413793
x455: 0.655172413793
x456: 0.655172413793
x457: 0.655172413793
x458: 0.655172413793
x459: 0.655172413793
x460: 0.655172413793
x461: 0.655172413793
x462: 0.655172413793
x463: 0.655172413793
x464: 0.655172413793
x465: 0.655172413793
x466: 0.655172413793
x467: 0.655172413793
x468: 0.655172413793
x469: 0.655172413793
x470: 0.655172413793
x471: 0.655172413793
x472: 0.655172413793
x473: 0.655172413793
x474: 0.655172413793
x475: 0.655172413793
x476: 0.655172413793
x477: 0.655172413793
x478: 0.655172413793
x479: 0.655172413793
x480: 0.655172413793
x481: 0.655172413793
x482: 0.655172413793
x483: 0.655172413793
x484: 0.655172413793
x485: 0.655172413793
x486: 0.655172413793
x487: 0.655172413793
x488: 0.655172413793
x489: 0.655172413793
x490: 0.655172413793
x491: 0.655172413793
x492: 0.655172413793
x493: 0.655172413793
x494: 0.655172413793
x495: 0.655172413793
x496: 0.655172413793
x497: 0.655172413793
x498: 0.655172413793
x499: 0.655172413793
x500: 0.655172413793
x501: 0.655172413793
x502: 0.655172413793
x503: 0.655172413793
x504: 0.655172413793
x505: 0.655172413793
x506: 0.655172413793
x507: 0.655172413793
x508: 0.655172413793
x509: 0.655172413793
x510: 0.655172413793
x511: 0.655172413793
x512: 0.655172413793
x513: 0.655172413793
x514: 0.655172413793
x515: 0.655172413793
x516: 0.655172413793
x517: 0.655172413793
x518: 0.655172413793
x519: 0.655172413793
x520: 0.655172413793
x521: 0.655172413793
x522: 0.655172413793
x523: 0.655172413793
x524: 0.655172413793
x525: 0.655172413793
x526: 0.655172413793
x527: 0.655172413793
x528: 0.655172413793
x529: 0.655172413793
x530: 0.655172413793
x531: 0.655172413793
x532: 0.655172413793
x533: 0.655172413793
x534: 0.655172413793
x535: 0.655172413793
x536: 0.655172413793
x537: 0.655172413793
x538: 0.655172413793
x539: 0.655172413793
x540: 0.655172413793
x541: 0.655172413793
x542: 0.655172413793
x543: 0.655172413793
x544: 0.655172413793
x545: 0.655172413793
x546: 0.655172413793
x547: 0.655172413793
x548: 0.655172413793
x549: 0.655172413793
x550: 0.655172413793
x551: 0.655172413793
x552: 0.655172413793
x553: 0.655172413793
x554: 0.655172413793
x555: 0.655172413793
x556: 0.655172413793
x557: 0.655172413793
x558: 0.655172413793
x559: 0.655172413793
x560: 0.655172413793
x561: 0.655172413793
x562: 0.655172413793
x563: 0.655172413793
x564: 0.655172413793
x565: 0.655172413793
x566: 0.655172413793
x567: 0.655172413793
x568: 0.655172413793
x569: 0.655172413793
x570: 0.655172413793
x571: 0.655172413793
x572: 0.655172413793
x573: 0.655172413793
x574: 0.655172413793
x575: 0.655172413793
x576: 0.655172413793
x577: 0.655172413793
x578: 0.655172413793
x579: 0.655172413793
x580: 0.655172413793
x581: 0.655172413793
x582: 0.655172413793
x583: 0.655172413793
x584: 0.655172413793
x585: 0.655172413793
x586: 0.655172413793
x587: 0.655172413793
x588: 0.655172413793
x589: 0.655172413793
x590: 0.655172413793
x591: 0.655172413793
x592: 0.655172413793
x593: 0.655172413793
x594: 0.655172413793
x595: 0.655172413793
x596: 0.655172413793
x597: 0.655172413793
x598: 0.655172413793
x599: 0.655172413793
x600: 0.655172413793
x601: 0.655172413793
x602: 0.655172413793
x603: 0.655172413793
x604: 0.655172413793
x605: 0.655172413793
x606: 0.655172413793
x607: 0.655172413793
x608: 0.655172413793
x609: 0.655172413793
x610: 0.655172413793
x611: 0.655172413793
x612: 0.655172413793
x613: 0.655172413793
x614: 0.655172413793
x615: 0.655172413793
x616: 0.655172413793
x617: 0.655172413793
x618: 0.655172413793
x619: 0.655172413793
x620: 0.655172413793
x621: 0.655172413793
x622: 0.655172413793
x623: 0.655172413793
x624: 0.655172413793
x625: 0.655172413793
x626: 0.655172413793
x627: 0.655172413793
x628: 0.655172413793
x629: 0.655172413793
x630: 0.655172413793
x631: 0.655172413793
x632: 0.655172413793
x633: 0.655172413793
x634: 0.655172413793
x635: 0.655172413793
x636: 0.655172413793
x637: 0.655172413793
x638: 0.655172413793
x639: 0.655172413793
x640: 0.655172413793
x641: 0.655172413793
x642: 0.655172413793
x643: 0.655172413793
x644: 0.655172413793
x645: 0.655172413793
x646: 0.655172413793
x647: 0.655172413793
x648: 0.655172413793
x649: 0.655172413793
x650: 0.655172413793
x651: 0.655172413793
x652: 0.655172413793
x653: 0.655172413793
x654: 0.655172413793
x655: 0.655172413793
x656: 0.655172413793
x657: 0.655172413793
x658: 0.655172413793
x659: 0.655172413793
x660: 0.655172413793
x661: 0.655172413793
x662: 0.655172413793
x663: 0.655172413793
x664: 0.655172413793
x665: 0.655172413793
x666: 0.655172413793
x667: 0.655172413793
x668: 0.655172413793
x669: 0.655172413793
x670: 0.655172413793
x671: 0.655172413793
x672: 0.655172413793
x673: 0.655172413793
x674: 0.655172413793
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