Fun with chaos
By Thomas Stig Jacobsen
Graphical display of the 100 first values:
Based on: 
k: 2.5
fk(x0): 0.2
Duplicate values: 998
Here comes the data:
x0: 0.2
x1: 0.4
x2: 0.6
x3: 0.6
x4: 0.6
x5: 0.6
x6: 0.6
x7: 0.6
x8: 0.6
x9: 0.6
x10: 0.6
x11: 0.6
x12: 0.6
x13: 0.6
x14: 0.6
x15: 0.6
x16: 0.6
x17: 0.6
x18: 0.6
x19: 0.6
x20: 0.6
x21: 0.6
x22: 0.6
x23: 0.6
x24: 0.6
x25: 0.6
x26: 0.6
x27: 0.6
x28: 0.6
x29: 0.6
x30: 0.6
x31: 0.6
x32: 0.6
x33: 0.6
x34: 0.6
x35: 0.6
x36: 0.6
x37: 0.6
x38: 0.6
x39: 0.6
x40: 0.6
x41: 0.6
x42: 0.6
x43: 0.6
x44: 0.6
x45: 0.6
x46: 0.6
x47: 0.6
x48: 0.6
x49: 0.6
x50: 0.6
x51: 0.6
x52: 0.6
x53: 0.6
x54: 0.6
x55: 0.6
x56: 0.6
x57: 0.6
x58: 0.6
x59: 0.6
x60: 0.6
x61: 0.6
x62: 0.6
x63: 0.6
x64: 0.6
x65: 0.6
x66: 0.6
x67: 0.6
x68: 0.6
x69: 0.6
x70: 0.6
x71: 0.6
x72: 0.6
x73: 0.6
x74: 0.6
x75: 0.6
x76: 0.6
x77: 0.6
x78: 0.6
x79: 0.6
x80: 0.6
x81: 0.6
x82: 0.6
x83: 0.6
x84: 0.6
x85: 0.6
x86: 0.6
x87: 0.6
x88: 0.6
x89: 0.6
x90: 0.6
x91: 0.6
x92: 0.6
x93: 0.6
x94: 0.6
x95: 0.6
x96: 0.6
x97: 0.6
x98: 0.6
x99: 0.6
x100: 0.6
x101: 0.6
x102: 0.6
x103: 0.6
x104: 0.6
x105: 0.6
x106: 0.6
x107: 0.6
x108: 0.6
x109: 0.6
x110: 0.6
x111: 0.6
x112: 0.6
x113: 0.6
x114: 0.6
x115: 0.6
x116: 0.6
x117: 0.6
x118: 0.6
x119: 0.6
x120: 0.6
x121: 0.6
x122: 0.6
x123: 0.6
x124: 0.6
x125: 0.6
x126: 0.6
x127: 0.6
x128: 0.6
x129: 0.6
x130: 0.6
x131: 0.6
x132: 0.6
x133: 0.6
x134: 0.6
x135: 0.6
x136: 0.6
x137: 0.6
x138: 0.6
x139: 0.6
x140: 0.6
x141: 0.6
x142: 0.6
x143: 0.6
x144: 0.6
x145: 0.6
x146: 0.6
x147: 0.6
x148: 0.6
x149: 0.6
x150: 0.6
x151: 0.6
x152: 0.6
x153: 0.6
x154: 0.6
x155: 0.6
x156: 0.6
x157: 0.6
x158: 0.6
x159: 0.6
x160: 0.6
x161: 0.6
x162: 0.6
x163: 0.6
x164: 0.6
x165: 0.6
x166: 0.6
x167: 0.6
x168: 0.6
x169: 0.6
x170: 0.6
x171: 0.6
x172: 0.6
x173: 0.6
x174: 0.6
x175: 0.6
x176: 0.6
x177: 0.6
x178: 0.6
x179: 0.6
x180: 0.6
x181: 0.6
x182: 0.6
x183: 0.6
x184: 0.6
x185: 0.6
x186: 0.6
x187: 0.6
x188: 0.6
x189: 0.6
x190: 0.6
x191: 0.6
x192: 0.6
x193: 0.6
x194: 0.6
x195: 0.6
x196: 0.6
x197: 0.6
x198: 0.6
x199: 0.6
x200: 0.6
x201: 0.6
x202: 0.6
x203: 0.6
x204: 0.6
x205: 0.6
x206: 0.6
x207: 0.6
x208: 0.6
x209: 0.6
x210: 0.6
x211: 0.6
x212: 0.6
x213: 0.6
x214: 0.6
x215: 0.6
x216: 0.6
x217: 0.6
x218: 0.6
x219: 0.6
x220: 0.6
x221: 0.6
x222: 0.6
x223: 0.6
x224: 0.6
x225: 0.6
x226: 0.6
x227: 0.6
x228: 0.6
x229: 0.6
x230: 0.6
x231: 0.6
x232: 0.6
x233: 0.6
x234: 0.6
x235: 0.6
x236: 0.6
x237: 0.6
x238: 0.6
x239: 0.6
x240: 0.6
x241: 0.6
x242: 0.6
x243: 0.6
x244: 0.6
x245: 0.6
x246: 0.6
x247: 0.6
x248: 0.6
x249: 0.6
x250: 0.6
x251: 0.6
x252: 0.6
x253: 0.6
x254: 0.6
x255: 0.6
x256: 0.6
x257: 0.6
x258: 0.6
x259: 0.6
x260: 0.6
x261: 0.6
x262: 0.6
x263: 0.6
x264: 0.6
x265: 0.6
x266: 0.6
x267: 0.6
x268: 0.6
x269: 0.6
x270: 0.6
x271: 0.6
x272: 0.6
x273: 0.6
x274: 0.6
x275: 0.6
x276: 0.6
x277: 0.6
x278: 0.6
x279: 0.6
x280: 0.6
x281: 0.6
x282: 0.6
x283: 0.6
x284: 0.6
x285: 0.6
x286: 0.6
x287: 0.6
x288: 0.6
x289: 0.6
x290: 0.6
x291: 0.6
x292: 0.6
x293: 0.6
x294: 0.6
x295: 0.6
x296: 0.6
x297: 0.6
x298: 0.6
x299: 0.6
x300: 0.6
x301: 0.6
x302: 0.6
x303: 0.6
x304: 0.6
x305: 0.6
x306: 0.6
x307: 0.6
x308: 0.6
x309: 0.6
x310: 0.6
x311: 0.6
x312: 0.6
x313: 0.6
x314: 0.6
x315: 0.6
x316: 0.6
x317: 0.6
x318: 0.6
x319: 0.6
x320: 0.6
x321: 0.6
x322: 0.6
x323: 0.6
x324: 0.6
x325: 0.6
x326: 0.6
x327: 0.6
x328: 0.6
x329: 0.6
x330: 0.6
x331: 0.6
x332: 0.6
x333: 0.6
x334: 0.6
x335: 0.6
x336: 0.6
x337: 0.6
x338: 0.6
x339: 0.6
x340: 0.6
x341: 0.6
x342: 0.6
x343: 0.6
x344: 0.6
x345: 0.6
x346: 0.6
x347: 0.6
x348: 0.6
x349: 0.6
x350: 0.6
x351: 0.6
x352: 0.6
x353: 0.6
x354: 0.6
x355: 0.6
x356: 0.6
x357: 0.6
x358: 0.6
x359: 0.6
x360: 0.6
x361: 0.6
x362: 0.6
x363: 0.6
x364: 0.6
x365: 0.6
x366: 0.6
x367: 0.6
x368: 0.6
x369: 0.6
x370: 0.6
x371: 0.6
x372: 0.6
x373: 0.6
x374: 0.6
x375: 0.6
x376: 0.6
x377: 0.6
x378: 0.6
x379: 0.6
x380: 0.6
x381: 0.6
x382: 0.6
x383: 0.6
x384: 0.6
x385: 0.6
x386: 0.6
x387: 0.6
x388: 0.6
x389: 0.6
x390: 0.6
x391: 0.6
x392: 0.6
x393: 0.6
x394: 0.6
x395: 0.6
x396: 0.6
x397: 0.6
x398: 0.6
x399: 0.6
x400: 0.6
x401: 0.6
x402: 0.6
x403: 0.6
x404: 0.6
x405: 0.6
x406: 0.6
x407: 0.6
x408: 0.6
x409: 0.6
x410: 0.6
x411: 0.6
x412: 0.6
x413: 0.6
x414: 0.6
x415: 0.6
x416: 0.6
x417: 0.6
x418: 0.6
x419: 0.6
x420: 0.6
x421: 0.6
x422: 0.6
x423: 0.6
x424: 0.6
x425: 0.6
x426: 0.6
x427: 0.6
x428: 0.6
x429: 0.6
x430: 0.6
x431: 0.6
x432: 0.6
x433: 0.6
x434: 0.6
x435: 0.6
x436: 0.6
x437: 0.6
x438: 0.6
x439: 0.6
x440: 0.6
x441: 0.6
x442: 0.6
x443: 0.6
x444: 0.6
x445: 0.6
x446: 0.6
x447: 0.6
x448: 0.6
x449: 0.6
x450: 0.6
x451: 0.6
x452: 0.6
x453: 0.6
x454: 0.6
x455: 0.6
x456: 0.6
x457: 0.6
x458: 0.6
x459: 0.6
x460: 0.6
x461: 0.6
x462: 0.6
x463: 0.6
x464: 0.6
x465: 0.6
x466: 0.6
x467: 0.6
x468: 0.6
x469: 0.6
x470: 0.6
x471: 0.6
x472: 0.6
x473: 0.6
x474: 0.6
x475: 0.6
x476: 0.6
x477: 0.6
x478: 0.6
x479: 0.6
x480: 0.6
x481: 0.6
x482: 0.6
x483: 0.6
x484: 0.6
x485: 0.6
x486: 0.6
x487: 0.6
x488: 0.6
x489: 0.6
x490: 0.6
x491: 0.6
x492: 0.6
x493: 0.6
x494: 0.6
x495: 0.6
x496: 0.6
x497: 0.6
x498: 0.6
x499: 0.6
x500: 0.6
x501: 0.6
x502: 0.6
x503: 0.6
x504: 0.6
x505: 0.6
x506: 0.6
x507: 0.6
x508: 0.6
x509: 0.6
x510: 0.6
x511: 0.6
x512: 0.6
x513: 0.6
x514: 0.6
x515: 0.6
x516: 0.6
x517: 0.6
x518: 0.6
x519: 0.6
x520: 0.6
x521: 0.6
x522: 0.6
x523: 0.6
x524: 0.6
x525: 0.6
x526: 0.6
x527: 0.6
x528: 0.6
x529: 0.6
x530: 0.6
x531: 0.6
x532: 0.6
x533: 0.6
x534: 0.6
x535: 0.6
x536: 0.6
x537: 0.6
x538: 0.6
x539: 0.6
x540: 0.6
x541: 0.6
x542: 0.6
x543: 0.6
x544: 0.6
x545: 0.6
x546: 0.6
x547: 0.6
x548: 0.6
x549: 0.6
x550: 0.6
x551: 0.6
x552: 0.6
x553: 0.6
x554: 0.6
x555: 0.6
x556: 0.6
x557: 0.6
x558: 0.6
x559: 0.6
x560: 0.6
x561: 0.6
x562: 0.6
x563: 0.6
x564: 0.6
x565: 0.6
x566: 0.6
x567: 0.6
x568: 0.6
x569: 0.6
x570: 0.6
x571: 0.6
x572: 0.6
x573: 0.6
x574: 0.6
x575: 0.6
x576: 0.6
x577: 0.6
x578: 0.6
x579: 0.6
x580: 0.6
x581: 0.6
x582: 0.6
x583: 0.6
x584: 0.6
x585: 0.6
x586: 0.6
x587: 0.6
x588: 0.6
x589: 0.6
x590: 0.6
x591: 0.6
x592: 0.6
x593: 0.6
x594: 0.6
x595: 0.6
x596: 0.6
x597: 0.6
x598: 0.6
x599: 0.6
x600: 0.6
x601: 0.6
x602: 0.6
x603: 0.6
x604: 0.6
x605: 0.6
x606: 0.6
x607: 0.6
x608: 0.6
x609: 0.6
x610: 0.6
x611: 0.6
x612: 0.6
x613: 0.6
x614: 0.6
x615: 0.6
x616: 0.6
x617: 0.6
x618: 0.6
x619: 0.6
x620: 0.6
x621: 0.6
x622: 0.6
x623: 0.6
x624: 0.6
x625: 0.6
x626: 0.6
x627: 0.6
x628: 0.6
x629: 0.6
x630: 0.6
x631: 0.6
x632: 0.6
x633: 0.6
x634: 0.6
x635: 0.6
x636: 0.6
x637: 0.6
x638: 0.6
x639: 0.6
x640: 0.6
x641: 0.6
x642: 0.6
x643: 0.6
x644: 0.6
x645: 0.6
x646: 0.6
x647: 0.6
x648: 0.6
x649: 0.6
x650: 0.6
x651: 0.6
x652: 0.6
x653: 0.6
x654: 0.6
x655: 0.6
x656: 0.6
x657: 0.6
x658: 0.6
x659: 0.6
x660: 0.6
x661: 0.6
x662: 0.6
x663: 0.6
x664: 0.6
x665: 0.6
x666: 0.6
x667: 0.6
x668: 0.6
x669: 0.6
x670: 0.6
x671: 0.6
x672: 0.6
x673: 0.6
x674: 0.6
x675: 0.6
x676: 0.6
x677: 0.6
x678: 0.6
x679: 0.6
x680: 0.6
x681: 0.6
x682: 0.6
x683: 0.6
x684: 0.6
x685: 0.6
x686: 0.6
x687: 0.6
x688: 0.6
x689: 0.6
x690: 0.6
x691: 0.6
x692: 0.6
x693: 0.6
x694: 0.6
x695: 0.6
x696: 0.6
x697: 0.6
x698: 0.6
x699: 0.6
x700: 0.6
x701: 0.6
x702: 0.6
x703: 0.6
x704: 0.6
x705: 0.6
x706: 0.6
x707: 0.6
x708: 0.6
x709: 0.6
x710: 0.6
x711: 0.6
x712: 0.6
x713: 0.6
x714: 0.6
x715: 0.6
x716: 0.6
x717: 0.6
x718: 0.6
x719: 0.6
x720: 0.6
x721: 0.6
x722: 0.6
x723: 0.6
x724: 0.6
x725: 0.6
x726: 0.6
x727: 0.6
x728: 0.6
x729: 0.6
x730: 0.6
x731: 0.6
x732: 0.6
x733: 0.6
x734: 0.6
x735: 0.6
x736: 0.6
x737: 0.6
x738: 0.6
x739: 0.6
x740: 0.6
x741: 0.6
x742: 0.6
x743: 0.6
x744: 0.6
x745: 0.6
x746: 0.6
x747: 0.6
x748: 0.6
x749: 0.6
x750: 0.6
x751: 0.6
x752: 0.6
x753: 0.6
x754: 0.6
x755: 0.6
x756: 0.6
x757: 0.6
x758: 0.6
x759: 0.6
x760: 0.6
x761: 0.6
x762: 0.6
x763: 0.6
x764: 0.6
x765: 0.6
x766: 0.6
x767: 0.6
x768: 0.6
x769: 0.6
x770: 0.6
x771: 0.6
x772: 0.6
x773: 0.6
x774: 0.6
x775: 0.6
x776: 0.6
x777: 0.6
x778: 0.6
x779: 0.6
x780: 0.6
x781: 0.6
x782: 0.6
x783: 0.6
x784: 0.6
x785: 0.6
x786: 0.6
x787: 0.6
x788: 0.6
x789: 0.6
x790: 0.6
x791: 0.6
x792: 0.6
x793: 0.6
x794: 0.6
x795: 0.6
x796: 0.6
x797: 0.6
x798: 0.6
x799: 0.6
x800: 0.6
x801: 0.6
x802: 0.6
x803: 0.6
x804: 0.6
x805: 0.6
x806: 0.6
x807: 0.6
x808: 0.6
x809: 0.6
x810: 0.6
x811: 0.6
x812: 0.6
x813: 0.6
x814: 0.6
x815: 0.6
x816: 0.6
x817: 0.6
x818: 0.6
x819: 0.6
x820: 0.6
x821: 0.6
x822: 0.6
x823: 0.6
x824: 0.6
x825: 0.6
x826: 0.6
x827: 0.6
x828: 0.6
x829: 0.6
x830: 0.6
x831: 0.6
x832: 0.6
x833: 0.6
x834: 0.6
x835: 0.6
x836: 0.6
x837: 0.6
x838: 0.6
x839: 0.6
x840: 0.6
x841: 0.6
x842: 0.6
x843: 0.6
x844: 0.6
x845: 0.6
x846: 0.6
x847: 0.6
x848: 0.6
x849: 0.6
x850: 0.6
x851: 0.6
x852: 0.6
x853: 0.6
x854: 0.6
x855: 0.6
x856: 0.6
x857: 0.6
x858: 0.6
x859: 0.6
x860: 0.6
x861: 0.6
x862: 0.6
x863: 0.6
x864: 0.6
x865: 0.6
x866: 0.6
x867: 0.6
x868: 0.6
x869: 0.6
x870: 0.6
x871: 0.6
x872: 0.6
x873: 0.6
x874: 0.6
x875: 0.6
x876: 0.6
x877: 0.6
x878: 0.6
x879: 0.6
x880: 0.6
x881: 0.6
x882: 0.6
x883: 0.6
x884: 0.6
x885: 0.6
x886: 0.6
x887: 0.6
x888: 0.6
x889: 0.6
x890: 0.6
x891: 0.6
x892: 0.6
x893: 0.6
x894: 0.6
x895: 0.6
x896: 0.6
x897: 0.6
x898: 0.6
x899: 0.6
x900: 0.6
x901: 0.6
x902: 0.6
x903: 0.6
x904: 0.6
x905: 0.6
x906: 0.6
x907: 0.6
x908: 0.6
x909: 0.6
x910: 0.6
x911: 0.6
x912: 0.6
x913: 0.6
x914: 0.6
x915: 0.6
x916: 0.6
x917: 0.6
x918: 0.6
x919: 0.6
x920: 0.6
x921: 0.6
x922: 0.6
x923: 0.6
x924: 0.6
x925: 0.6
x926: 0.6
x927: 0.6
x928: 0.6
x929: 0.6
x930: 0.6
x931: 0.6
x932: 0.6
x933: 0.6
x934: 0.6
x935: 0.6
x936: 0.6
x937: 0.6
x938: 0.6
x939: 0.6
x940: 0.6
x941: 0.6
x942: 0.6
x943: 0.6
x944: 0.6
x945: 0.6
x946: 0.6
x947: 0.6
x948: 0.6
x949: 0.6
x950: 0.6
x951: 0.6
x952: 0.6
x953: 0.6
x954: 0.6
x955: 0.6
x956: 0.6
x957: 0.6
x958: 0.6
x959: 0.6
x960: 0.6
x961: 0.6
x962: 0.6
x963: 0.6
x964: 0.6
x965: 0.6
x966: 0.6
x967: 0.6
x968: 0.6
x969: 0.6
x970: 0.6
x971: 0.6
x972: 0.6
x973: 0.6
x974: 0.6
x975: 0.6
x976: 0.6
x977: 0.6
x978: 0.6
x979: 0.6
x980: 0.6
x981: 0.6
x982: 0.6
x983: 0.6
x984: 0.6
x985: 0.6
x986: 0.6
x987: 0.6
x988: 0.6
x989: 0.6
x990: 0.6
x991: 0.6
x992: 0.6
x993: 0.6
x994: 0.6
x995: 0.6
x996: 0.6
x997: 0.6
x998: 0.6
x999: 0.6
x1000: 0.6