Talk:Feigenbaum constant calculation: Difference between revisions
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==true value of Feigenbaum's constant== |
==true value of Feigenbaum's constant== |
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Since the true value of Feigenbaum's constant isn't shown here on this Rosetta Code task, I added the displaying of it in the REXX example, along with the displaying of the number of correct decimal digits for each (<big>'''i'''</big>) iteration. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 06:28, 19 September 2018 (UTC) |
Since the true value of Feigenbaum's constant isn't shown here on this Rosetta Code task, I added the displaying of it in the REXX example, along with the displaying of the number of correct decimal digits for each (<big>'''i'''</big>) iteration. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 06:28, 19 September 2018 (UTC) |
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==degree of accuracy with more precision during computing== |
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I was experimenting with increasing the number of decimal digits (precision) with the REXX example. |
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For '''10''' decimal digits: |
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<pre> |
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Using 10 iterations for maxJ, with 10 decimal digits: |
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correct |
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────i──── ──digits─── ─────d───── |
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2 0 3.218511415 |
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3 1 4.385677676 |
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4 2 4.600948689 |
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5 2 4.65513455 |
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6 3 4.666093465 |
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7 3 4.668532629 |
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8 4 4.669075367 |
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9 3 4.661840596 |
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10 1 4.716700473 |
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11 1 4.865131579 |
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12 0 33.77777778 |
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13 0 -0.004986149584 |
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14 0 -0.004986146524 |
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15 0 -0.003986261738 |
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16 0 -0.0178044264 |
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17 0 -0.169923567 |
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18 0 -0.2743411539 |
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19 0 -0.2916348706 |
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20 0 -0.2917038238 |
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true value= 4.669201609 |
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</pre> |
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For '''20''' decimal digits: |
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<pre> |
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Using 10 iterations for maxJ, with 20 decimal digits: |
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correct |
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────i──── ──digits─── ──────────d────────── |
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2 0 3.2185114220380879119 |
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3 1 4.3856775985683390848 |
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4 2 4.6009492765380753389 |
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5 2 4.655130495391980231 |
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6 3 4.6661119478285698075 |
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7 3 4.668548581446857975 |
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8 4 4.6690606606480870955 |
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9 4 4.6691715553802316722 |
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10 4 4.6691951560255308919 |
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11 6 4.6692002291211212557 |
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12 7 4.6692013127842230631 |
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13 7 4.6692015485437548544 |
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14 9 4.6692016005633566634 |
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15 7 4.6692015330312737776 |
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16 6 4.6692023823679005527 |
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17 4 4.6691972211443265305 |
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18 6 4.6692074719138228098 |
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19 4 4.6694187571119124281 |
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20 3 4.6688146048792985728 |
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true value= 4.6692016091029906719 |
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</pre> |
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For '''30''' decimal digits: |
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<pre> |
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Using 10 iterations for maxJ, with 30 decimal digits: |
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correct |
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────i──── ──digits─── ───────────────d─────────────── |
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2 0 3.21851142203808791227050453077 |
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3 1 4.3856775985683390857449485682 |
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4 2 4.60094927653807535781169469969 |
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5 2 4.65513049539198013648625498649 |
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6 3 4.66611194782857138833121364654 |
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7 3 4.66854858144684094804454708811 |
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8 4 4.66906066064826823913257549468 |
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9 4 4.6691715553795113888859465442 |
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10 4 4.66919515603001717402161720542 |
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11 6 4.66920022908685649793393149233 |
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12 7 4.66920131329420417113719511412 |
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13 7 4.66920154578090670783369507315 |
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14 7 4.66920159553749390966169074155 |
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15 9 4.66920160619815215840788706632 |
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16 9 4.66920160848080435144581223484 |
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17 9 4.66920160896974538458267849027 |
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18 10 4.66920160907444981238909862845 |
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19 10 4.66920160909687888294310165196 |
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20 12 4.66920160910169069039564432665 |
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true value= 4.66920160910299067185320382047 |
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</pre> |
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For '''40''' decimal digits: |
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<pre> |
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Using 10 iterations for maxJ, with 40 decimal digits: |
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correct |
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i digits d |
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2 0 3.218511422038087912270504530742813256018 |
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3 1 4.385677598568339085744948568775522346173 |
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4 2 4.600949276538075357811694698623834984934 |
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5 2 4.655130495391980136486254995856898818963 |
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6 3 4.666111947828571388331213696711776471107 |
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7 3 4.668548581446840948044543680148146102083 |
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8 4 4.669060660648268239132599822630273970875 |
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9 4 4.669171555379511388886004609897560033836 |
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10 4 4.669195156030017174021108801191558304938 |
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11 6 4.669200229086856497938353781003810044639 |
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12 7 4.66920131329420417116475494118414885682 |
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13 7 4.669201545780906707506058109960038118631 |
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14 7 4.669201595537493910292470639266101619701 |
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15 9 4.669201606198152157723831098067070167449 |
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16 9 4.669201608480804423294067936197345435789 |
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17 9 4.66920160896974470048248536837343166496 |
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18 10 4.669201609074452566227981315990238717244 |
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19 10 4.66920160909687879470513360848001376754 |
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20 12 4.669201609101681681186958959033209022075 |
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true value= 4.669201609102990671853203820466201617258 |
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</pre> |
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For '''50''' decimal digits: |
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<pre> |
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Using 10 iterations for maxJ, with 50 decimal digits: |
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correct |
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i digits d |
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2 0 3.2185114220380879122705045307428132560288203779709 |
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3 1 4.3856775985683390857449485687755223461032163565761 |
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4 2 4.6009492765380753578116946986238349850235524966338 |
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5 2 4.6551304953919801364862549958568988194754604973163 |
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6 3 4.6661119478285713883312136967117764807190589709335 |
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7 3 4.6685485814468409480445436801481462655432879036191 |
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8 4 4.6690606606482682391325998226302726377996820048001 |
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9 4 4.6691715553795113888860046098975670882406762637156 |
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10 4 4.6691951560300171740211088011914920933921530026738 |
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11 6 4.6692002290868564979383537810040672174088979117872 |
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12 7 4.6692013132942041711647549411855711837281506913619 |
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13 7 4.669201545780906707506058109930429736433895282946 |
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14 7 4.6692015955374939102924706392896460400580631742226 |
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15 9 4.669201606198152157723831097078594524390001462635 |
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16 9 4.6692016084808044232940679458986228433868918971945 |
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17 9 4.6692016089697447004824853219383733420478533710096 |
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18 10 4.6692016090744525662279815203708867655911039176535 |
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19 10 4.6692016090968787947051350378647834642184844514321 |
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20 12 4.6692016091016816811869601608458025942520519239165 |
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true value= 4.6692016091029906718532038204662016172581855774758 |
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</pre> |
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For '''60''' decimal digits: |
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<pre> |
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Using 10 iterations for maxJ, with 60 decimal digits: |
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correct |
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i digits d |
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2 0 3.21851142203808791227050453074281325602882037797108219914195 |
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3 1 4.38567759856833908574494856877552234610321635657649780870002 |
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4 2 4.60094927653807535781169469862383498502355249663354337228864 |
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5 2 4.65513049539198013648625499585689881947546049738522607840669 |
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6 3 4.66611194782857138833121369671177648071905897173694216387654 |
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7 3 4.66854858144684094804454368014814626554328789665434875726458 |
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8 4 4.66906066064826823913259982263027263779968209542149739645327 |
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9 4 4.6691715553795113888860046098975670882406765731707896864092 |
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10 4 4.66919515603001717402110880119149209339214790860575667043884 |
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11 6 4.66920022908685649793835378100406721740888804890682292715866 |
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12 7 4.66920131329420417116475494118557118372824888898657591993058 |
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13 7 4.6692015457809067075060581099304297364315643304525960728651 |
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14 7 4.66920159553749391029247063928964604007454741248894160626657 |
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15 9 4.66920160619815215772383109707859452442133651601886184881893 |
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16 9 4.66920160848080442329406794589862284279286838186077964235606 |
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17 9 4.66920160896974470048248532193837334390738554123097139976161 |
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18 10 4.66920160907445256622798152037088675394609964381174635788482 |
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19 10 4.66920160909687879470513503786478367762266653874157074386282 |
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20 12 4.66920160910168168118696016084580172992808891003148562640334 |
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true value= 4.66920160910299067185320382046620161725818557747576863274565 |
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</pre> |
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For '''70''' decimal digits: |
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<pre> |
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Using 10 iterations for maxJ, with 70 decimal digits: |
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correct |
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i digits d |
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2 0 3.218511422038087912270504530742813256028820377971082199141994437483264 |
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3 1 4.385677598568339085744948568775522346103216356576497808699630752612707 |
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4 2 4.600949276538075357811694698623834985023552496633543372295593454453943 |
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5 2 4.655130495391980136486254995856898819475460497385226078363311588173369 |
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6 3 4.666111947828571388331213696711776480719058971736942163972368911928369 |
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7 3 4.668548581446840948044543680148146265543287896654348757317309551877191 |
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8 4 4.669060660648268239132599822630272637799682095421497400522886796129394 |
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9 4 4.669171555379511388886004609897567088240676573170789783804375123155331 |
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10 4 4.669195156030017174021108801191492093392147908605756405516325953901305 |
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11 6 4.669200229086856497938353781004067217408888048906823830162962197636106 |
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12 7 4.669201313294204171164754941185571183728248888986548913352218691391234 |
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13 7 4.669201545780906707506058109930429736431564330452605295006133445674219 |
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14 7 4.669201595537493910292470639289646040074547412490596040512697122945726 |
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15 9 4.669201606198152157723831097078594524421336516011873717994576148241557 |
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16 9 4.669201608480804423294067945898622842792868381815074127666008519547807 |
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17 9 4.669201608969744700482485321938373343907385540992447405914541777669855 |
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18 10 4.669201609074452566227981520370886753946099646679618269983331571360562 |
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19 10 4.669201609096878794705135037864783677622666525741836726551719975589237 |
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20 12 4.669201609101681681186960160845801729928088893244076177775471467408333 |
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true value= 4.669201609102990671853203820466201617258185577475768632745651343004134 |
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</pre> |