Talk:Feigenbaum constant calculation
Description needed
The task would be improved if there was a clearer description of how to calculate the constant given than the hidden, math-centric Wikipedia text. The target audience are programmers, and a I think a given method of calculation would allow for better comparison of solutions. Paddy3118 (talk) 10:47, 18 September 2018 (UTC)
true value of Feigenbaum's constant
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 (i) iteration. -- Gerard Schildberger (talk) 06:28, 19 September 2018 (UTC)
degree of accuracy with more precision during computing
I was experimenting with increasing the number of decimal digits (precision) with the REXX example.
For 10 decimal digits:
Using 10 iterations for maxJ, with 10 decimal digits: correct ────i──── ──digits─── ─────d───── 2 0 3.218511415 3 1 4.385677676 4 2 4.600948689 5 2 4.65513455 6 3 4.666093465 7 3 4.668532629 8 4 4.669075367 9 3 4.661840596 10 1 4.716700473 11 1 4.865131579 12 0 33.77777778 13 0 -0.004986149584 14 0 -0.004986146524 15 0 -0.003986261738 16 0 -0.0178044264 17 0 -0.169923567 18 0 -0.2743411539 19 0 -0.2916348706 20 0 -0.2917038238 21 0 -1.282351899 22 0 -4.760586838 23 0 -3.741736856 24 0 -3.754125525 25 0 -0.09190415307 true value= 4.669201609
For 20 decimal digits:
Using 10 iterations for maxJ, with 20 decimal digits: correct ────i──── ──digits─── ──────────d────────── 2 0 3.2185114220380879119 3 1 4.3856775985683390848 4 2 4.6009492765380753389 5 2 4.655130495391980231 6 3 4.6661119478285698075 7 3 4.668548581446857975 8 4 4.6690606606480870955 9 4 4.6691715553802316722 10 4 4.6691951560255308919 11 6 4.6692002291211212557 12 7 4.6692013127842230631 13 7 4.6692015485437548544 14 9 4.6692016005633566634 15 7 4.6692015330312737776 16 6 4.6692023823679005527 17 4 4.6691972211443265305 18 6 4.6692074719138228098 19 4 4.6694187571119124281 20 3 4.6688146048792985728 21 2 4.6712853146119749655 22 2 4.6215243376551173582 23 2 4.6832793670928330607 24 0 1.6761036199854529178 25 0 1.3068879789412108804 true value= 4.6692016091029906719
For 30 decimal digits:
Using 10 iterations for maxJ, with 30 decimal digits: correct ────i──── ──digits─── ───────────────d─────────────── 2 0 3.21851142203808791227050453077 3 1 4.3856775985683390857449485682 4 2 4.60094927653807535781169469969 5 2 4.65513049539198013648625498649 6 3 4.66611194782857138833121364654 7 3 4.66854858144684094804454708811 8 4 4.66906066064826823913257549468 9 4 4.6691715553795113888859465442 10 4 4.66919515603001717402161720542 11 6 4.66920022908685649793393149233 12 7 4.66920131329420417113719511412 13 7 4.66920154578090670783369507315 14 7 4.66920159553749390966169074155 15 9 4.66920160619815215840788706632 16 9 4.66920160848080435144581223484 17 9 4.66920160896974538458267849027 18 10 4.66920160907444981238909862845 19 10 4.66920160909687888294310165196 20 12 4.66920160910169069039564432665 true value= 4.66920160910299067185320382047
For 40 decimal digits:
Using 10 iterations for maxJ, with 40 decimal digits: correct ────i──── ──digits─── ────────────────────d──────────────────── 2 0 3.218511422038087912270504530742813256018 3 1 4.385677598568339085744948568775522346173 4 2 4.600949276538075357811694698623834984934 5 2 4.655130495391980136486254995856898818963 6 3 4.666111947828571388331213696711776471107 7 3 4.668548581446840948044543680148146102083 8 4 4.669060660648268239132599822630273970875 9 4 4.669171555379511388886004609897560033836 10 4 4.669195156030017174021108801191558304938 11 6 4.669200229086856497938353781003810044639 12 7 4.66920131329420417116475494118414885682 13 7 4.669201545780906707506058109960038118631 14 7 4.669201595537493910292470639266101619701 15 9 4.669201606198152157723831098067070167449 16 9 4.669201608480804423294067936197345435789 17 9 4.66920160896974470048248536837343166496 18 10 4.669201609074452566227981315990238717244 19 10 4.66920160909687879470513360848001376754 20 12 4.669201609101681681186958959033209022075 true value= 4.669201609102990671853203820466201617258
For 50 decimal digits:
Using 10 iterations for maxJ, with 50 decimal digits: correct ────i──── ──digits─── ─────────────────────────d───────────────────────── 2 0 3.2185114220380879122705045307428132560288203779709 3 1 4.3856775985683390857449485687755223461032163565761 4 2 4.6009492765380753578116946986238349850235524966338 5 2 4.6551304953919801364862549958568988194754604973163 6 3 4.6661119478285713883312136967117764807190589709335 7 3 4.6685485814468409480445436801481462655432879036191 8 4 4.6690606606482682391325998226302726377996820048001 9 4 4.6691715553795113888860046098975670882406762637156 10 4 4.6691951560300171740211088011914920933921530026738 11 6 4.6692002290868564979383537810040672174088979117872 12 7 4.6692013132942041711647549411855711837281506913619 13 7 4.669201545780906707506058109930429736433895282946 14 7 4.6692015955374939102924706392896460400580631742226 15 9 4.669201606198152157723831097078594524390001462635 16 9 4.6692016084808044232940679458986228433868918971945 17 9 4.6692016089697447004824853219383733420478533710096 18 10 4.6692016090744525662279815203708867655911039176535 19 10 4.6692016090968787947051350378647834642184844514321 20 12 4.6692016091016816811869601608458025942520519239165 true value= 4.6692016091029906718532038204662016172581855774758
For 60 decimal digits:
Using 10 iterations for maxJ, with 60 decimal digits: correct ────i──── ──digits─── ──────────────────────────────d────────────────────────────── 2 0 3.21851142203808791227050453074281325602882037797108219914195 3 1 4.38567759856833908574494856877552234610321635657649780870002 4 2 4.60094927653807535781169469862383498502355249663354337228864 5 2 4.65513049539198013648625499585689881947546049738522607840669 6 3 4.66611194782857138833121369671177648071905897173694216387654 7 3 4.66854858144684094804454368014814626554328789665434875726458 8 4 4.66906066064826823913259982263027263779968209542149739645327 9 4 4.6691715553795113888860046098975670882406765731707896864092 10 4 4.66919515603001717402110880119149209339214790860575667043884 11 6 4.66920022908685649793835378100406721740888804890682292715866 12 7 4.66920131329420417116475494118557118372824888898657591993058 13 7 4.6692015457809067075060581099304297364315643304525960728651 14 7 4.66920159553749391029247063928964604007454741248894160626657 15 9 4.66920160619815215772383109707859452442133651601886184881893 16 9 4.66920160848080442329406794589862284279286838186077964235606 17 9 4.66920160896974470048248532193837334390738554123097139976161 18 10 4.66920160907445256622798152037088675394609964381174635788482 19 10 4.66920160909687879470513503786478367762266653874157074386282 20 12 4.66920160910168168118696016084580172992808891003148562640334 true value= 4.66920160910299067185320382046620161725818557747576863274565
For 70 decimal digits:
Using 10 iterations for maxJ, with 70 decimal digits: correct ────i──── ──digits─── ───────────────────────────────────d─────────────────────────────────── 2 0 3.218511422038087912270504530742813256028820377971082199141994437483264 3 1 4.385677598568339085744948568775522346103216356576497808699630752612707 4 2 4.600949276538075357811694698623834985023552496633543372295593454453943 5 2 4.655130495391980136486254995856898819475460497385226078363311588173369 6 3 4.666111947828571388331213696711776480719058971736942163972368911928369 7 3 4.668548581446840948044543680148146265543287896654348757317309551877191 8 4 4.669060660648268239132599822630272637799682095421497400522886796129394 9 4 4.669171555379511388886004609897567088240676573170789783804375123155331 10 4 4.669195156030017174021108801191492093392147908605756405516325953901305 11 6 4.669200229086856497938353781004067217408888048906823830162962197636106 12 7 4.669201313294204171164754941185571183728248888986548913352218691391234 13 7 4.669201545780906707506058109930429736431564330452605295006133445674219 14 7 4.669201595537493910292470639289646040074547412490596040512697122945726 15 9 4.669201606198152157723831097078594524421336516011873717994576148241557 16 9 4.669201608480804423294067945898622842792868381815074127666008519547807 17 9 4.669201608969744700482485321938373343907385540992447405914541777669855 18 10 4.669201609074452566227981520370886753946099646679618269983331571360562 19 10 4.669201609096878794705135037864783677622666525741836726551719975589237 20 12 4.669201609101681681186960160845801729928088893244076177775471467408333 true value= 4.669201609102990671853203820466201617258185577475768632745651343004134
- Is the term 'true value' appropriate here? Increasing the number of digits results in more and more digits of this "constant". The true value may have an imfimite number of digits. The approximations shown here are quite stable.--Walter Pachl 02:07, 16 November 2018 (UTC)
true value= 4.669201609 true value= 4.6692016091029906719 true value= 4.66920160910299067185320382047 true value= 4.669201609102990671853203820466201617258 true value= 4.6692016091029906718532038204662016172581855774758 true value= 4.66920160910299067185320382046620161725818557747576863274565 true value= 4.669201609102990671853203820466201617258185577475768632745651343004134
- The approximations shown above are all the same value (taken from the same variable), the only difference is the number of decimal digits (precision) being used when the value was displayed (plus the value will be rounded within the precision being used). -- Gerard Schildberger (talk) 03:21, 16 November 2018 (UTC)
- The true value shown (for each program execution) is the true value (taken from a value that is assigned), rounded to the number of decimal digits in use for the program. For the true value, the actual constant within the program is accurate to 115 decimal digits. All computed values shown for the output are, by definition, approximations, limited by the number of decimal digits and the number of iterations. -- Gerard Schildberger (talk) 02:52, 16 November 2018 (UTC)
- Showing the true value of is in the same vein. It's only accurate (or true) up to the number of (decimal) digits for , rounded to the number of decimal digits shown. -- Gerard Schildberger (talk) 02:56, 16 November 2018 (UTC)