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Talk:Feigenbaum constant calculation: Difference between revisions
Talk:Feigenbaum constant calculation (view source)
Revision as of 01:21, 18 November 2018
, 5 years ago→degree of accuracy with more precision during computing: added a comment about the calculations diverging.
m (→degree of accuracy with more precision during computing: updated a run with more iterations.) |
(→degree of accuracy with more precision during computing: added a comment about the calculations diverging.) |
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Line 201:
19 10 4.66920160909687879470513503786478367762266653874157074386282
20 12 4.66920160910168168118696016084580172992808891003148562640334
21 13 4.66920160910271032783721020862911185778172326442565716536709
22 14 4.66920160910293063053977814120551764178343752008225932597126
23 14 4.66920160910297781286849594159066394676899035975117693184181
24 14 4.66920160910298791784924597861351311575702672457052187681814
25 16 4.66920160910299008203028907572873571164451680641851773878632
true value= 4.66920160910299067185320382046620161725818557747576863274565
Line 206 ⟶ 211:
For '''70''' decimal digits:
<pre>
Using 10 iterations for maxJ, with 70 decimal digits:▼
correct
────i──── ──digits─── ───────────────────────────────────d───────────────────────────────────
Line 229 ⟶ 232:
19 10 4.669201609096878794705135037864783677622666525741836726551719975589237
20 12 4.669201609101681681186960160845801729928088893244076177775471467408333
21 13 4.669201609102710327837210208629111857781724142614997374915326806800362
22 14 4.66920160910293063053977814120551764178343912104101642911388967884521
23 14 4.669201609102977812868495941590663946768960431441218530680922308996195
24 14 4.669201609102987917849245978613513115757246210043045367998209732838256
25 16 4.669201609102990082030289075728735711642616959039291006563095888962633
true value= 4.669201609102990671853203820466201617258185577475768632745651343004134
</pre>
For '''80''' decimal digits:
<pre>
correct
────i──── ──digits─── ────────────────────────────────────────d────────────────────────────────────────
2 0 3.218511422038087912270504530742813256028820377971082199141994437483271226037644
3 1 4.3856775985683390857449485687755223461032163565764978086996307526127059403885727
4 2 4.6009492765380753578116946986238349850235524966335433722955934544543297715255263
5 2 4.65513049539198013648625499585689881947546049738522607836331158816512330701185
6 3 4.6661119478285713883312136967117764807190589717369421639723689119899863948191767
7 3 4.6685485814468409480445436801481462655432878966543487573173095514004033372611035
8 4 4.6690606606482682391325998226302726377996820954214974005228867986774308919065374
9 4 4.6691715553795113888860046098975670882406765731707897838043751138046951387299861
10 4 4.6691951560300171740211088011914920933921479086057564055163259615974354982832945
11 6 4.669200229086856497938353781004067217408888048906823830162962242800073690648252
12 7 4.6692013132942041711647549411855711837282488889865489133522172264691137798051217
13 7 4.6692015457809067075060581099304297364315643304526052950061428053412995477405222
14 7 4.6692015955374939102924706392896460400745474124905960405127779853884788591538808
15 9 4.669201606198152157723831097078594524421336516011873717994000712974012683245483
16 9 4.6692016084808044232940679458986228427928683818150741276727477649124978493132468
17 9 4.6692016089697447004824853219383733439073855409924474058836052813335649172765848
18 10 4.6692016090744525662279815203708867539460996466796182702147591041819366993698455
19 10 4.6692016090968787947051350378647836776226665257418367260642987724054233659298261
20 12 4.6692016091016816811869601608458017299280888932440761709767910747509918644406354
21 13 4.6692016091027103278372102086291118577817241426149973921672976705446842793794715
22 14 4.6692016091029306305397781412055176417834391210410168137358073785476857294775448
23 14 4.6692016091029778128684959415906639467689604314412120973278560695067487724011958
24 14 4.6692016091029879178492459786135131157572462100430915357209982548433093297570592
25 16 4.6692016091029900820302890757287357116426169590391741098422496772889977674631437
true value= 4.6692016091029906718532038204662016172581855774757686327456513430041343302113147
</pre>
::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)
Line 248 ⟶ 290:
::: Showing the ''true value'' of <big><big><math>\pi</math></big></big> is in the same vein. It's only accurate (or true) up to the number of (decimal) digits for <big><big><math>\pi</math></big></big>, rounded to the number of decimal digits shown. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 02:56, 16 November 2018 (UTC)
::: Adding more decimal digits (for the REXX calculations) will result in more digits of Feigenbaum constant, provided that enough iterations are used, ... up to some point. When that point is reached, the calculations start diverging and less (accurate) decimal digits are produced (calculated). -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 01:20, 18 November 2018 (UTC)
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