Talk:Feigenbaum constant calculation: Difference between revisions
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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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19 10 4.66920160909687879470513503786478367762266653874157074386282 |
19 10 4.66920160909687879470513503786478367762266653874157074386282 |
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20 12 4.66920160910168168118696016084580172992808891003148562640334 |
20 12 4.66920160910168168118696016084580172992808891003148562640334 |
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21 13 4.66920160910271032783721020862911185778172326442565716536709 |
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22 14 4.66920160910293063053977814120551764178343752008225932597126 |
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23 14 4.66920160910297781286849594159066394676899035975117693184181 |
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24 14 4.66920160910298791784924597861351311575702672457052187681814 |
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25 16 4.66920160910299008203028907572873571164451680641851773878632 |
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true value= 4.66920160910299067185320382046620161725818557747576863274565 |
true value= 4.66920160910299067185320382046620161725818557747576863274565 |
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For '''70''' decimal digits: |
For '''70''' decimal digits: |
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<pre> |
<pre> |
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⚫ | |||
correct |
correct |
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────i──── ──digits─── ───────────────────────────────────d─────────────────────────────────── |
────i──── ──digits─── ───────────────────────────────────d─────────────────────────────────── |
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19 10 4.669201609096878794705135037864783677622666525741836726551719975589237 |
19 10 4.669201609096878794705135037864783677622666525741836726551719975589237 |
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20 12 4.669201609101681681186960160845801729928088893244076177775471467408333 |
20 12 4.669201609101681681186960160845801729928088893244076177775471467408333 |
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21 13 4.669201609102710327837210208629111857781724142614997374915326806800362 |
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22 14 4.66920160910293063053977814120551764178343912104101642911388967884521 |
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23 14 4.669201609102977812868495941590663946768960431441218530680922308996195 |
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24 14 4.669201609102987917849245978613513115757246210043045367998209732838256 |
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25 16 4.669201609102990082030289075728735711642616959039291006563095888962633 |
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true value= 4.669201609102990671853203820466201617258185577475768632745651343004134 |
true value= 4.669201609102990671853203820466201617258185577475768632745651343004134 |
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</pre> |
</pre> |
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For '''80''' decimal digits: |
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<pre> |
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⚫ | |||
correct |
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────i──── ──digits─── ────────────────────────────────────────d──────────────────────────────────────── |
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2 0 3.218511422038087912270504530742813256028820377971082199141994437483271226037644 |
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3 1 4.3856775985683390857449485687755223461032163565764978086996307526127059403885727 |
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4 2 4.6009492765380753578116946986238349850235524966335433722955934544543297715255263 |
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5 2 4.65513049539198013648625499585689881947546049738522607836331158816512330701185 |
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6 3 4.6661119478285713883312136967117764807190589717369421639723689119899863948191767 |
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7 3 4.6685485814468409480445436801481462655432878966543487573173095514004033372611035 |
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8 4 4.6690606606482682391325998226302726377996820954214974005228867986774308919065374 |
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9 4 4.6691715553795113888860046098975670882406765731707897838043751138046951387299861 |
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10 4 4.6691951560300171740211088011914920933921479086057564055163259615974354982832945 |
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11 6 4.669200229086856497938353781004067217408888048906823830162962242800073690648252 |
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12 7 4.6692013132942041711647549411855711837282488889865489133522172264691137798051217 |
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13 7 4.6692015457809067075060581099304297364315643304526052950061428053412995477405222 |
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14 7 4.6692015955374939102924706392896460400745474124905960405127779853884788591538808 |
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15 9 4.669201606198152157723831097078594524421336516011873717994000712974012683245483 |
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16 9 4.6692016084808044232940679458986228427928683818150741276727477649124978493132468 |
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17 9 4.6692016089697447004824853219383733439073855409924474058836052813335649172765848 |
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18 10 4.6692016090744525662279815203708867539460996466796182702147591041819366993698455 |
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19 10 4.6692016090968787947051350378647836776226665257418367260642987724054233659298261 |
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20 12 4.6692016091016816811869601608458017299280888932440761709767910747509918644406354 |
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21 13 4.6692016091027103278372102086291118577817241426149973921672976705446842793794715 |
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22 14 4.6692016091029306305397781412055176417834391210410168137358073785476857294775448 |
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23 14 4.6692016091029778128684959415906639467689604314412120973278560695067487724011958 |
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24 14 4.6692016091029879178492459786135131157572462100430915357209982548433093297570592 |
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25 16 4.6692016091029900820302890757287357116426169590391741098422496772889977674631437 |
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true value= 4.6692016091029906718532038204662016172581855774757686327456513430041343302113147 |
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</pre> |
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::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) |
::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) |
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::: 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) |
::: 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) |
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::: 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) |