Anonymous user
Talk:Feigenbaum constant calculation: Difference between revisions
m
→degree of accuracy with more precision during computing: added arrow pointing to last accurate decimal digit.
m (added a comment.) |
m (→degree of accuracy with more precision during computing: added arrow pointing to last accurate decimal digit.) |
||
| (10 intermediate revisions by 2 users not shown) | |||
Line 2:
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. [[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 10:47, 18 September 2018 (UTC)
All the solutions seem to be based on the paper [http://keithbriggs.info/documents/how-to-calc.pdf How to calculate the Feigenbaum constants on your PC. Aust. Math. Soc. Gazette 16, 89.], from [http://keithbriggs.info Keith Briggs]. [[User:Laurence|Laurence]] ([[User talk:Laurence|talk]]) 18:04, 20 November 2019 (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 (<big>'''i'''</big>) iteration. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 06:28, 19 September 2018 (UTC)
[http://www.plouffe.fr/simon/constants/feigenbaum.txt Here] is the value of the Feigenbaum's constant up to 1,018 decimal places. [[User:Laurence|Laurence]] ([[User talk:Laurence|talk]]) 18:04, 20 November 2019 (UTC)
==degree of accuracy with more precision during computing==
Line 36 ⟶ 39:
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
</pre>
Line 64 ⟶ 72:
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
</pre>
Line 92 ⟶ 105:
19 10 4.66920160909687888294310165196
20 12 4.66920160910169069039564432665
21 12 4.66920160910308071307717015249
22 10 4.66920160909753242748934828099
23 11 4.66920160912480010881711811908
24 12 4.66920160910412904696305071057
25 9 4.66920160831045435278064326969
↑
true value= 4.66920160910299067185320382047
</pre>
Line 120 ⟶ 138:
19 10 4.66920160909687879470513360848001376754
20 12 4.669201609101681681186958959033209022075
21 13 4.669201609102710327837251895947327626516
22 14 4.669201609102930630539149782358669774031
23 14 4.669201609102977812872078849723792590704
24 14 4.669201609102987917842550686945063648103
25 16 4.669201609102990082109591039030679816186
↑
true value= 4.669201609102990671853203820466201617258
</pre>
Line 148 ⟶ 171:
19 10 4.6692016090968787947051350378647834642184844514321
20 12 4.6692016091016816811869601608458025942520519239165
21 13 4.6692016091027103278372102086291147081441587520389
22 14 4.6692016091029306305397781412054635772954039489788
23 14 4.6692016091029778128684959415909409745410570226985
24 14 4.6692016091029879178492459786120026677307662966576
25 16 4.6692016091029900820302890757279774163961895200742
↑
true value= 4.6692016091029906718532038204662016172581855774758
</pre>
Line 176 ⟶ 204:
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
</pre>
For '''70''' decimal digits:
<pre>
Using 10 iterations for maxJ, with 70 decimal digits:▼
correct
────i──── ──digits─── ───────────────────────────────────d───────────────────────────────────
Line 204 ⟶ 235:
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
<pre>
true value= 4.669201609
Line 218 ⟶ 288:
true value= 4.669201609102990671853203820466201617258185577475768632745651343004134
</pre>
::: 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). -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk: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. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 02:52, 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)
::: Adding more decimal digits (for the REXX calculations) will result in more (accurate) 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)
| |||