Metallic ratios: Difference between revisions
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Golden ration, where b = 1:
Value after 615 iterations: 1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<lang Mathematica>ClearAll[FindMetallicRatio]
FindMetallicRatio[b_, digits_] :=
Module[{n, m, data, acc, old, done = False},
{n, m} = {1, 1};
old = -100;
data = {};
While[done == False,
{n, m} = {m, b m + n};
AppendTo[data, {m, m/n}];
If[Length[data] > 15,
If[-N[Log10[Abs[data[[-1, 2]] - data[[-2, 2]]]]] > digits,
done = True
]
]
];
acc = -N[Log10[Abs[data[[-1, 2]] - data[[-2, 2]]]]];
<|"sequence" -> Join[{1, 1}, data[[All, 1]]],
"ratio" -> data[[All, 2]], "acc" -> acc,
"steps" -> Length[data]|>
]
Do[
out = FindMetallicRatio[b, 32];
Print["b=", b];
Print["b=", b, " first 15=", Take[out["sequence"], 15]];
Print["b=", b, " ratio=", N[Last[out["ratio"]], {\[Infinity], 33}]];
Print["b=", b, " Number of steps=", out["steps"]];
,
{b, 0, 9}
]
out = FindMetallicRatio[1, 256];
out["steps"]
N[out["ratio"][[-1]], 256]</lang>
{{out}}
<pre>b=0
b=0 first 15={1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
b=0 ratio=1.00000000000000000000000000000000
b=0 Number of steps=16
b=1
b=1 first 15={1,1,2,3,5,8,13,21,34,55,89,144,233,377,610}
b=1 ratio=1.61803398874989484820458683436564
b=1 Number of steps=78
b=2
b=2 first 15={1,1,3,7,17,41,99,239,577,1393,3363,8119,19601,47321,114243}
b=2 ratio=2.41421356237309504880168872420970
b=2 Number of steps=44
b=3
b=3 first 15={1,1,4,13,43,142,469,1549,5116,16897,55807,184318,608761,2010601,6640564}
b=3 ratio=3.30277563773199464655961063373525
b=3 Number of steps=33
b=4
b=4 first 15={1,1,5,21,89,377,1597,6765,28657,121393,514229,2178309,9227465,39088169,165580141}
b=4 ratio=4.236067977499789696409173668731276
b=4 Number of steps=28
b=5
b=5 first 15={1,1,6,31,161,836,4341,22541,117046,607771,3155901,16387276,85092281,441848681,2294335686}
b=5 ratio=5.19258240356725201562535524577016
b=5 Number of steps=25
b=6
b=6 first 15={1,1,7,43,265,1633,10063,62011,382129,2354785,14510839,89419819,551029753,3395598337,20924619775}
b=6 ratio=6.162277660168379331998893544432719
b=6 Number of steps=23
b=7
b=7 first 15={1,1,8,57,407,2906,20749,148149,1057792,7552693,53926643,385039194,2749201001,19629446201,140155324408}
b=7 ratio=7.14005494464025913554865124576352
b=7 Number of steps=21
b=8
b=8 first 15={1,1,9,73,593,4817,39129,317849,2581921,20973217,170367657,1383914473,11241683441,91317382001,741780739449}
b=8 ratio=8.123105625617660549821409855974077
b=8 Number of steps=20
b=9
b=9 first 15={1,1,10,91,829,7552,68797,626725,5709322,52010623,473804929,4316254984,39320099785,358197153049,3263094477226}
b=9 ratio=9.10977222864644365500113714088140
b=9 Number of steps=19
614
1.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137484754088075386891752126633862223536931793180060766726354433389086595939582905638322661319928290267880675208766892501711696207032221043216269548626296313614</pre>
=={{header|Nim}}==
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