Metallic ratios: Difference between revisions

=={{header|Java}}==

<lang java>

import java.math.BigDecimal;

import java.math.BigInteger;

import java.math.MathContext;

import java.util.ArrayList;

import java.util.List;

public class MetallicRatios {

private static String[] ratioDescription = new String[] {"Platinum", "Golden", "Silver", "Bronze", "Copper", "Nickel", "Aluminum", "Iron", "Tin", "Lead"};

public static void main(String[] args) {

int elements = 15;

for ( int b = 0 ; b < 10 ; b++ ) {

System.out.printf("Lucas sequence for %s ratio, where b = %d:%n", ratioDescription[b], b);

System.out.printf("First %d elements: %s%n", elements, lucasSequence(1, 1, b, elements));

int decimalPlaces = 32;

BigDecimal[] ratio = lucasSequenceRatio(1, 1, b, decimalPlaces+1);

System.out.printf("Value to %d decimal places after %s iterations : %s%n", decimalPlaces, ratio[1], ratio[0]);

System.out.printf("%n");

}

int b = 1;

int decimalPlaces = 256;

System.out.printf("%s ratio, where b = %d:%n", ratioDescription[b], b);

BigDecimal[] ratio = lucasSequenceRatio(1, 1, b, decimalPlaces+1);

System.out.printf("Value to %d decimal places after %s iterations : %s%n", decimalPlaces, ratio[1], ratio[0]);

}

private static BigDecimal[] lucasSequenceRatio(int x0, int x1, int b, int digits) {

BigDecimal x0Bi = BigDecimal.valueOf(x0);

BigDecimal x1Bi = BigDecimal.valueOf(x1);

BigDecimal bBi = BigDecimal.valueOf(b);

MathContext mc = new MathContext(digits);

BigDecimal fractionPrior = x1Bi.divide(x0Bi, mc);

int iterations = 0;

while ( true ) {

iterations++;

BigDecimal x = bBi.multiply(x1Bi).add(x0Bi);

BigDecimal fractionCurrent = x.divide(x1Bi, mc);

if ( fractionCurrent.compareTo(fractionPrior) == 0 ) {

break;

}

x0Bi = x1Bi;

x1Bi = x;

fractionPrior = fractionCurrent;

}

return new BigDecimal[] {fractionPrior, BigDecimal.valueOf(iterations)};

}

private static List<BigInteger> lucasSequence(int x0, int x1, int b, int n) {

List<BigInteger> list = new ArrayList<>();

BigInteger x0Bi = BigInteger.valueOf(x0);

BigInteger x1Bi = BigInteger.valueOf(x1);

BigInteger bBi = BigInteger.valueOf(b);

if ( n > 0 ) {

list.add(x0Bi);

}

if ( n > 1 ) {

list.add(x1Bi);

}

while ( n > 2 ) {

BigInteger x = bBi.multiply(x1Bi).add(x0Bi);

list.add(x);

n--;

x0Bi = x1Bi;

x1Bi = x;

}

return list;

}

}

</lang>

{{out}}

<pre>

Lucas sequence for Platinum ratio, where b = 0:

First 15 elements: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Value to 32 decimal places after 1 iterations : 1

Lucas sequence for Golden ratio, where b = 1:

First 15 elements: [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610]

Value to 32 decimal places after 78 iterations : 1.61803398874989484820458683436564

Lucas sequence for Silver ratio, where b = 2:

First 15 elements: [1, 1, 3, 7, 17, 41, 99, 239, 577, 1393, 3363, 8119, 19601, 47321, 114243]

Value to 32 decimal places after 44 iterations : 2.41421356237309504880168872420970

Lucas sequence for Bronze ratio, where b = 3:

First 15 elements: [1, 1, 4, 13, 43, 142, 469, 1549, 5116, 16897, 55807, 184318, 608761, 2010601, 6640564]

Value to 32 decimal places after 34 iterations : 3.30277563773199464655961063373525

Lucas sequence for Copper ratio, where b = 4:

First 15 elements: [1, 1, 5, 21, 89, 377, 1597, 6765, 28657, 121393, 514229, 2178309, 9227465, 39088169, 165580141]

Value to 32 decimal places after 28 iterations : 4.23606797749978969640917366873128

Lucas sequence for Nickel ratio, where b = 5:

First 15 elements: [1, 1, 6, 31, 161, 836, 4341, 22541, 117046, 607771, 3155901, 16387276, 85092281, 441848681, 2294335686]

Value to 32 decimal places after 25 iterations : 5.19258240356725201562535524577016

Lucas sequence for Aluminum ratio, where b = 6:

First 15 elements: [1, 1, 7, 43, 265, 1633, 10063, 62011, 382129, 2354785, 14510839, 89419819, 551029753, 3395598337, 20924619775]

Value to 32 decimal places after 23 iterations : 6.16227766016837933199889354443272

Lucas sequence for Iron ratio, where b = 7:

First 15 elements: [1, 1, 8, 57, 407, 2906, 20749, 148149, 1057792, 7552693, 53926643, 385039194, 2749201001, 19629446201, 140155324408]

Value to 32 decimal places after 22 iterations : 7.14005494464025913554865124576352

Lucas sequence for Tin ratio, where b = 8:

First 15 elements: [1, 1, 9, 73, 593, 4817, 39129, 317849, 2581921, 20973217, 170367657, 1383914473, 11241683441, 91317382001, 741780739449]

Value to 32 decimal places after 20 iterations : 8.12310562561766054982140985597408

Lucas sequence for Lead ratio, where b = 9:

First 15 elements: [1, 1, 10, 91, 829, 7552, 68797, 626725, 5709322, 52010623, 473804929, 4316254984, 39320099785, 358197153049, 3263094477226]

Value to 32 decimal places after 20 iterations : 9.10977222864644365500113714088140

Golden ratio, where b = 1:

Value to 256 decimal places after 615 iterations : 1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144

</pre>