Feigenbaum constant calculation: Difference between revisions

<lang ring># Project : Feigenbaum constant calculation

next</lang>

<pre>Feigenbaum constant calculation:

13 4.66920537</pre>

=={{header|Scala}}==

===Imperative, ugly===

<lang Scala>object Feigenbaum1 extends App {

val (max_it, max_it_j) = (13, 10)

var (a1, a2, d1, a) = (1.0, 0.0, 3.2, 0.0)

println(" i d")

var i: Int = 2

while (i <= max_it) {

a = a1 + (a1 - a2) / d1

for (_ <- 0 until max_it_j) {

var (x, y) = (0.0, 0.0)

for (_ <- 0 until 1 << i) {

y = 1.0 - 2.0 * y * x

x = a - x * x

}

a -= x / y

}

val d: Double = (a1 - a2) / (a - a1)

printf("%2d %.8f\n", i, d)

d1 = d

a2 = a1

a1 = a

i += 1

}

}</lang>

===Functional Style, Tail recursive===

{{Out}}Best seen running in your browser either by [https://scalafiddle.io/sf/OjA3sae/0 ScalaFiddle (ES aka JavaScript, non JVM)] or [https://scastie.scala-lang.org/04eS3BfCShmrA7I8ZmQfJA Scastie (remote JVM)].

<lang Scala>object Feigenbaum2 extends App {

private val (max_it, max_it_j) = (13, 10)

private def result = {

@scala.annotation.tailrec

def outer(i: Int, d1: Double, a2: Double, a1: Double, acc: Seq[Double]): Seq[Double] = {

@scala.annotation.tailrec

def center(j: Int, a: Double): Double = {

@scala.annotation.tailrec

def inner(k: Int, end: Int, x: Double, y: Double): (Double, Double) =

if (k < end) inner(k + 1, end, a - x * x, 1.0 - 2.0 * y * x) else (x, y)

val (x, y) = inner(0, 1 << i, 0.0, 0.0)

if (j < max_it_j) {

center(j + 1, a - (x / y))

} else a

}

if (i <= max_it) {

val a = center(0, a1 + (a1 - a2) / d1)

val d: Double = (a1 - a2) / (a - a1)

outer(i + 1, d, a1, a, acc :+ d)

} else acc

}

outer(2, 3.2, 0, 1.0, Seq[Double]()).zipWithIndex

}

println(" i ≈ δ")

result.foreach { case (δ, i) => println(f"${i + 2}%2d $δ%.8f") }

}</lang>