the logistic map - bifurcation diagram / La suite logistique - diagramme de bifurcation / published by https://github.com/dacr/code-examples-manager #e294d28a-aa97-4a4a-9a97-3cef7d22fd65/86f53aeb447c7a600e80272ab7a21d76413b68de

math-logistic-map-2.sc

// summary : the logistic map - bifurcation diagram / La suite logistique - diagramme de bifurcation
// keywords : math, logistic-map, fractal, chaos, breeze, bifurcation-diagram
// publish : gist
// authors : David Crosson
// license : Apache NON-AI License Version 2.0 (https://raw.githubusercontent.com/non-ai-licenses/non-ai-licenses/main/NON-AI-APACHE2)
// id : e294d28a-aa97-4a4a-9a97-3cef7d22fd65
// created-on : 2021-02-26T15:34:32Z
// managed-by : https://github.com/dacr/code-examples-manager
// execution : scala ammonite script (http://ammonite.io/) - run as follow 'amm scriptname.sc'

// logistic map info -> https://en.wikipedia.org/wiki/Logistic_map
// veritasium video -> https://www.youtube.com/watch?v=ovJcsL7vyrk

import $ivy.`org.plotly-scala::plotly-render:0.8.1`
import plotly._ ,element._ ,layout._ ,Plotly._
import java.math.MathContext

val computeMathContext = new MathContext(10) // constraint the total number of digits
val valuesKeeperRoundContext = new MathContext(4) // constraint the total number of digits

def logMap(xn: BigDecimal, r: BigDecimal): BigDecimal = r * xn * (1 - xn)

def logMapAnalysis(givenR: Double, maxGenerations: Int, ignoreGenerationsBelow:Int, givenX0:Double = 0.5): Set[BigDecimal] = {
  val r = BigDecimal(givenR, computeMathContext)
  val x0 = BigDecimal(givenX0, computeMathContext)
  def generations = {
    LazyList
      .from(1)
      .scanLeft(Tuple2(x0, Set.empty[BigDecimal])) {
        case ((xp, values), gen) if gen < ignoreGenerationsBelow => logMap(xp, r) -> values
        case ((xp, values), _) =>
          val xn = logMap(xp, r)
          xn -> (values + xn.round(valuesKeeperRoundContext))
      }
  }
  generations.drop(maxGenerations).head match {
    case (xn, values) => values
  }
}

// =================================================================================================

val points = {
  LazyList
    .iterate(1.5d)(_ + 0.001d)
    .takeWhile(_ < 4.0d)
    .flatMap(r => logMapAnalysis(r, 100, 50).map(value => r -> value.toDouble))
}
val (xs, ys) =  points.unzip

println("Number of points generated : "+points.size)
// =================================================================================================

val plotlyData = Seq(
  Scatter(xs, ys)
    .withName("LogisticMap")
    .withMode(ScatterMode(ScatterMode.Markers))
    .withMarker(Marker().withSize(1))
)


val plotlyLayout = Layout().withTitle("LogisticMapTrend").withHeight(800).withWidth(1200)

plot("plot.html", plotlyData, plotlyLayout)


//scala.io.StdIn.readLine("Press enter to quit")