the logistic map / La suite logistique / published by https://github.com/dacr/code-examples-manager #d39c9323-49f4-46ec-a7a2-f81d5fdf0893/b1cbc7bc2fa30e9641aaa280f4a6b57d9518a3f1

math-logistic-map-1.sc

// summary : the logistic map / La suite logistique
// keywords : math, logistic-map, fractal, chaos, breeze
// 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 : d39c9323-49f4-46ec-a7a2-f81d5fdf0893
// 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._

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

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

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

val points = {
  LazyList
    .iterate(0d)(_ + 0.001d)
    .takeWhile(_ <= 1.0d)
    .map(x => x->logMap(x, 1.5))
}
val (xs, ys) =  points.unzip

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

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

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


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

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


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