Phillip Trelford's Array

A quick search for “F# Mandelbrot” gave an article written by Luke Hoban back in 2007, that draws a Fractal to the console.

Time for a makeover with a sprinkling of Active patterns, Reactive programming, Parallel execution and Silverlight.

Simply draw a rectangle onto the Fractal to zoom in:

“Complex” maths using F# PowerPack library and an Active Pattern:

open Microsoft.FSharp.Math

let maxIteration = 255
let modSquared (c : Complex) = 
    c.RealPart * c.RealPart + c.ImaginaryPart * c.ImaginaryPart
    
let (|Escaped|DidNotEscape|) c =
    let rec compute z iterations =
        if(modSquared z >= 4.0) 
            then Escaped iterations
        elif iterations = maxIteration
            then DidNotEscape
        else compute ((z * z) + c) (iterations + 1)
    compute c 0

Tomas Petricek’s original Reactive Rectangles sample to select the zoom area:

let rec waiting() = async {
  let! md = Async.AwaitObservable(main.MouseLeftButtonDown)
  let rc = new Canvas(Background = transparentGray)
  main.Children.Add(rc) 
  do! drawing(rc, md.GetPosition(main)) }

and drawing(rc:Canvas, pos) = async {
  let! evt = Async.AwaitObservable(main.MouseLeftButtonUp, main.MouseMove)
  match evt with
  | Choice1Of2(up) -> 
      rc.Background <- SolidColorBrush(colorSelect.CurrentColor)
      do! waiting() 
  | Choice2Of2(move) ->
      moveControl rc pos (move.GetPosition(main))
      do! drawing(rc, pos) }

do waiting() |> Async.StartImmediate

Parallel rendering over up to 4 cores using Async workflows:

do! [0..3] 
    |> List.map (fun y -> async {
        render points (y,(height/4),4) buffer
    })
    |> Async.Parallel

Resources:

• Luke Hoban’s Blog – F#: http://blogs.msdn.com/b/lukeh/archive/2007/11/14/f.aspx
• Tomas Petricek – “Recording and samples from my Reactive F# talk”: http://tomasp.net/blog/reactive-talk.aspx
• MSDN - Async.Parallel<'T> Method (F#): http://msdn.microsoft.com/en-us/library/ee353779.aspx
• Cameron Taggart - Create F# Silverlight Apps from Visual Studio 2010 Shell: http://blog.ctaggart.com/2010/11/create-f-silverlight-apps-from-visual.html

Source: FractalZoom.zip (3.89 kb)