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# Sierpinski triangle, WPF

Draws a Sierpinski triangle using WPF

 ``` 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 42: 43: 44: 45: 46: 47: 48: 49: 50: 51: 52: 53: 54: 55: 56: 57: 58: 59: 60: 61: 62: 63: 64: 65: 66: 67: ``` ``````// Requires reference to // PresentationCore, PresentationFramework, // System.Windows.Presentation, System.Xaml, WindowsBase open System open System.Windows open System.Windows.Media open System.Windows.Shapes open System.Windows.Controls type Point = { X:float; Y:float } type Triangle = { A:Point; B:Point; C:Point } let transform (p1, p2, p3) = let x1 = p1.X + 0.5 * (p2.X - p1.X) + 0.5 * (p3.X - p1.X) let y1 = p1.Y + 0.5 * (p2.Y - p1.Y) + 0.5 * (p3.Y - p1.Y) let x2 = p1.X + 1.0 * (p2.X - p1.X) + 0.5 * (p3.X - p1.X) let y2 = p1.Y + 1.0 * (p2.Y - p1.Y) + 0.5 * (p3.Y - p1.Y) let x3 = p1.X + 0.5 * (p2.X - p1.X) + 1.0 * (p3.X - p1.X) let y3 = p1.Y + 0.5 * (p2.Y - p1.Y) + 1.0 * (p3.Y - p1.Y) { A = { X = x1; Y = y1 }; B = { X = x2; Y = y2 }; C= { X = x3; Y = y3 }} let generateFrom triangle = seq { yield transform (triangle.A, triangle.B, triangle.C) yield transform (triangle.B, triangle.C, triangle.A) yield transform (triangle.C, triangle.A, triangle.B) } let nextGeneration triangles = Seq.collect generateFrom triangles let render (target:Canvas) (brush:Brush) triangle = let points = new PointCollection() points.Add(new System.Windows.Point(triangle.A.X, triangle.A.Y)) points.Add(new System.Windows.Point(triangle.B.X, triangle.B.Y)) points.Add(new System.Windows.Point(triangle.C.X, triangle.C.Y)) let polygon = new Polygon() polygon.Points <- points polygon.Fill <- brush target.Children.Add(polygon) |> ignore let win = new Window() let canvas = new Canvas() canvas.Background <- Brushes.White let brush = new SolidColorBrush(Colors.Black) brush.Opacity <- 1.0 let renderTriangle = render canvas brush let triangle = let p1 = { X = 190.0; Y = 170.0 } let p2 = { X = 410.0; Y = 210.0} let p3 = { X = 220.0; Y = 360.0} { A = p1; B = p2; C = p3 } let root = seq { yield triangle } let generations = Seq.unfold (fun state -> Some(state, (nextGeneration state))) root |> Seq.take 7 Seq.iter (fun gen -> Seq.iter renderTriangle gen) generations win.Content <- canvas win.Show() [] do let app = new Application() in app.Run() |> ignore ``````
namespace System
namespace System.Windows
namespace System.Media
type Point =
{X: float;
Y: float;}

Full name: Script.Point
Point.X: float
Multiple items
val float : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float

--------------------
type float = Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>
Point.Y: float
type Triangle =
{A: Point;
B: Point;
C: Point;}

Full name: Script.Triangle
Triangle.A: Point
Triangle.B: Point
Triangle.C: Point
val transform : p1:Point * p2:Point * p3:Point -> Triangle

Full name: Script.transform
val p1 : Point
val p2 : Point
val p3 : Point
val x1 : float
val y1 : float
val x2 : float
val y2 : float
val x3 : float
val y3 : float
val generateFrom : triangle:Triangle -> seq<Triangle>

Full name: Script.generateFrom
val triangle : Triangle
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val seq : sequence:seq<'T> -> seq<'T>

Full name: Microsoft.FSharp.Core.Operators.seq

--------------------
type seq<'T> = Collections.Generic.IEnumerable<'T>

Full name: Microsoft.FSharp.Collections.seq<_>
val nextGeneration : triangles:seq<Triangle> -> seq<Triangle>

Full name: Script.nextGeneration
val triangles : seq<Triangle>
module Seq

from Microsoft.FSharp.Collections
val collect : mapping:('T -> #seq<'U>) -> source:seq<'T> -> seq<'U>

Full name: Microsoft.FSharp.Collections.Seq.collect
val render : target:'a -> brush:'b -> triangle:'c -> unit

Full name: Script.render
val target : 'a
val brush : 'b
val triangle : 'c
val points : obj
val polygon : obj
val ignore : value:'T -> unit

Full name: Microsoft.FSharp.Core.Operators.ignore
val win : obj

Full name: Script.win
val canvas : obj

Full name: Script.canvas
val brush : obj

Full name: Script.brush
val renderTriangle : (Triangle -> unit)

Full name: Script.renderTriangle
val triangle : Triangle

Full name: Script.triangle
val root : seq<Triangle>

Full name: Script.root
val generations : seq<seq<Triangle>>

Full name: Script.generations
val unfold : generator:('State -> ('T * 'State) option) -> state:'State -> seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.unfold
val state : seq<Triangle>
union case Option.Some: Value: 'T -> Option<'T>
val take : count:int -> source:seq<'T> -> seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.take
val iter : action:('T -> unit) -> source:seq<'T> -> unit

Full name: Microsoft.FSharp.Collections.Seq.iter
val gen : seq<Triangle>
Multiple items