Problem Statement

Create and display a dragon curve fractal. (You may either display the curve directly or write it to an image file.)

Here are some brief notes the algorithms used and how they might suit various languages. This always has F at even positions and S at odd. Eg. after 3 levels F_S_F_S_F_S_F_S. The +/- turns in between bend to the left or right the same as the "successive approximation" method above. Read more at for instance Joel Castellanos' L-system page. Variations are possible if you have only a single symbol for line draw, for example the Icon and Unicon and Xfractint code. The angles can also be broken into 45-degree parts to keep the expansion in a single direction rather than the endpoint rotating around. The string rewrites can be done recursively without building the whole string, just follow its instructions at the target level. See for example C by IFS Drawing code. The effect is the same as "recursive with parameter" above but can draw other curves defined by L-systems.

Let's start with the solution:

open System.Windows
open System.Windows.Media

let m = Matrix(0.0, 0.5, -0.5, 0.0, 0.0, 0.0)

let step segs =
  seq { for a: Point, b: Point in segs do
          let x = a + 0.5 * (b - a) + (b - a) * m
          yield! [a, x; b, x] }

let rec nest n f x =
  if n=0 then x else nest (n-1) f (f x)

[<System.STAThread>]
do
  let path = Shapes.Path(Stroke=Brushes.Black, StrokeThickness=0.001)
  path.Data <-
    PathGeometry
      [ for a, b in nest 13 step (seq [Point(0.0, 0.0), Point(1.0, 0.0)]) ->
          PathFigure(a, [(LineSegment(b, true) :> PathSegment)], false) ]
  (Application()).Run(Window(Content=Controls.Viewbox(Child=path))) |> ignore