"Hello World" is too simplistic, so whenever I learn a new language, I always implement a "Hello Mandelbrot" program. I realize there are probably implementations already out there (who doesn't like making fractals? :P), but figured I'd give it a try without hunting around first.

I'd really appreciate comments from everyone here as to the implementation and style. Do you see any room for improvements? Did I do something wrong? Or naive? Or good? :) Any constructive criticism is greatly appreciated.

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{\rtf1\ansi\ansicpg\lang1024\noproof65001\uc1 \deff0{\fonttbl{\f0\fnil\fcharset0\fprq1 Consolas;}}{\colortbl;??\red0\green0\blue255;\red255\green255\blue255;\red0\green128\blue0;\red0\green0\blue0;\red128\green128\blue128;\red128\green0\blue0;}??\fs20 \cf1 #light\par ??\cf3 // F# Mandelbrot Set Generator, 11.19.08, Matt Valerio, [link:thevalerios.net] ??\par ??\cf1 open\cf0 System.Drawing\par ??\cf1 open\cf0 System.Windows.Forms\par ??\cf1 open\cf0 Microsoft.FSharp.Math\par ??\par ??\cf1 let\cf0 ShowForm (f : Form) =\par ??\cf1 #if \cf0 INTERACTIVE\par ??\cf5 f.Show()\par ??\cf1 #endif\par ??#if \cf0 COMPILED\par ?? Application.Run(f)\par ??\cf1 #endif\cf0 \par ??\par ??\cf1 type\cf0 BitmapForm = \par ?? \cf1 inherit\cf0 Form \par ?? \cf1 val\cf0 \cf1 private\cf0 pictureBox : PictureBox\par ?? \cf1 new\cf0 (size : Size) \cf1 as\cf0 this = \par ?? \{\par ?? pictureBox = \cf1 new\cf0 PictureBox()\par ?? \} \cf1 then\par ??\cf0 this.SuspendLayout()\par ?? this.pictureBox.BorderStyle <- System.Windows.Forms.BorderStyle.Fixed3D\par ?? this.pictureBox.Name <- \cf6 "pictureBox"\par ??\cf0 this.pictureBox.Size <- size\par ?? this.pictureBox.Dock <- System.Windows.Forms.DockStyle.Fill\par ?? this.pictureBox.SizeMode <- PictureBoxSizeMode.StretchImage\par ?? this.Controls.Add(this.pictureBox) \par ?? this.Name <- \cf6 "BitmapForm"\cf0 \par ?? this.Size <- size \par ?? this.ResumeLayout() \par ?? \cf1 member\cf0 this.Bitmap \cf1 with\cf0 set value = this.pictureBox.Image <- value\par ??\par ??\cf1 let\cf0 SetBitmap (bitmap : #Image) (form : #BitmapForm) =\par ?? form.Bitmap <- bitmap\par ?? form\par ?? \par ??\cf1 let\cf0 MagnitudeSquared (c : complex) = c.r * c.r + c.i * c.i\par ??\par ??\cf1 type\cf0 Extents<'a> = \{ Xmin : 'a; Xmax : 'a; Ymin : 'a; Ymax : 'a \} \cf1 with\par ??\cf0 \cf1 override\cf0 t.ToString() = sprintf \cf6 "(%A,%A)-(%A,%A)"\cf0 t.Xmin t.Ymin t.Xmax t.Ymax\par ??\par ??\cf1 let\cf0 \cf1 inline\cf0 interp y1 y2 x1 x2 x =\par ?? \cf1 let\cf0 ymax = max y1 y2\par ?? \cf1 let\cf0 ymin = min y1 y2\par ?? \cf1 let\cf0 xmax = max x1 x2\par ?? \cf1 let\cf0 xmin = min x1 x2\par ?? ((ymax-ymin)/(xmax-xmin))*(x-xmin)+ymin\par ??\par ??\cf1 let\cf0 MapX (size : Size) (extents : Extents<float>) x =\par ?? interp extents.Xmax extents.Xmin 0.0 (float size.Width) x\par ?? \par ??\cf1 let\cf0 MapY (size : Size) (extents : Extents<float>) y =\par ?? interp extents.Ymax extents.Ymin 0.0 (float size.Height) y \par ??\par ??\cf1 let\cf0 Mandelbrot (maxIter : int) (c : complex) =\par ?? \cf1 let\cf0 \cf1 rec\cf0 MandelbrotInner z iter =\par ?? \cf1 if\cf0 (iter = maxIter) || (z |> MagnitudeSquared >= 4.0) \cf1 then\cf0 iter \par ?? \cf1 else\par ??\cf0 MandelbrotInner (z*z+c) (iter+1) \par ?? MandelbrotInner c 0\par ??\par ??\cf1 let\cf0 colorMap = [(0, Color.Black); (3, Color.Red); (6, Color.Blue); (10, Color.Chartreuse); \par ?? (20, Color.Magenta); (50, Color.DarkTurquoise); (100, Color.White)]\par ??\par ??\cf1 let\cf0 PickColor (map : (int * Color) list) (n : int) = \par ?? \cf1 let\cf0 InterpolateColor i1 (c1:Color) i2 (c2:Color) = \par ?? \cf1 let\cf0 r = interp (int c1.R) (int c2.R) i1 i2 n\par ?? \cf1 let\cf0 g = interp (int c1.G) (int c2.G) i1 i2 n\par ?? \cf1 let\cf0 b = interp (int c1.B) (int c2.B) i1 i2 n\par ?? Color.FromArgb(r,g,b) \par ?? \cf1 let\cf0 \cf1 rec\cf0 PickColorInternal map =\par ?? \cf1 match\cf0 map \cf1 with\par ??\cf0 | [] \cf1 ->\cf0 Color.Black\par ?? | [(_,c)] \cf1 ->\cf0 c\par ?? | (i1,c1)::((i2,c2)::_ \cf1 as\cf0 t) \cf1 ->\cf0 \cf1 if\cf0 (i1 <= n) && (n <= i2) \cf1 then\cf0 \par ?? InterpolateColor i1 c1 i2 c2\par ?? \cf1 else\cf0 \par ?? PickColorInternal t\par ?? PickColorInternal map\par ?? \par ??\cf1 let\cf0 MakeMandelbrotBitmap (maxIter : int) (size : Size) (extents : Extents<float>) = \par ?? \cf1 let\cf0 b = \cf1 new\cf0 Bitmap(size.Width, size.Height, Imaging.PixelFormat.Format24bppRgb)\par ?? \cf1 for\cf0 w \cf1 in\cf0 [0 .. size.Width-1] \cf1 do\par ??\cf0 \cf1 for\cf0 h \cf1 in\cf0 [0 .. size.Height-1] \cf1 do\par ??\cf0 \cf1 let\cf0 x = MapX size extents (float w)\par ?? \cf1 let\cf0 y = MapY size extents (float h) \par ?? \cf1 let\cf0 c = Complex.Create (x,y)\par ?? b.SetPixel(w, h, c |> Mandelbrot maxIter |> PickColor colorMap)\par ?? b\par ?? \par ??\cf1 let\cf0 MakeForm size = \par ?? \cf1 let\cf0 f = \cf1 new\cf0 BitmapForm(size)\par ?? f.Text <- \cf6 "F# Mandelbrot"\cf0 \par ?? f\par ?? \par ??\cf1 let\cf0 maxIter = 100;\par ??\cf1 let\cf0 size = \cf1 new\cf0 Size(700,600) \par ??\cf1 let\cf0 extents = \{Xmin = -2.0; Xmax = 1.0; Ymin = -2.0; Ymax = 2.0\} \par ??\par ??MakeForm size\par ??|> SetBitmap (MakeMandelbrotBitmap maxIter size extents) \par ??|> ShowForm\par ??}

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#light

// F# Mandelbrot Set Generator, 11.19.08, Matt Valerio

open System.Drawing

open System.Windows.Forms

open Microsoft.FSharp.Math

let ShowForm (f : Form) =

#if INTERACTIVE

f.Show()

#endif

#if COMPILED

Application.Run(f)

#endif

type BitmapForm =

inherit Form

val private pictureBox : PictureBox

new (size : Size) as this =

{

pictureBox = new PictureBox()

} then

this.SuspendLayout()

this.pictureBox.BorderStyle <- System.Windows.Forms.BorderStyle.Fixed3D

this.pictureBox.Name <- "pictureBox"

this.pictureBox.Size <- size

this.pictureBox.Dock <- System.Windows.Forms.DockStyle.Fill

this.pictureBox.SizeMode <- PictureBoxSizeMode.StretchImage

this.Controls.Add(this.pictureBox)

this.Name <- "BitmapForm"

this.Size <- size

this.ResumeLayout()

member this.Bitmap with set value = this.pictureBox.Image <- value

let SetBitmap (bitmap : #Image) (form : #BitmapForm) =

form.Bitmap <- bitmap

form

let MagnitudeSquared (c : complex) = c.r * c.r + c.i * c.i

type Extents<'a> = { Xmin : 'a; Xmax : 'a; Ymin : 'a; Ymax : 'a } with

override t.ToString() = sprintf "(%A,%A)-(%A,%A)" t.Xmin t.Ymin t.Xmax t.Ymax

let inline interp y1 y2 x1 x2 x =

let ymax = max y1 y2

let ymin = min y1 y2

let xmax = max x1 x2

let xmin = min x1 x2

((ymax-ymin)/(xmax-xmin))*(x-xmin)+ymin

let MapX (size : Size) (extents : Extents<float>) x =

interp extents.Xmax extents.Xmin 0.0 (float size.Width) x

let MapY (size : Size) (extents : Extents<float>) y =

interp extents.Ymax extents.Ymin 0.0 (float size.Height) y

let Mandelbrot (maxIter : int) (c : complex) =

let rec MandelbrotInner z iter =

if (iter = maxIter) || (z |> MagnitudeSquared >= 4.0) then iter

else

MandelbrotInner (z*z+c) (iter+1)

MandelbrotInner c 0

let colorMap = [(0, Color.Black); (3, Color.Red); (6, Color.Blue); (10, Color.Chartreuse);

(20, Color.Magenta); (50, Color.DarkTurquoise); (100, Color.White)]

let PickColor (map : (int * Color) list) (n : int) =

let InterpolateColor i1 (c1:Color) i2 (c2:Color) =

let r = interp (int c1.R) (int c2.R) i1 i2 n

let g = interp (int c1.G) (int c2.G) i1 i2 n

let b = interp (int c1.B) (int c2.B) i1 i2 n

Color.FromArgb(r,g,b)

let rec PickColorInternal map =

match map with

| [] -> Color.Black

| [(_,c)] -> c

| (i1,c1)::((i2,c2)::_ as t) -> if (i1 <= n) && (n <= i2) then

InterpolateColor i1 c1 i2 c2

else

PickColorInternal t

PickColorInternal map

let MakeMandelbrotBitmap (maxIter : int) (size : Size) (extents : Extents<float>) =

let b = new Bitmap(size.Width, size.Height, Imaging.PixelFormat.Format24bppRgb)

for w in [0 .. size.Width-1] do

for h in [0 .. size.Height-1] do

let x = MapX size extents (float w)

let y = MapY size extents (float h)

let c = Complex.Create (x,y)

b.SetPixel(w, h, c |> Mandelbrot maxIter |> PickColor colorMap)

b

let MakeForm size =

let f = new BitmapForm(size)

f.Text <- "F# Mandelbrot"

f

let maxIter = 100;

let size = new Size(700,600)

let extents = {Xmin = -2.0; Xmax = 1.0; Ymin = -2.0; Ymax = 2.0}

MakeForm size

|> SetBitmap (MakeMandelbrotBitmap maxIter size extents)

|> ShowForm

I'm particularly fond of the color picking algorithm using a list of (int,Color) tuples as a "color map". This really illustrates the power of F# pattern matching.

Any comments? :)