MANDELZOOM

mandelzoom.fsx

open System.Drawing
open System.Numerics
open System.Windows.Forms

// Absolute Square function for complex numbers
type System.Numerics.Complex with
  member this.Length = this.Real * this.Real + this.Imaginary * this.Imaginary

// PART ONE: select any square region of the complex plane to be examined.

let title = "Mandelbrot Set"
// Number of rows and columns in the pic array 
let rows = 400
let columns = 400
// The coordinates of the southwest corner 
let acorner = -2.0 // real part
let bcorner = -1.25 // imaginary part
// Length of each side
let side = 2.5 

// PART TWO. adjusts the array pic to match the square of interest 

// Distance within the square (determined by the southwest corner and length of each side)
// between each adjacent pixels
let gap = side / float (columns)

let maxIterations = 1000

// PART THREE: the heart of the program. Here a search is made for the
// complex numbers c in the Mandelbrot set, and colors are assigned to the // numbers that are, in a special sense, nearby.

// PART THREE: step 1

// Transforms pixel positions into corresponding complex numbers
let transformPixelPositionToComplexNumber x y = 
  new Complex((float) x * gap + acorner, (float) y * gap - (bcorner + side))
// PART THREE: step 3

// A point in the complex plane c belong to the Mandelbrot Set 
// if the sequence Z(n+1) = Z(n)^2 + c stays bounded. 
// By definition Z(0) = 0
let rec MandelbrotSeq (z : Complex) c iterationNumber = 
  if (z.Length > 4.0) then iterationNumber
  else if (iterationNumber = maxIterations) then maxIterations
  else 
    let nextValue = z * z + c
    MandelbrotSeq nextValue c (iterationNumber + 1)

// PART THREE: step 4
// Map number of iterations to convergence to a color
let colorMap n maxIterations = 
  match n with
  | n when (n < maxIterations && n > 0) -> mandelbrotColorSchemeWikipedia.[n % 16]
  | _ -> Color.FromArgb(0, 0, 0)

/// Returns whether or not the given complex number is in the set to the
/// best possible accuracy we can get from the given number of iterations
let inMandelbrotSet num = 
  let res = MandelbrotSeq Complex.Zero num 0 
  colorMap res maxIterations

/// Sets up the canvas and generates the set on it
let generateBitMapWithMandelbrotSet (rows : int) (columns : int) = 
  let bmp = new Bitmap(rows, columns)
  for m in 0..(rows - 1) do
    for n in 0..(columns - 1) do
      let c = transformPixelPositionToComplexNumber m n
      bmp.SetPixel(m, n, (inMandelbrotSet c))
  bmp