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So, the application must map the points in the bitmap plane to points in the complex plane so that you can tell whether a pixel is part of the complex plane. It is easy to perform this mapping in just a few lines of F# code: #light open Microsoft.FSharp.Math open Microsoft.FSharp.Math.Notation let scalingFactor = 1.0 / 200.0 let offset = -1.0 let mapPlane (x, y) = let fx = ((float x) * scalingFactor) + offset let fy = ((float y) * scalingFactor) + offset complex fx fy Once this is complete, you just need to cycle through all the points in your bitmap plane, mapping them to the complex plane using the mapPlane function. Then you need to test whether the complex number is in the Mandelbrot set using the function isInMandelbrotSet. Then you set the color of the pixel. The full program is as follows: #light open System open System.Drawing open System.Windows.Forms open Microsoft.FSharp.Math open Microsoft.FSharp.Math.Notation let cMax = complex 1.0 1.0 let cMin = complex -1.0 -1.0 let iterations = 18 let isInMandelbrotSet c0 = let rec check n c = (n = iterations) or (cMin < c) && (c < cMax) && check (n + 1) ((c * c) + c0) check 0 c0 let scalingFactor = 1.0 / 200.0 let offset = -1.0 let mapPlane (x, y) = let fx = ((float x) * scalingFactor) + offset let fy = ((float y) * scalingFactor) + offset complex fx fy

A QMultiHash is a hash for assigning several values to each key. You insert values using the insert( key, value ) method. Although the keys and values are available through the same methods as when using the QHash, it is common to use the values( key ) method to get a list of values associated with a given key.

Livingston: 37signals wasn t begun as a startup, correct Heinemeier Hansson: 37signals was founded by Jason Fried as a web design

shop in 1999. It transitioned from a consulting company to a product company with the creation of Basecamp. I m part of the 37signals 2.0 management team.

QMap and QMultiMap are used in exactly the same way as QHash and QMultiMap. The differences are described in the introduction to the associative containers section.

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Heinemeier Hansson: It was not an overnight transition. While we were developing Basecamp, 37signals had a lot of client work, so we couldn t dedicate more than about a third of our time to it. It wasn t a client project; it was something that we created as an internal tool to help us manage our client work. Livingston: Take me back to the time of the Basecamp launch and the transition.

let form = let image = new Bitmap(400, 400) for x = 0 to image.Width - 1 do for y = 0 to image.Height - 1 do let isMember = isInMandelbrotSet ( mapPlane (x, y) ) if isMember then image.SetPixel(x,y, Color.Black) let temp = new Form() in temp.Paint.Add(fun e -> e.Graphics.DrawImage(image, 0, 0)) temp [<STAThread>] do Application.Run(form) This program produces the image of the Mandelbrot set in Figure 7-2.

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