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A complex number belongs to the Mandelbrot set if zn converges for n. You can test each number c in the complex plane and decide whether the number belongs to the Mandelbrot set. Since it s not practical to perform an infinite computation to test each number of the complex plane, there is an approximation of the test based on a theorem that if the distance of zi from the origin passes 2, then the sequence will diverge and the corresponding z0 will not belong to the set. The code to compute membership of the Mandelbrot set is as follows: open Microsoft.FSharp.Math let sqrMod (x:complex) = x.r * x.r + x.i * x.i let rec mandel maxit (z:Complex) (c: Complex) count = if (sqrMod(z) < 4.0) && (count < maxit) then mandel maxit ((z * z) + c) c (count + 1) else count A simple visual representation of the Mandelbrot set is to simply color all the points belonging to the set. In this way, you obtain the black portion of Figure 11-7. How can you obtain the richness of color The trick is to color points depending on how fast the sequence reaches the distance of 2 from the origin. You use 250 colors and map the [0, maxit] interval to the [0, 250] discrete color interval.

UndoChanges() is called on all child objects in the collection so that they can restore their individual states After a child object s state has been restored, the child object s edit level is checked to see when it was added to the collection If the collection s new edit level is less than the edit level when the child object was added, then it is a new child object that now must be discarded // if item is below its point of addition, remove If (childEditLevelAdded > _editLevel) RemoveAt(index); The same process occurs for the objects in DeletedList again, UndoChanges() is called on each child object Then there s a check to see if the child object was a newly added object that can now be discarded: if (childEditLevelAdded > _editLevel) { // if item is below its point of addition, remove DeletedList.

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Likewise, you can watch the title of the form change by running the following code in F# Interactive: form.Text <- "Programming is Fun!" Setting properties dynamically is frequently to configure objects, such as forms, that support many potential configuration parameters that evolve over time. The object created here was bound to the name form. Binding this value to a new name doesn t create a new form; rather, two different handles now refer to the same object (they are said to alias the same object). For example, the following code sets the title of the same form, despite it being accessed via a different name: let form2 = form form2.Text <- "F# Forms are Fun"

RemoveAt(index); } A bit more work is required when dealing with the deleted child objects It is possible that the undo operation needs to undelete an object Remember that the IsDeleted flag is automatically maintained by UndoChanges(), so it is possible that the child object is no longer marked for deletion In such a case, the object must be moved back into the active list: else { // if item is no longer deleted move back to main list if (!childIsDeleted) UnDeleteChild(child); } At the end of the process, the collection object and all its child objects will be in the state they were when CopyState() was last called Any changes, additions, or deletions will have been undone..

Now let s look at a practical example of creating markup on the fly. In the previous chapter, we made a lot of improvements to the image gallery script. The JavaScript is unobtrusive and degrades gracefully. We also made some accessibility enhancements. There s still something that bothers me though. Take a look at the markup in gallery.html: <!DOCTYPE html> <html lang="en"> <head> <meta charset="utf-8" /> <title>Image Gallery</title> <link rel="stylesheet" href="styles/layout.css" media="screen" /> </head> <body> <h1>Snapshots</h1> <ul id="imagegallery"> <li> <a href="images/fireworks.jpg" title="A fireworks display"> <img src="images/thumbnail_fireworks.jpg" alt="Fireworks" /> </a> </li> <li> <a href="images/coffee.jpg" title="A cup of black coffee" > <img src="images/thumbnail_coffee.jpg" alt="Coffee" /> </a> </li> <li> <a href="images/rose.jpg" title="A red, red rose"> <img src="images/thumbnail_rose.jpg" alt="Rose" /> </a> </li> <li> <a href="images/bigben.jpg" title="The famous clock"> <img src="images/thumbnail_bigben.jpg" alt="Big Ben" /> </a> </li> </ul> <img id="placeholder" src="images/placeholder.gif" alt="my image gallery" /> <p id="description">Choose an image.</p> <script src="scripts/showPic.js"></script> </body> </html> The XHTML file contains an image and a paragraph solely for the use of the showPic script. It s preferable to separate the structure and the behavior entirely. If these elements exist just to be manipulated by DOM methods, then it makes sense to also create them using DOM methods. The first step is straightforward: remove those elements from the gallery.html document. For the next step, let s create those elements using JavaScript.

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