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Figure 6.11
Fractals made by LabVIEW. The white part of the graph is the region of convergence. |
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The experimental possibilities are endless. Once you obtain part of an image, you can recalculate on a magnified scale, or you can make variations in the program. In the original version, you're only investigating whether the starting values are close enough to the target value of 1 after a certain number of iterations. If they are, you'll mark the corresponding starting value with white, otherwise with black. You can also investigate how well you reach the target value of 1 after a fixed number of iterations, and you can mark this quantity with color. You'll end up with colorful topographic maps, which are attractive in their own right. You can usually do the programming modifications for this purpose in about a minute. |
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You can accomplish steps A through C, and the subsequent visualization, easily with LabVIEW. Note that you won't be able to use the Formula Node to implement the formula in Eq. 6.3a, since you can't treat complex numbers with this tool. You would need a formula node that operates with complex numbersa good idea for a future version of LabVIEW. Right now, you still have to convert Eq. 6.3a directly. |
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Iterative Function Systems |
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The previous program shows that you can produce fascinating images from relatively simple mathematical relationships. You can actually create |
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