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Introduction | Mandelbrot Set | Image Characteristics | Parallel Algorithm Design | Partitioning | Agglomeration | Output Synchronization | Token-Passing | Polling | Performance Analysis | Conclusion | Bibliography | Slides

Parallel Fractal Image Generation

While the generation of fractal images like the Mandelbrot set seems to be of little more than academic value, there are other fractal objects that are of more relevance to the real world. Fractal models are used today to predict all kinds of systems that show chaotic behavior, such as the weather, population growth, or brain waves. We used the Mandelbrot set here because it is simple to generate, yet nicely demonstrates all characteristics of a fractal object. The program could be easily adapted to generate other fractal objects by changing the iteration formula.

More important, though, are the insights we gained into the methods for generating sequential data (like the lines of a fractal image) with a parallel algorithm: We found that a synchronization mechanism is needed in order to output the sequential data in-order, but we also realized that the parallel processing environment introduces a random factor even if the nodes are synchronized. Thus, we concluded that the only way to achieve in-order output is to have one node responsible for performing all the output. While this sounds like bad parallel design, we realized that the memory requirements of the master node can be kept low by chunking the output, and we observed that by using non-blocking communication, we can actually output data more efficiently than with a serial algorithm.

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