JuliaMandelbrot分形图形逃逸时间算法的并行实现论文.docVIP

Julia/Mandelbrot分形图形逃逸时间算法的并行实现 摘 要 利用并行计算来提高计算能力已经成为解决大数据量计算问题的切实可行的技术。通过对分形图形中最为经典的Julia分形集和Mandelbrot分形集的串并行算法转化，提高了分形集的生成速度。 首先，对实验的开发环境及工具进行了简单地介绍；其次，了Julia / Mandelbrot分形集的逃逸时间算法。再次，分析该算法的并行性，得出数据分解方案和该算法的并行实现方案，然后讨论了如何计算该并行程序的执行时间及如何将分形图像数据写进位图文件的方法，在并行设计的最后阶段，简要介绍了图形界面的开发。最后，在集群环境下，编译、运行该并行程序。通过记录并行程序的执行时间和CPU个数，计算并行程序的加速比，看到了并行计算的优越性。 实验验证了并行程序和串行程序在相同的输入情况下，执行结果是相同的，但并行程序每次的执行时间是不完全相同的，以及随着CPU个数的增加，并行计算加速比的增长幅度在不断减缓。该实验较好地达到了预定的目标。 关键词　并行计算；Julia分形集和Mandelbrot分形集；逃逸时间算法 Abstract Using Parallel Computing to solve problems with great data quantity which greatly improves the capability of computing has become a practical and feasible technology. Transforming the most classical Julia Fractal Set and Mandelbrot Fractal Set from sequential to parallel improves the speed of its generating. The article first gives a general description to the experiment’ s development environment as well as development tool ;then introducing the Escape time algorithm of the Julia and Mandelbrot Set .In the following, it analyzes the parallelism of this algorithm ,obtains the data decomposition and realizes the parallel algorithm .Next ,it discusses how to calculate the execution time of this parallel program and how to write the fractal image data into a BMP format file .In the last stage of this design, it briefly introduces the development of the graphical interface. Finally, under the environment of the Cluster, it compiles, executes the program. By recording the program’s execution time and the number of the CPU, it calculates the speed up and shows the superiority of parallel computing. The experiment proves that under the same input, the sequential and parallel program has the same result, but the execution time is not exactly the same every time, and with CPU number increasing, the speed up grows slowly.The experiment achieves the anticipative goal. Keywords Parallel Computing; Julia Fractal Set and Mandelbrot Fractal Set; Escape time algorithm 目 录 摘 要 I Abstract