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Design of a fractal generator for on-the-fly generation of textures for Mali GPU
Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Electronics and Telecommunications.
2011 (English)MasteroppgaveStudent thesis
Abstract [en]

The Mandelbrot set, shown on the front page of this report, is perhaps the most well-known example of a fractal. Fractals is a certain family of shapes with a very distinctive, interesting shape. The term was coined by Benoit B. Mandelbrot, for whom the Mandelbrot set is named after. The Mandelbrot set and other fractals are traditionally used for aesthetic purposes, such as in art, clothing, computer games, etc. However, there are also several practical applications for fractals, such as image compression. The Mandelbrot set is infinitely complex, making it desirable to generate images of arbitrary sections of the set. Several software programs that generate such images exists, but due to the computationally expensive nature of this task, these implementations are typically very slow, even on modern computers. However, the problem can be shown to be highly parallelizable, suggesting that a hardware implementation of such as generator should be able to generate smooth real-time zoom animations, unlike existing software implementations. A hardware fractal generator for the Mandelbrot set has been designed and implemented in Verilog-2001. The design is very scalable, having a parameter specifying the number of fractal point generators (cores) the synthesis tool should implement. Furthermore, it is designed so that the floating point units in the cores are utilized nearly 100% of the time under normal operation. The design was tested on a Xilinx Virtex-6 FPGA with up to 16 cores, and it was shown that the design was faster than a reference software solution running on a desktop computer when the number of cores was set to 2 or more. Additionally, a simplified Mandelbrot set algorithm is proposed and studied experimentally. In the simplified algorithm, the break condition in the algorithm loop is (|z_re| > 2) || (|z_im| > 2) as opposed to the standard |z| > 2. The images produced using the simplified algorithm was judged to be nearly indistinguishable from those produced with the standard algorithm, and therefore preferred as it is easier to implement. Finally some future work is proposed. The integration of the fractal generator with the Mali-400 GPU originally planned as part of this thesis is left as future work. It is also suggested to consider designing a custom fixed-point format for use internally in the fractal generator, as the standard binary32 floating-point format (FP32) is shown to be badly suited for this application.

Place, publisher, year, edition, pages
Institutt for elektronikk og telekommunikasjon , 2011. , 80 p.
Keyword [no]
ntnudaim:6176, MTEL elektronikk, Design av digitale systemer
URN: urn:nbn:no:ntnu:diva-13697Local ID: ntnudaim:6176OAI: diva2:441764
Available from: 2011-09-19 Created: 2011-09-19

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