Design of a fractal generator for on-the-fly generation of textures for Mali GPU
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
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
Place, publisher, year, edition, pages
Institutt for elektronikk og telekommunikasjon , 2011. , 80 p.
ntnudaim:6176, MTEL elektronikk, Design av digitale systemer
IdentifiersURN: urn:nbn:no:ntnu:diva-13697Local ID: ntnudaim:6176OAI: oai:DiVA.org:ntnu-13697DiVA: diva2:441764
Kjeldsberg, Per Gunnar, FørsteamanuensisGjermundnes, Øystein