Complex Fractal

Final Project for Moravian University CSCI 392: High Performance Computing.

Program

Each version of the complex fractal generator has its own dependencies. The serial version should compile on all systems that support complex arithmetic.

The shared version requires a compiler with OpenMP support. The CUDA version requires the nvcc compiler and thrust libraries. For better performance on your machine, change the flag -arch=sm_86 in NVCFLAGS in the makefile to your gpu's compute capability.

Building

To build all versions simply run

make

If you wish to compile with additional floating point precision, add -DEXTENDED_PRECISION to CPPFLAGS in the makefile.

NOTE: extended precision is NOT supported in the CUDA version.

Running

Any version of the program can be used to generate a visualizer compatible .grid file. All versions of the program support the same command line arguments.

The performance flag outputs information in the format of:

<PROGRAM>,<FRACTAL>,<DEGREE>,<CONSTANT_REAL>,<CONSTANT_IMAG>,<RADIUS>,<MAX_ITERATIONS>,<HORIZONTAL_SAMPLES>,<VERTICAL_SAMPLES>,<LOWER_REAL>,<LOWER_IMAG>,<UPPER_REAL>,<UPPER_IMAG>,<RUNTIME>

Note that the runtime is an average runtime from multiple runs. The number of runs can be adjusted directly in src/fractals.c in NUM_RUNS or set in CPPFLAGS by adding -DNUM_RUNS=N.

Usage: <PROGRAM> [-v] [-i iterations] [-x x_res] [-y y_res] [-z magnification] [-d degree] [-c constant] [-r radius] [-l lower_left] [-u upper_right] [-o output_grid] -f fractal
Options:
  -i, --iterations <value>        the number of iterations (default: 100)
  -x, --x-res <value>             the horizontal resolution (default: terminal width)
  -y, --y-res <value>             the vertical resolution (default: terminal height)
  -l, --lower-left <value>        Set the lower left corner of the fractal area (default: -2-2i)
  -u, --upper-right <value>       Set the upper right corner of the fractal area (default: 2+2i)
  -z, --magnification <value>     Set the magnification factor (default: 1)
  -d, --degree <value>            Set the degree for fractals that use it (default: 2)
  -c, --constant <value>          Set the constant for fractals that use it (default: 0+0i)
  -r, --radius <value>            Set the radius for fractals that use it (default: 2)
  -o, --output <filename>         the output filename (default: fractal.grid)
  -f, --fractal <type>            the fractal type (default: mandelbrot)
      supported fractals: mandelbrot, tricorn, multibrot, multicorn, burning_ship, julia
  -p, --performance               print performance info
  -v, --verbose                   verbose output
  -h, --help                      prints this help message

Examples

build/shared-fractals -x2000 -y2000 -z 2 -o burning_ship.grid -f burning_ship

Generates a 2000x2000 burning ship fractal grid zoomed in 2x and saves it to burning_ship.grid

build/serial-fractals -x500 -y500 -i35 -c 0.285+0.01i -r 20 -o julia.grid -f julia

Generates a 500x500 julia fractal grid which has a maximum of 30 iterations for $c = 0.285 + 0.01i$ and a radius of 20 to julia.grid.

Visualizations

The program fractal-render renders .grid files into txt, png's, and animated gifs. The renderer program requires LibGD to be installed.

Usage: fractal-render -i input.grid [-r renderer] [-o output.ext]
Options:
  -i, --input <input grid>        the grid to be rendered, if the file name is '-' reads from stdin
  -r, --renderer <renderer>       the renderer to use, defaults to the text renderer
      renderers:   txt, png, gif (TODO, with additional features)
  -d, --delay <delay>             the delay between animation frames in 1/100 s
  -o, --output <output file>      the file to output the result of rendering, if not given defaults to fractal.out.
  -v, --verbose                   verbose output
  -h, --help                      prints this help and exits

Building

To build simply run

make

Examples

Some example visualizations are provided in examples, they can be regenerated with

make examples/julia.png
make examples/multicorn.gif

Presentation

Building the presentation requires a pandoc installation.

To build the presentation run

make presentation

Resources

• LibreText on The Mandelbrot Set
• LibreText on Julia Sets
• Various Algorithms for Plotting the Mandelbrot Set
• Pseudocode for Julia Set
• Another HPC implemenation of Mandelbrot set rendering
• Blog Post on CUDA Mandelbrot Set

Contributors

• JP Appel