visualizing the mandelbrot set

Parallel Mandelbrot Set Generation

For this project, we built a high-performance Mandelbrot set generator and visualization pipeline using Serial C++, OpenMP, and UPC++, and evaluated our implementations on Perlmutter, a DOE supercomputer. The goal was to explore how different shared-memory and PGAS programming models handle an “embarrassingly parallel” computation—pixel-wise iteration of the Mandelbrot recurrence—and a more coordination-heavy stage: histogram coloring.

Our pipeline consists of two major components:

• Escape-time computation: For every pixel in the output image, we compute how many iterations of ( z \leftarrow z^2 + c ) are required before the magnitude exceeds 2. This stage parallelizes perfectly, since each pixel is fully independent.
• Histogram coloring: A multi-pass algorithm that builds a global histogram of iteration counts, prefixes it, and maps each pixel’s iteration depth to a normalized hue. Unlike escape-time computation, histogram coloring requires aggregation across the full image, making parallelization significantly less trivial.

We implemented and compared three variants:

• Serial C++: A baseline implementation of the escape-time algorithm and histogram coloring.
• OpenMP: Multithreaded parallelization of both the escape-time loop and the histogram passes. The embarrassingly-parallel first phase scales extremely well, while global reductions in histogram coloring introduce some synchronization cost.
• UPC++: A distributed PGAS version that partitions work across ranks and uses futures, reductions, and RPCs to aggregate histogram data. Despite communication overhead, UPC++ achieves the fastest runtimes overall, though it does not scale strongly with additional nodes due to global synchronization requirements.

Across all image sizes, OpenMP beats the serial version by up to 5×, while UPC++ delivers the strongest absolute performance. The project highlights the trade-offs between shared-memory vs. PGAS programming models, especially when global reductions limit scalability.

Source Code:: https://github.com/evanmwilliams/mandelbrot