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Introduction

This directory contains a parallel (non-naive) implementation of a Mandelbrot set generator in Python 3. This implementation demonstrates both a non-trivial use case for Pythons multiprocessing.Pool.map(), as well as a relatively straightforward implementation of a Mandelbrot set generator. For performance reasons, this implementation of the set generator is implemented iteratively, rather than recursively.

Usage

Run make demo for a quick demo.

usage: mandelbrot.py [-h] [--recurse_depth RECURSE_DEPTH]
                     [--resolution RESOLUTION] [--verbose] [--display]
                     [--output OUTPUT]

Simple parallel mandlebrot set visualization. Requires Python 3.3 or better.

optional arguments:
  -h, --help            show this help message and exit
  --recurse_depth RECURSE_DEPTH, -d RECURSE_DEPTH
                        Maximum recursion depth before returning from
                        mandlebrot calculation. (default: 128)
  --resolution RESOLUTION, -n RESOLUTION
                        Image resolution in [cols]x[rows] format. (default:
                        640x480)
  --verbose, -v         Display every P_c calculation and point mapping
  --display, -p         Use matplotlib to display the image in a GUI window as
                        soon as computation is finished.
  --output OUTPUT, -o OUTPUT
                        Specify an output file to save the result to.

Note that this program is not truly rigorous - as the recursion depth is necessarily finite, it is possible that some points marked as being members of the Mandelbrot set will be false-positives (in the case where a given number would diverge to infinity after some number of iterations greater than the recursion depth). To improve the accuracy of the program, simply use a higher recursion depth.

Performance

Test Machines

Machine Number CPU Cores / Threads RAM Number of NUMA Nodes Number of Sockets
1 i7-2640M @ 2.80GHz 2C/4T 12GB @ 1333MHz 1 1
2 2x E5520 @ 2.27GHz 8C/16T 96Gb @ ? MHz 2 2

Test Results

Machine Number Resolution Recursion Depth Threads used Elapsed Seconds
1 256x256 256 1 10.120744660000128
1 256x256 256 2 5.375709760000973
1 256x256 256 4 5.240381178999087
1 512x512 256 1 39.85520727000039
1 512x512 256 2 21.903679931001534
1 512x512 256 4 22.977132228999835
2 256x256 256 1 22.127644610009156
2 256x256 256 8 3.386901296908036
2 256x256 256 16 3.0181645220145583
2 512x512 256 1 88.4461338800611
2 512x512 256 8 13.539519277052023
2 512x512 256 16 12.352946505998261
2 1024x1024 256 16 49.16464102698956