2.0 KiB
Introduction
Calculating Mandelbrot using different ways. It tries to imitate the Mandelbrot calculation by Zom-B but be faster in doing so.
This project started by trying to reproduce this zoom sequence but in higher resolution:
https://en.wikipedia.org/wiki/File:Mandelbrot_sequence_new.gif
The generator used for this version is available here:
https://github.com/josch/mandelbrot_zomb
Overview
mandel:
- straight forward "long double" based mandelbrot
- this is obviously the fastest implementation but has limited precision
mandel_mpfr:
- mandelbrot using the arbitrary precision mpfr library
mandel_quad:
- mandelbrot using gcc libquad
mandel_dd:
- mandelbrot using custom double double math
- this is the fastest implementation given double double precision
mandel_dd_aa:
- with antialiasing
- it is more than three times faster than the Zom-B version (see below)
How to compile
Compile by running make.
How to execute
Each of the tools takes as arguments the width, height, coordinates and magnification. Output is in PPM format on standard output.
$ ./mandel_dd_aa 1920 1080 0.0 0.0 1.0 > out.ppm
You can compress the ppm by using:
$ convert out.ppm -format png out.png
And even compress it further by doing:
$ optipng -o4 -i0 out.png
$ advpng -z4 out.png
= How to generate zoom animation =
The shell script (with a small python helper) run.sh will generate and
execute a list of commands to create a zooming sequence of images.
You can create a video of the resulting sequence using:
$ avconv -i out_%05d.png out.mp4
Or a gif animation by using:
$ convert -delay 20 -loop 0 out_*.png out.gif
Benchmark
Benchmark against mandelbrot computation by Zom-B:
at zoom coordinates:
- x = -0.743643887037158704752191506114774
- y = 0.131825904205311970493132056385139
1 to 1e32 in 100 steps at 320x240 and no AA took
- mandel_dd 1:28 h
- mandel_zomb 2:45 h
1.0e17 at 1920x1080 with 5xAA took
- mandel_dd_aa 2:38 h
- mandel_zomb 8:40 h