The Rolymo, multi-threaded, fractal generator efficiently produces stunning image plots of the Mandelbrot set (and other fractals). User control ranges from leaving all settings on their defaults to selecting colour-mapping choices, dimensions, and iteration maximums, amongst other command-line arguments.
The Mandelbrot set is the set of complex numbers c for which the function f(x) = z^2 + c does not diverge when iterated from z = 0.
Similarly, Julia sets are the sets of complex numbers z for which the function f(x) = z^2 + c does not diverge when iterated from c = constant (to be specified by the user).
- Multiple-precision floating-point support
- Julia set plotting
- Output to the NetPBM family of image files -
.pbm,.pgm, and.ppm - ASCII art output to the terminal
The following dependencies must be installed to system if compiling with make mp:
- The GNU Multiple Precision Arithmetic Library (GMP), version 5.0.0 or later
- The GNU Multiple Precision Floating-Point Reliable Library (MPFR), version 3.0.0 or later
- The GNU Multiple Precision Complex Library (MPC)
From the program's root directory, make compiles the mandelbrot binary. To enable multiple-precision support, the aforementioned GNU multiple-precision arithmetic libraries must be install to system. The package is then built with make mp.
Run the program with ./mandelbrot. By default, without any command-line arguments, the program outputs var/mandelbrot.pnm - a 550 px by 500 px, 24-bit colour Mandelbrot set plot.
Help can be provided with ./mandelbrot --help.
Usage: ./mandelbrot [OPTION]...
./mandelbrot --help
A Mandelbrot and Julia set plotter.
Mandatory arguments to long options are mandatory for short options too.
Output parameters:
-c SCHEME, --colour=SCHEME Specify colour palette to use (default = Rainbow)
SCHEME may be:
0 = ASCII
1 = Black and white
2 = White and black
3 = Greyscale
4 = Rainbow
5 = Vibrant rainbow
6 = Red and white
7 = Fire
8 = Red hot
9 = Matrix
Black and white schemes are 1-bit
Greyscale schemes are 8-bit
Coloured schemes are full 24-bit
-o FILE Output file name (default = 'var/mandelbrot.pnm')
-r WIDTH, --width=WIDTH The width of the image file in pixels
If using a 1-bit colour scheme, WIDTH must be a multiple of 8 to allow for
bit-width pixels
-s HEIGHT, --height=HEIGHT The height of the image file in pixels
-t Output to stdout (or, with -o, text file) using ASCII characters as shading
Distributed computing setup:
-g ADDR, --worker=ADDR Have computer work for a master at the respective IP address
-G COUNT, --master=COUNT Setup computer as a network master, expecting COUNT workers to connect
-p PORT Communicate over the given port (default = 7939)
Plot type:
-j CONST, --julia=CONST Plot Julia set with specified constant parameter
Plot parameters:
-i NMAX, --iterations=NMAX The maximum number of function iterations before a number is deemed to be within the set
A larger maximum leads to a preciser plot but increases computation time
-m MIN, --min=MIN Minimum value to plot
-M MAX, --max=MAX Maximum value to plot
Default parameters (standard-precision):
Julia Set:
MIN = -2 + -2i
MAX = 2 + 2i
ITERATIONS = 100
WIDTH = 800
HEIGHT = 800
Mandelbrot set:
MIN = -2 + -1.25i
MAX = 0.75 + 1.25i
ITERATIONS = 100
WIDTH = 550
HEIGHT = 500
Optimisation:
-A, --multiple Enable multiple-precision mode (default = 128 bits significand)
MPFR floating-points will be used for calculations
The precision is better than '-X', but will be considerably slower
--precision=PREC Specify number of bits to use for the MPFR significand (default = 128 bits)
-T COUNT, --threads=COUNT Use COUNT number of processing threads (default = processor count)
-X, --extended Extend precision (64 bits, compared to standard-precision 53 bits)
The extended floating-point type will be used for calculations
This will increase precision at high zoom but may be slower
-z MEM, --memory=MEM Limit memory usage to MEM megabytes (default = 80% of free RAM)
Log settings:
--log Output log to file
Without '--log-file', file defaults to var/mandelbrot.log
Option may be used with '-v'
--log-file=FILE Specify filepath of log file (default = var/mandelbrot.log)
Option may be used with '-v'
-l LEVEL, --log-level=LEVEL Only log messages more severe than LEVEL (default = INFO)
LEVEL may be:
0 = NONE (log nothing)
1 = FATAL
2 = ERROR
3 = WARNING
4 = INFO
5 = DEBUG
-v, --verbose Redirect log to stderr
Miscellaneous:
--help Display this help message and exit
Examples:
./mandelbrot
./mandelbrot -j "0.1 - 0.2e-2i" -o "juliaset.pnm"
./mandelbrot -t
./mandelbrot -i 200 --width=5500 --height=5000 --colour=9
./mandelbrot -g 192.168.1.31 -p 1337
./mandelbrot -G 5 -p 1337 -A --precision=128 -r 33000 -s 30000 -x -1.749957,300
Given that a single run of the program may compute trillions of complex operations, optimisation is an important part of the project. The code has been refactored to improve speed, however readability, maintainability, and modularity must still be prioritised.
There are two command-line arguments to increase/decrease the amount of resources used by Rolymo:
| Argument | Description |
|---|---|
-T/--threads |
Specify the number of multi-processing threads to be used. Generally, Rolymo utilises 100% of a CPU core, so for maximum performance it is recommended (and default) to set at the number of processing cores on your machine. |
-z/--memory |
Use below a specified maximum of memory for the working image array allocation. This value is, by default, specified in MB, but can be given with other magnitude prexfixes (i.e. kB, GB, etc). As a default, Rolymo will use a maximum of 80% of the free physical memory on offer. This prevents usage of slow, swap memory and also gives space for other, regular programs, and the OS, to run comfortably. |
GCC flags (in Makefile located in the $COPT and $LDOPT variables) are used to heavily optimise the output code with (mainly) the sacrifice of some floating point rounding precision. The following flags are set by default:
Compiler: -flto -Ofast -march=native
Linker: -flto -Ofast
| Flag | Description |
|---|---|
-flto |
Perform link-time optimisation |
-Ofast |
Enable all -O3 optimisations along with, most impactful for this program, -ffast-math |
-march=native |
Optimise for the user's machine |