A demonstration for exploring the Mandelbrot Set using Python. Similarly, CUDA and OpenCL solutions for comparison.
On GNU/Linux or UNIX derivative, refer to the OS specific instructions for CUDA installation. Depending on the CUDA version, GCC 13 or older is required and must be in your path before newer GCC releases.
On Windows, install Build Tools for Visual Studio 2019. Select only "Desktop Environment with C++" when installing. I tried version 16.11.25 from March 14, 2023, having no issues.
Open a shell with Miniforge activated. On Windows, launch "Anaconda Prompt (miniforge3)" from the Start Menu. Optionally, execute the vcvars64.bat command, including the quotes around it. It configures the VC build environment. The VC environment is required for installing pycuda and running the pyopencl and pycuda demonstrations.
"C:\Program Files (x86)\Microsoft Visual Studio\2019\BuildTools\VC\Auxiliary\Build\vcvars64.bat"
First, install Miniforge for your platform using the default options. Re-open your command shell to begin the installation. If you'd prefer that Conda's base environment not be activated on startup, run the following command when Conda is activated.
conda config --set auto_activate_base falseQuick installation using requirements file.
Note: Choose one Intel Math Kernel Library (MKL) or OpenBLAS support for NumPy.
# Create Conda environment.
conda env create -n mandel --file reqs_mkl.yml
conda env create -n mandel --file reqs_openblas.yml
# Activate the Conda environment.
conda activate mandel
# Prevent Conda from switching the BLAS library, choose same one.
conda config --env --add pinned_packages "blas=*=mkl"
conda config --env --add pinned_packages "blas=*=openblas"
# Pin the Numba version.
conda config --env --add pinned_packages "numba==0.61.2"
# Pin setuptools to suppress the pkg_resources deprecation warning.
conda config --env --add pinned_packages "setuptools==79.0.1"
# Continue to "Using vendor-supplied OpenCL drivers"Manual installation allowing specific Python/Numba versions.
Note: Choose one MKL or OpenBLAS support for NumPy.
# Create a Conda environment.
conda create -n mandel python=3.12 "blas=*=mkl"
conda create -n mandel python=3.12 "blas=*=openblas"
# Activate the Conda environment.
conda activate mandel
# Prevent Conda from switching the BLAS library, choose same one.
conda config --env --add pinned_packages "blas=*=mkl"
conda config --env --add pinned_packages "blas=*=openblas"
# Pin the Numba version.
conda config --env --add pinned_packages "numba==0.61.2"
# Pin setuptools to suppress the pkg_resources deprecation warning.
conda config --env --add pinned_packages "setuptools==79.0.1"
# Install Numba.
conda install numba
# The CUDA target built-in to Numba is deprecated, with further
# development moved to the NVIDIA numba-cuda package.
# Optionally, install the numba-cuda module.
conda install numba-cuda
# Install dependencies.
conda install appdirs platformdirs siphash24 tbb tbb-devel
conda install MarkupSafe mako pytools typing-extensions
# Install PyOpenCL from miniforge versus pip. This way, searching ICDs
# in <conda-root>/envs/<env-name>/etc/OpenCL/vendors/ is possible.
conda install pyopenclThe imaging library and library for drawing and handling keyboard events
have many dependencies. You can try conda install pillow pygame to
see the list. Optionally, answer n to exit the installation.
Alternately, install Pillow and Pygame via pip.
pip install pillow pygameUsing AMD graphics? Install the ROCm OpenCL Runtime via the OS package manager.
# Arch Linux, CachyOS
sudo pacman -S rocm-opencl-runtimeInstall a Conda Forge package for the OpenCL ICD loader to look
in /etc/OpenCL/vendors or copy the ICD files. Choose one.
# Install a package to include searching the `/etc` path
conda install ocl-icd-system
# Or copy the ICD file(s) to the Conda environment path
cp /etc/OpenCL/vendors/*.icd "$CONDA_PREFIX"/etc/OpenCL/vendors/A benefit using Intel's OpenCL CPU runtime is auto-vectorization.
conda install intel-opencl-rt # on x86-64 Linux or WindowsChoose conda or pip for the PyCUDA installation. The former requires
the least amount of effort. Simply install cuda-nvcc matching or older
than your display driver. The latter, pip installation, requires nvcc
in your path and have a supported GCC version.
# Choose one only, conda or pip.
# Do not install cuda-nvcc newer than your display driver.
conda install pycuda cuda-nvcc==12.9.* # running 575 driver
conda install pycuda cuda-nvcc==12.8.* # running 570 driver
conda install pycuda cuda-nvcc==12.6.* # running 560 driver
conda install pycuda cuda-nvcc==12.4.* # running 550 driver
conda install pycuda cuda-nvcc==12.2.* # running 535 driver
# Pin the CUDA version to prevent it from updating.
# Specify the same version used in the prior step.
conda config --env --add pinned_packages "cuda-nvcc==12.4.*"
# Alternatively, install pycuda via pip.
pip install pycuda # prefer system CUDA Toolkit installationIn the event pip failed, you may try manual installation on Unix platforms.
Adjust the path accordingly. Do this in the same Conda environment.
export CUDA_ROOT=/opt/cuda
export CUDA_INC_DIR=$CUDA_ROOT/include
export PATH=$CUDA_ROOT/bin:$PATH
# Set an environment to supported GCC path
export NVCC_PREPEND_FLAGS="-ccbin=/path/to/supported/gcc/bin"
# Another way is making symbolic links to supported compilers
# and have the CUDA bin path searched first in your PATH env
sudo ln -sf /usr/bin/gcc-12 $CUDA_ROOT/bin/gcc
sudo ln -sf /usr/bin/g++-12 $CUDA_ROOT/bin/g++
cd ~/Downloads
# Obtain pycuda file from pypi.org
tar xf pycuda-2024.1.2.tar.gz
cd pycuda-2024.1.2
./configure.py
make installRendering on the GPU requires double-precision support on the device.
On FreeBSD, install pocl for OpenCL on the CPU. It works quite well.
On Windows, run the build tools vcvars64.bat first for CUDA/OpenCL.
mandel_queue.py - Run parallel using a queue for IPC
mandel_stream.py - Run parallel using a socket for IPC
mandel_parfor.py - Run parallel using Numba's parfor loop
mandel_ocl.py - Run on the CPU or GPU using PyOpenCL
mandel_cuda.py - Run on the GPU using PyCUDA
mandel_kernel.py - Run on the GPU using Numba cuda.jit
python3 mandel_queue.py -h
python3 mandel_queue.py --shortcuts
python3 mandel_queue.py --config=app.ini 720p
python3 mandel_queue.py --config=app.ini 720p --num-samples=3
python3 mandel_queue.py --location 5
The mandel_cuda.py example may require an older GCC if using the
system CUDA installation.
# Checks /usr/local/cuda/bin/gcc, gcc-13, gcc-12, gcc-11, gcc-10, or gcc.
# Typically, /usr/local/cuda is a symbolic link to /opt/cuda* path.
python3 mandel_cuda.py
python3 mandel_cuda.py --ccbin=/usr/bin/gcc-12
python3 mandel_cuda.py --ccbin=gcc-12
Settings can be stored in a configuation file. If choosing to use a
configuration file, copy app.ini to user.ini and use that.
The user.ini file is ignored by git updates.
Usage: mandel_queue.py [--config filepath [section]] [options]
Options:
--version show program's version number and exit
-h, --help show this help message and exit
--shortcuts show keyboard shortcuts and exit
--width=ARG width of window [100-8000]: 800
--height=ARG height of window [100-5000]: 500
--location=ARG begin at app location [0-7]: 0
--center-x=ARG home center-x value [float]: -0.625
--center-y=ARG home center-y value [float]: 0.0
--zoom-scale=ARG home zoom magnification [float]: 0.95
--num-samples=ARG anti-aliasing factor [1-9]: 2
--perf-level=ARG performance level [1-64]: 25
--color-scheme=ARG select color scheme [1-7]: 1
--fast-zoom=ARG select fast zoom [0,1]: 1
--smooth-bench=ARG select smooth bench [0,1]: 0
CPU Options (mandel_parfor, mandel_queue, mandel_stream):
--num-threads=ARG number of threads to use: auto
CUDA Options (mandel_cuda):
--ccbin directory in which the C compiler resides
(or) specify the compiler executable name
GPU Options (mandel_cuda, mandel_ocl):
--fma=ARG select fused-multiply-add flag [0,1]: 0
--mixed-prec=ARG select mixed-precision flag [0,1,2,3,4]: 2
Depending on the architecture, mixed-prec=1 may run faster than 2.
0: double precision, fma=0 matching CPU results
1,2: slight mixed-precision and still matching CPU results (fma=0)
3: 1st sample double precision, supersampling float-float precision
4: 1st sample and supersampling float-float precision
mixed-prec=3,4 silently enables fma
Epilog:
Values exceeding the range specification are silently clipped
to the respective minimum or maximum value.
The number of iterations is computed dynamically based on the
performance level (lower equals more iterations).
Auto-zoom destinations
Color schemes
Most all options are accessible via a keyboard shortcut. Zooming does not exceed double-precision limit.
q) terminate the application and exit
r) Home) reset window back to the home location
]) PageDn) zoom in from the center of the window
[) PageUp) zoom out from the center of the window
e) export the window RGB values to image.png
a) Left) scroll window left
s) Down) scroll window down
d) Right) scroll window right
w) Up) scroll window up
Color scheme
F1-F7) select color scheme 1 through 7, respectively
Auto zoom
Specify option --fast-zoom for fast/slow zoom mode.
Specify option --smooth-bench for smooth/bench mode.
Press any key to end auto zoom.
z) auto zoom from scale 0.33 to near --location 1
x) auto zoom from scale 0.33 to near --location 2
c) auto zoom from scale 0.33 to near --location 3
v) auto zoom from scale 0.33 to near --location 4
b) auto zoom from scale 0.33 to near --location 5
g) auto zoom from scale 0.33 to near --location 6
t) auto zoom from scale 0.33 to near --location 7
Go to location
Display the image at location selection.
shift-z) location 1
shift-x) location 2
shift-c) location 3
shift-v) location 4
shift-b) location 5
shift-g) location 6
shift-t) location 7
Image quality
Supersampling involves sharpening using Unsharp Mask.
l)ow render without supersampling
n) render with 2x2 supersampling
m)edium render with 3x3 supersampling
h)igh render with 5x5 supersampling
u)ltra render with 7x7 supersampling
i) render with 9x9 supersampling
Performance level
Iterations are computed dynamically based on the performance level.
<) ,) decreasing performance level increases iterations ;min 1
>) .) increasing performance level decreases iterations ;max 64
Scroll movement
Double clicking sets center-x,center-y to the mouse x,y coordinates and renders the image.
`) set scroll factor to 0.002x for micro adjustments
1) set scroll factor to 0.1x width or height
2) set scroll factor to 0.2x width or height
3) set scroll factor to 0.3x width or height
4) set scroll factor to 0.4x width or height
5) set scroll factor to 0.5x width or height
6) set scroll factor to 0.6x width or height
7) set scroll factor to 0.7x width or height
8) set scroll factor to 0.8x width or height
9) set scroll factor to 0.9x width or height
0) set scroll factor to 1.0x width or height
The demo folder contains non-parallel demonstrations for creating the Mandelbrot Set, apply Anti-Aliasing, Gaussian Blur, and Unsharp Mask via a step-by-step approach.
Bright qualitative colour scheme (courtesy of Paul Tol). I also tried coloring using a slight modification of Bernstein polynomials.
Periodicity checking i.e. escape early if we detect repetition. Compute 2 more iterations to decrease the error term.
Unsharp Mask was adapted from Pillow code and made to run parallel.