A C++ implementation of Fractal art rendering (PNG/MP4).
This project is a C++ implementation of Julia Set and other fractal seet rendering with OpenGL. One example is Julia Set which is a fractal defined by a complex quadratic polynomial. This program allows you to generate and visualize Julia Set images.
- Generate high-resolution Julia Set images (PNG)
- Generate high-resolution Julia Set animations, eg. Zoom or rotation (AC1/MP4)
- Support multiple types of Julia sets
- Customisable Julia set parameters
To get started with Julia Set Render, follow these steps:
- Clone the repository:
git clone https://github.com/tao-pr/fractal-art-render.git- Install and configure prerequisites
- Latest XCode Commandline Tools
- CMake
- LLVM Compiler
- TBB
- OpenCV4
For MacOS users, simply run the following
# Install XCode commandline update (requires a restart)
softwareupdate --list # list the available update for XCode Commandline Tools
softwareupdate -i <label> # install the available update (specify the label got from previous command)
# Install LLVM
brew install llvm@16
# then follow an instruction on `brew info llvm@16` to bootstrap your environment
# Install TBB
brew install tbb
# Install OpenCV
brew install opencv
# Install OpenH264 video codec
brew install openh264- Build the project and run the executable:
./make.sh && bin/julia 0 -0.75 50 0.0001The executable accepts the following positional arguments
./bin/julia {re} {im} {step_size} {num_iters} {scale} {fractal_type} {centre} {animation_params}{re} and {im} represent a complex number (C) we want to explore a fractal set on, e.g. for Julia set (z_next = z_current^2 + C).
See example of arguments in the next section. After run, it will write an output image to fractal.png.
Some examples of how to generate Julia set render as PNG.
# Simple Julia (degree2)
./make.sh && bin/julia 0.285 0.01 200 0.001
./make.sh && bin/julia 0.285 0.01 200 0.001 1 julia 0.4784,0.1832
./make.sh && bin/julia -0.4 0.6 200 0.001
./make.sh && bin/julia 0.285 0 60 0.001
./make.sh && bin/julia -0.70176 0.3842 60 0.001
./make.sh && bin/julia 0.285 0.01 200 0.001
./make.sh && bin/julia -0.835 -0.2321 50 0.001 1.2
./make.sh && bin/julia -0.7269 0.1889 500 0.001
./make.sh && bin/julia -0.7269 0.1889 500 0.001 1.5
./make.sh && bin/julia -0.3905407802 -0.5867879073 150 0.001 # Siegel disks
./make.sh && bin/julia -2 1 10 0.001 2
./make.sh && bin/julia -1.77578 0 10 0.001 2 # Peitgen et al 1992
./make.sh && bin/julia 0 1 30 0.001 2 # Dendritic
# Degree4 Julia
./make.sh && bin/julia 0.6 0.55 70 0.001 0.99 degree4
./make.sh && bin/julia -2 1 10 0.001 1.5 degree4
./make.sh && bin/julia 0 1 15 0.001 1.5 degree4
# Complex Julia
./make.sh && bin/julia 0.6 0.55 10 0.001 1.2 complex
./make.sh && bin/julia -0.3905407802 -0.5867879073 30 0.001 1 complex
./make.sh && bin/julia -2 1 10 0.001 1.5 complex
./make.sh && bin/julia 0 1 8 0.001 1.5 complex 0.006,-0.012For animation. The format of the params are "{animationType}:{numFrames}:{params=value},{params=value}". Note that for zooming, the program will always zoom into the {centre} coordinate of the render.
# Zoom-in animation example #1
# 360 frames (15s video)
# Taking 13 minutes to render on Apple M1
./make.sh && bin/julia -0.835 -0.2321 50 0.0016 2 julia 0.551982975934,0.551982975934 zoom:380:ratio=0.92,decayEvery=5,decay=-5,maxIters=900
# Zoom-in animation example #2
# 280 frames (12s videos)
# Taking 37 minutes to render on Apple M1
./make.sh && bin/julia 0.285 0.01 200 0.001 1.1 julia 0.473669790468,0.188451675429 zoom:280:ratio=0.92,decayEvery=3,decay=-8,maxIters=1000
# Zoom-in animation example #3
# 290 frames (12s video)
# Taking 13 minutes to render on Apple M1
./make.sh && bin/julia -0.3905407802 -0.5867879073 20 0.001 1.3 complex 0.021882444987,0.753229532908 zoom:290:ratio=0.92,decay=-2,decayEvery=6,maxIters=800
# Zoom-in animation example #4
# This animation render is quite a CPU-heavy one, as most of its visible coordinates
# will not escape early. It also produces significantly the largest output file.
# 210 frames (9s video)
# Taking 47 minutes to render on Apple M1
./make.sh && bin/julia -0.7269 0.1889 500 0.0016 1.5 julia 0.497930476513736,-0.098793300393041 zoom:240:ratio=0.94,decay=-24,decayEvery=2,maxIters=3500
# Zoom-in animation example #5
#
./make.sh && bin/julia -0.835 -0.2321 60 0.001 1.2 julia 0.092446006940281,-0.284429809138125 zoom:320:ratio=0.94,decay=-2,decayEvery=3,maxIters=960
# Translation animation example #1 (real value walk)
./make.sh && bin/julia 0.285 0.01 200 0.001 1.1 julia 0.4784,0.1832 complex:25:stepRe=0.0002,decay=0
# Translation animation example #2 (imaginary walk)
./make.sh && bin/julia 0.285 0.01 200 0.001 1.1 julia 0.4784,0.1832 complex:25:stepRe=0,stepIm=0.001,decay=0
./make.sh && bin/julia 0.285 0.01 200 0.001 1.1 julia 0.4784,0.1832 complex:25:stepRe=0,stepIm=-0.001,decay=-5,decayEvery=10
# Rotation animation example #1
./make.sh && bin/julia -0.4 0.6 250 0.001 1 julia 0,0 rotate:30:decay=0,angle=0.001
# Rotation animation example #2
./make.sh && bin/julia 0.162 1.04 14 0.001 1.8 julia -0.019280780364,-0.474818652422 rotate:40:decay=0,angle=0.15707963268
# Rotation animation example #3
./make.sh && bin/julia -1.476 0 25 0.001 1.8 julia 0,0 rotate:32:angle=0.2094395102,decay=5,decayEvery=4,minIters=8Rendering a sequence of Julia set zoomings takes substantial amount of work for CPU. An ARM-powered laptop (Macbook M1) could generate some amount of heat with just 10 seconds of video render (240 frames).
Rendering frame #117
Preparing parallel tasks...
Submitted 8610312 parallel render tasks (3912x2200)
Finished 8610312 parallel render tasks (3912x2200)
Resized from 3912 x 2200 to 1920 x 1080
bound = 4.87265e-06, res = 3.98671e-09
Rendering frame #118
Preparing parallel tasks...
Submitted 8606400 parallel render tasks (3912x2201)
Finished 8606400 parallel render tasks (3912x2201)
Resized from 3912 x 2201 to 1920 x 1080
bound = 4.38538e-06, res = 3.58804e-09
Rendering frame #119
Preparing parallel tasks...
Submitted 8610312 parallel render tasks (3912x2200)
Finished 8610312 parallel render tasks (3912x2200)
Resized from 3912 x 2200 to 1920 x 1080
Press any key to exit..
See sample rendered images in /samples dir.
Contributions are welcome! If you have any ideas, suggestions, or bug reports, please open an issue or submit a pull request.
This project is licensed under the MIT License. See the LICENSE file for more information.
React
Typescript
Django
Laravel
Facebook
Microsoft
Google
Alibaba
D3
Tencent