Fractal Art Render

A C++ implementation of Fractal art rendering (PNG/MP4).

Table of Contents

• Introduction
• Features
• Getting Started
• How to Render
• Contributing
• License

Introduction

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.

Features

• 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

Getting Started

To get started with Julia Set Render, follow these steps:

1. Clone the repository:

git clone https://github.com/tao-pr/fractal-art-render.git

2. 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

3. Build the project and run the executable:

./make.sh && bin/julia 0 -0.75 50 0.0001

How to Render

The 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.

Still images

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,-0.012

Animation (render as mp4)

For 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=8

Rendering 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..

Samples

See sample rendered images in /samples dir.

Contributing

Contributions are welcome! If you have any ideas, suggestions, or bug reports, please open an issue or submit a pull request.

License

This project is licensed under the MIT License. See the LICENSE file for more information.