Newton–Riemann

Tool for creating 360° videos of Newton fractals.

Example output of the tool can be found on my YouTube channel.

I don't know if it compiles on anything but linux.

Dependencies

The version numbers are just the version I have, it might work with earlier or later versions.

An NVIDIA GPU is required to run the code.

• CUDA 7.5.18-4. For the code in src/.
• GCC 6.1.1 (also tested with version 5.4.0). For the code in genfunc/ and ppm/.
• FFmpeg 3.0.2. For creating video files from the frames.
• ImageMagick 6.9.5-2. For creating PNG files from the frames.
• Python 2.7.12. For embedding 360° metadata in the video files.

Usage

The tool can be used with the Makefile directly, or can be run with the script newton-frame.sh.

Use make if you wish to create a single frame, and the script if you wish to create many frames.

Usage with make

Edit the file func.str to contain the mathematical function you wish to create a Newton fractal for. It supports standard mathematical ASCII-notation, some examples are:

sin(x)
x^5 - x - 1
exp(2*x) - 1

After you have created the func.str file, just run make, which will create a 4K image file called img.png. If you wish to create an MP4 360° video file that can be uploaded to YouTube, call make spherical-video.mp4.

Usage with script

The script newton-frame.sh is used to create many frames, which can be used to create animated videos. The usage of the script can be found by running the script without parameters, and is shown below:

Usage: ./newton-frame.sh function file-pattern frame-start frame-end

  function:     The function to make a newton fractal of. Use t for frame number.
  file-pattern: A printf style pattern for the filenames of the frames.
  frame-start:  The index of the first frame, and the first value used for t.
  frame-end:    The index of the last frame, and the last value used for t.

The command to produce this video is shown below.

./newton-frame.sh 'exp(x) + (t+1)*0.005' out/frame%03d.png 0 999

If the computations gets interrupted, you can resume from the last frame by running the resume.sh script.

Changing the iteration count

The number of iterations of Newton's method performed on each pixel can be changed in the file newton.cu, defined by the macro NEWTON_ITERS.