mandelbrot_wave.cpp File Reference

Animate a mandelbrot-like fractal with a variable coeficient. More...

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Detailed Description

Animate a mandelbrot-like fractal with a variable coeficient.

Author

Mitch Richling https://www.mitchr.me

Standards

C++20

See also

https://www.mitchr.me/SS/mandelbrotWave/index.html

Copyright

Copyright (c) 1988-2022, Mitchell Jay Richling https://www.mitchr.me All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Details

Iterate \(f(x)=z^5+a\cdot z+c\) as one would \(f(z)=z^2+c\) to render a Mandelbrot set. Vary the parameter \(a\) by moving it around the unit circle, and drop out an image for each \(a\). The resulting images may be rendered into movies like this:

• Make a gif convert -delay 1 -loop 0 -dispose previous mandelbrot_wave_???.tiff mandelbrot_wave_mean.gif
• Make a smaller gif gif convert -delay 1 -loop 0 -dispose previous -resize 50% mandelbrot_wave_???.tiff mandelbrot_wave_mean_50.gif
• For a GIF that runs forward and backward: convert -delay 1 -loop 0 -dispose previous $(ls mandelbrot_wave_???.tiff) $(ls -r mandelbrot_wave_???.tiff) mandelbrot_wave_wavy.gif
• Convert all the TIFF files into PNG so we can use ffmpeg to make a WEBM movie ls mandelbrot_wave_???.tiff | xargs -P 0 -I{} sh -c 'echo {}; convert {} $(echo {} | sed "s/\.tiff$/.png/;")'
• Convert the PNGs into a WEBM ffmpeg -r 15 -i mandelbrot_wave_%03d.png mandelbrot_wave_mean.webm
• Clean up the PNGs rm mandelbrot_wave_???..png

Note the frames are rendered 8x larger than the final images. I use an 8x, mean scale down to smooth the image out a bit.

Definition in file mandelbrot_wave.cpp.