This is a project I made for rendering, animating, and exploring Newton Fractals. I wrote most of the starting code when I was on vacation with family, and it ended up being both an interesting and fun project to work on. It uses OpenGL and C++.
Looking at a single fractal (e.g. the Mandelbrot set) can be very interesting, but most of the videos about these fractals zoom way into the fractal instead of just showing a static image. I thought to myself, I wonder if there's a way to animate them? (In fact, this was a question I had years ago, when I was interested in making a fractal music visualiser (I failed).)
This project uses polynomials with real coefficients to generate Newton Fractals. Heuristically, slightly changing the coefficients of the polynomials will result in a similarly "small" change in the resulting fractal, though this is far from obvious and probably requires techniques from complex dynamics to answer adequately. Fortunately for me, continuously or smoothly varying the coefficients produces an animation of the fractal; this is the principle that underlies the project.
Producing the smooth variation of the coefficients is a whole thing, and I will write a blog post on my website in the near future detailing this aspect.
If I do continue working on this project, I'm hoping to implement:
- Animation controls to pause, speed up, or slow down the animation or control other animation parameters.
- An "information panel" that allows a user to view details about the pixel beneath their mouse and about the fractal itself.
- Camera controls: zoom, pan, and possible rotate.
- A way to set the colour palate used by the shaders.
- A way to set a seed so animations or fractals are reproducible.