i already explained how i got interested in fractals in this page, but what you need to know is that i first experimented with escape-time fractals on my calculator...

after some fiddling, i realized that rendering fractals this way was

1. inefficient
2. giving ugly results
3. insanely annoying to tweak

with this in mind i started working on a tiny program written in rust to render escape-time fractals.

when i started working on this project, i wanted to get pretty pictures as early as possible.

i used serde – which is a rust crate – to directly (de)serialize the struct representing a fractal configuration (formula, position, zoom, coloring, etc.), which made it easy to tinker with some formulas and get a few renders.

the rendering part of the program was also very simple and quite rustic, if i dare say.

after establishing the basic functionality of my software, i posted some of my renders on a certain fractal discord server. someone on this server pointed out that my images were not anti-aliased.

indeed, without anti-aliasing, my renders looked a bit crispy. i was given a link to a google collab notebook which explained a sampling scheme allowing for anti-aliased image outputs. however, i wanted to try and implement anti-aliasing myself.

spoiler: there is a reason why signal processing classes exist ;)

even after watching countless videos and trying a lot of different hacks, my results were not convincing and i had to give up and use the implementation from the colab... it works wonders by the way.

some of its key tricks are:

• to use fibonacci lattices to generate uniformly distributed sampling points over a square
• to have a different yet very similar sampling pattern for each pixel, as shown in the figure below

this allows for a good approximation of each pixel's average color while reducing aliasing effects which partly originate from sampling with the same sampling pattern everywhere.

did you know ? manually editing floating point numbers to change the render position/zoom in a text parameter file for exploring a fractal is a bit finicky.

this is why i created a simple gui with a preview. it made exploration much easier. it has now evolved into quite a polished one in my opinion.

at some time, i also added the use of simd operations to speed up computation and theoretically, it almost halved rendering time.

working on this project was a lot of fun and i learned a lot, especially about anti-aliasing, which is – in my opinion – a fascinating subject.

you can find some of my fractal renders

• on my deviantart page
• in the fractal gallery