Show HN: Fractal Garden – An Exhibition of Mathematical Beauty
fractal.garden
fractal.garden
in September I built this website, which explores some mesmerizing fractals. The idea behind it is to have a beautiful "garden" that instead of being filled with flowers and plants is filled with magnificent mathematical objects. The fractals are all interactive and you can play around with the options, changing colors, iterations, and more.
The whole thing is open source, so if you feel like it and have the time, please contribute to the project. It's tagged for the Hacktoberfest and contributions count toward your Hacktoberfest progress! Here's the link to the GitHub: https://github.com/trebeljahr/fractal-garden
The fractal garden, as such is part of what I am trying to do right now, picking awesome projects I always wanted to do and that are just outside my comfort zone (in terms of skills or knowledge). I then try to build as much of them as I can within a month, before moving on to the next project the next month.
I write summaries of the learnings I had during the projects on https://www.trebeljahr.com/
Let me know what you think and the ideas and feedback you have.
Enjoy your day and take care.
Cheers, Rico
It's because I didn't find a way to construct only parts of the fractals based on the viewport. Many of the fractals you can see in the garden are generated iteration by iteration and generating the next iteration for only the visible part is not a trivial problem to solve... I struggled thinking about a solution for this, but in the end gave up in favor of having more fractals.
For the Mandelbrot Set the above is not the case, but the zoom there is still very limited due to precision issues in WebGl (a float has only limited bits, even for high precision floats) and things get horribly slow if trying to implement arbitrary precision on the GPU.
There are some ideas around "perturbation theory" that can help to get more zoom on the Mandelbrot Set (still not infinite) but I had a very hard time wrapping my head around how to implement that in a shader.
But please, if you have ideas of how to fix this - the project is open source and it would be 100% awesome if it were possible to nicely zoom in/out of all of them.
I opened an issue on the repo: https://github.com/trebeljahr/fractal-garden/issues/22
In the final form it supported many types of fractals via a domain-specific language. You can still download the source from https://www.fractint.org/.
Porting this framework to your garden might be worthwhile?
(Note that the colours will change because of the way the code is written. Also, it will require more computation, so it's probably a good idea to only increase maxIterations when zoomed in.)
I wonder if you(or someone else) knows of a general tool for exploring L-systems? As you comment, 'all L-systems are related', but I've had a hard time navigating the theoretical literature on this. For several years now I've been looking for a way to examine a tree or other network and extrapolate a structural 'recipe' for it. I'll get this Algorithmic Beauty of Plants book but would love to hear of any resources you know for 'reverse engineering' L-systems from existing tree structures.
One pointer that might be worth exploring, which is not quite L-Systems but might be related is Fractal Compression. I've read that there are algorithms to compress images into a "closest" IFS – iterated function system.
https://en.wikipedia.org/wiki/Fractal_compression
Maybe one could come up with a way of going from an image via fractal compression to an IFS which could then be used as the basis for an L-system?
Most of the L-Systems that are on this site are from Paul Bourke – http://paulbourke.net/fractals/lsys/
Which is a really awesome resource!
https://en.wikipedia.org/wiki/L-system#Open_problems:~:text=....
edit: also would appricate to able to zoom in.
There is also ABOP - the Algorithmic Beauty of Plants http://algorithmicbotany.org/papers/#abop which has been a huge inspiration for this project.
Unfortunately I don’t yet have the skills to contribute to this effort. Hopefully following your algorithm descriptions will change that.