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L-System

en.wikipedia.org

112 pointslemonspat17 comments

I and my team made this: https://onlinemathtools.com/l-system-generator. You can enter the axiom and the rewrite rules and get a visualization of the grammar. Also, in the examples section, we added 9 most popular fractals.

If you are interested in some code and more examples: http://blog.rabidgremlin.com/2014/12/09/procedural-content-g...

This book is also very good: http://algorithmicbotany.org/papers/#abop

Daniel Shiffman also delves into them in the excellent Nature of Code: https://natureofcode.com/book/chapter-8-fractals/.

ITT: everyone posting their L-System applications

I think at this point, it’s an unofficial HN tradition every time L-systems are mentioned, and I kind of love it.

(e.g. https://news.ycombinator.com/item?id=21749806)

I'll add my two:

- https://twitter.com/lindenmoji tweets randomly generated L-systems using an emoji language (though the traditional rules work as well); you can @ and it will reply with an image

- https://lindenmayer.club/lindenmoji/#?curve=ab%0Aa%3D%E2%9E%... is an interactive playground for L-systems that shows both the visual output and the first few expansions of the specified rule

L systems are so magical to me. Opened up the world of procedural generation to me. And I look at trees differently now as a result. I also see fractals everywhere in the real world.

Aren't L-systems just fractals ?

Also, if someone can expand, what do you think of Stephen Wolfram's theory of everything[0] which to me seems quite similar to L-systems (I might be completely wrong here).

Has anyone combined cellular automata and L-systems, will that lead to....simulating evolution?

[0] https://writings.stephenwolfram.com/2020/04/finally-we-may-h... (Read How it Works section).

L-systems can be used to describe fractals but they aren’t fractals. They are formal languages.

Thanks, so L-Systems are to Fractals as Code is to Application.

Sort of. There are many fractals that are not described by L systems (whereas every application is written in code)

The Mandelbrot set cannot be described by an L-system. And not every L-system describes a fractal.

Fractals are sets - maps of the results of a recursive calculation using a seed formula. They happen to have deep structure, but it's implicit in the process and not obvious.

L-systems are explicit structural grammars with some simple recursion, and are much shallower. You can more or less predict the shape of a simple L-system just by looking at it. The recursion - usually not many levels - looks nice because we like modulated repetition. And some natural systems seem to have evolved similar macro-level structures. But they're pretty trivial conceptually.

Cellular automata are part way between the two.

None of the above really evolve, because they don't support natural selection or recombination.

There's a class of solution-explorers called genetic algorithms which were a thing before ML (kind of...) took over a similar space. GAs do evolve, but they're not particularly efficient and they suffer from the usual problem of getting stuck in local maxima.

It turns out that for interesting and open-ended evolution you need a much bigger parameter space than any of these toy algos - like the one nature has - and current computing can't handle that (yet).

For quick 2D sketching of an L-system design https://inkscape.org/ (Extensions->Render->L-System on menu in Inkscape) From an older version of Inkscape, but still similar functionality: https://thebrickinthesky.wordpress.com/2013/03/17/l-systems-...

lol, the timing of this is impeccable. I was literally just playing through Cyberpunk 2077 and thinking about procedurally generated cities.

You might like this: https://github.com/marian42/wavefunctioncollapse

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