5 ms·

L-System

112 points by lemonspat 6y ago

Rabidgremlin 6y ago
If you are interested in some code and more examples: http://blog.rabidgremlin.com/2014/12/09/procedural-content-generation-l-systems/ http://blog.rabidgremlin.com/2014/12/09/procedural-content-g...
- eindiran 6y ago
  This book is also very good: http://algorithmicbotany.org/papers/#abop http://algorithmicbotany.org/papers/#abop
- kimburgess 6y ago
  Daniel Shiffman also delves into them in the excellent Nature of Code: https://natureofcode.com/book/chapter-8-fractals/ https://natureofcode.com/book/chapter-8-fractals/.
chrisco255 6y ago
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.
pulkitsh1234 6y ago
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-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/#how-it-works https://writings.stephenwolfram.com/2020/04/finally-we-may-h... (Read How it Works section).
- bbotond 6y ago
  L-systems can be used to describe fractals but they aren’t fractals. They are formal languages.
  - pulkitsh1234 6y ago
    Thanks, so L-Systems are to Fractals as Code is to Application.
    - FredrikMeyer 6y ago
      Sort of. There are many fractals that are not described by L systems (whereas every application is written in code)
    - ogogmad 6y ago
      The Mandelbrot set cannot be described by an L-system. And not every L-system describes a fractal.
- TheOtherHobbes 6y ago
  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).
pkrumins 6y ago
I and my team made this: https://onlinemathtools.com/l-system-generator 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.
squirrelmaker 6y ago
For quick 2D sketching of an L-system design https://inkscape.org/ 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-and-penrose-p3-in-inkscape/ https://thebrickinthesky.wordpress.com/2013/03/17/l-systems-...
Yajirobe 6y ago
ITT: everyone posting their L-System applications
- deleted 6y ago
  [deleted]
- paulgb 6y ago
  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 https://news.ycombinator.com/item?id=21749806)
- beaugunderson 6y ago
  I'll add my two: - https://twitter.com/lindenmoji 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%A1%EF%B8%8Fb%0Ab%3D%E2%86%A9%EF%B8%8Fa 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
Guthur 6y ago
lol, the timing of this is impeccable. I was literally just playing through Cyberpunk 2077 and thinking about procedurally generated cities.
- sabellito 6y ago
  You might like this: https://github.com/marian42/wavefunctioncollapse https://github.com/marian42/wavefunctioncollapse

112 points by lemonspat 6y ago

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

eindiran 6y ago
This book is also very good: http://algorithmicbotany.org/papers/#abop http://algorithmicbotany.org/papers/#abop
kimburgess 6y ago
Daniel Shiffman also delves into them in the excellent Nature of Code: https://natureofcode.com/book/chapter-8-fractals/ https://natureofcode.com/book/chapter-8-fractals/.

chrisco255 6y ago

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.

pulkitsh1234 6y ago

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-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/#how-it-works https://writings.stephenwolfram.com/2020/04/finally-we-may-h... (Read How it Works section).

bbotond 6y ago
L-systems can be used to describe fractals but they aren’t fractals. They are formal languages.
- pulkitsh1234 6y ago
  Thanks, so L-Systems are to Fractals as Code is to Application.
  - FredrikMeyer 6y ago
    Sort of. There are many fractals that are not described by L systems (whereas every application is written in code)
  - ogogmad 6y ago
    The Mandelbrot set cannot be described by an L-system. And not every L-system describes a fractal.
TheOtherHobbes 6y ago
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).

pkrumins 6y ago

I and my team made this: https://onlinemathtools.com/l-system-generator 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.

squirrelmaker 6y ago

For quick 2D sketching of an L-system design https://inkscape.org/ 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-and-penrose-p3-in-inkscape/ https://thebrickinthesky.wordpress.com/2013/03/17/l-systems-...

Yajirobe 6y ago

ITT: everyone posting their L-System applications

deleted 6y ago
[deleted]
paulgb 6y ago
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 https://news.ycombinator.com/item?id=21749806)
beaugunderson 6y ago
I'll add my two: - https://twitter.com/lindenmoji 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%A1%EF%B8%8Fb%0Ab%3D%E2%86%A9%EF%B8%8Fa 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

Guthur 6y ago

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

sabellito 6y ago
You might like this: https://github.com/marian42/wavefunctioncollapse https://github.com/marian42/wavefunctioncollapse