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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

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).

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).