5 ms·

Lenia – Mathematical Life Forms

154 points by leephillips 7y ago

Quequau 7y ago
This has been submitted before. I found this discussion really interesting: https://news.ycombinator.com/item?id=18754433 https://news.ycombinator.com/item?id=18754433
- stareatgoats 7y ago
  In which it was credibly explained that this is not what it claims to be (models of life forms), and that there exist such platforms though i.e. AVIDA (https://en.wikipedia.org/wiki/Avida https://en.wikipedia.org/wiki/Avida)
  - vanderZwan 7y ago
    It is what it claims to be if you keep in mind that it's based on the Smoothlife extension[0] of Conway's Game Of Life. Words can have more than one definition. The abstract of the paper linked in the readme[1] makes it pretty clear that the usage of the word "life" should be interpreted as a reference to cellular automata: > A new system of artificial life called Lenia (from Latin lenis “smooth”), a two-dimensional cellular automaton with continuous spacetime state and generalized local rule, is reported. Computer simulations show that Lenia supports a great diversity of complex autonomous patterns or “life forms” bearing resemblance to real-world microscopic organisms. More than 400 species in 18 families have been identified, many discovered via interactive evolutionary computation. They differ from other cellular automata patterns in being geometric, metameric, fuzzy, resilient, adaptive and rule generic. [0] https://www.conwaylife.com/wiki/OCA:SmoothLife https://www.conwaylife.com/wiki/OCA:SmoothLife [1] https://www.complex-systems.com/abstracts/v28_i03_a01/ https://www.complex-systems.com/abstracts/v28_i03_a01/
  - posterboy 7y ago
    In which it was credibly explained that mimimi why do I not get more credit, I do much more valuable work.
aj7 7y ago
Wolfram, where are you?
amelius 7y ago
Can these life forms glide at arbitrary angles?
- c1ccccc1 7y ago
  Yes, from the video it looks like the rule is the same under rotations.
lordleft 7y ago
Give them a lossy mechanism for replication and we can have ourselves a digital Shakespeare in 4 billion years :)
11235813213455 7y ago
Made me think of https://en.wikipedia.org/wiki/Zernike_polynomials https://en.wikipedia.org/wiki/Zernike_polynomials
- posterboy 7y ago
  That is beautiful. Can't upvote though, as it did not remind me of anything. It's new to me. Wonder what it has to do with optics. the terms of R remind me a bit of the collatz sequence, as 2x^2-1 gives the first branches from the root (times 3).
  - 11235813213455 7y ago
    a practical use is for telescope mirrors https://en.wikipedia.org/wiki/Deformable_mirror#Deformable_mirror_parameters https://en.wikipedia.org/wiki/Deformable_mirror#Deformable_m..., the wavefront shape (decomposed in this Zernike basis) is applied to the mirror
georgewsinger 7y ago
Very interesting. Stephen Wolfram discusses continuous cellular automata in New Kind of Science, and basically concludes (IIRC) that they don't give many advantages over discrete automata for study. That said, the continuous cellular automata sure look very beautiful!
- jessriedel 7y ago
  I thought the word "cellular" referred to discrete space? (Wikipedia also suggests that cellular automata are discrete by definition.) If not, what distinguishes continuous cellular automata from general dynamical systems?
  - drongoking 7y ago
    I thought that cellular referred to each point (cell) having its own neighborhood and reacting individually. IIRC, cellular automata have been generalized (made continuous) in both space and time by various researchers, making them (as you point out) less "cellular". As for how they are different from general dynamical systems, the GDSs I've seen have a small set of differential equations that describe the whole system; a cellular automaton has the same rule for each cell but the system comprises a large number of cells. In other words, locality and massive parallelism. But this isn't my field so correct me if I'm wrong...
    - jessriedel 7y ago
      That definition of cellular automata would still include all local dynamical systems in physics, e.g., the wave equation, the heat equation, etc.
      - posterboy 7y ago
        except those aren't automata in the chomsky hierarchy
        jessriedel 7y ago
posterboy 7y ago
the pertinent question is, can it simulate a cellular grid?

154 points by leephillips 7y ago

This has been submitted before. I found this discussion really interesting: https://news.ycombinator.com/item?id=18754433 https://news.ycombinator.com/item?id=18754433

stareatgoats 7y ago
In which it was credibly explained that this is not what it claims to be (models of life forms), and that there exist such platforms though i.e. AVIDA (https://en.wikipedia.org/wiki/Avida https://en.wikipedia.org/wiki/Avida)
- vanderZwan 7y ago
  It is what it claims to be if you keep in mind that it's based on the Smoothlife extension[0] of Conway's Game Of Life. Words can have more than one definition. The abstract of the paper linked in the readme[1] makes it pretty clear that the usage of the word "life" should be interpreted as a reference to cellular automata: > A new system of artificial life called Lenia (from Latin lenis “smooth”), a two-dimensional cellular automaton with continuous spacetime state and generalized local rule, is reported. Computer simulations show that Lenia supports a great diversity of complex autonomous patterns or “life forms” bearing resemblance to real-world microscopic organisms. More than 400 species in 18 families have been identified, many discovered via interactive evolutionary computation. They differ from other cellular automata patterns in being geometric, metameric, fuzzy, resilient, adaptive and rule generic. [0] https://www.conwaylife.com/wiki/OCA:SmoothLife https://www.conwaylife.com/wiki/OCA:SmoothLife [1] https://www.complex-systems.com/abstracts/v28_i03_a01/ https://www.complex-systems.com/abstracts/v28_i03_a01/
- posterboy 7y ago
  In which it was credibly explained that mimimi why do I not get more credit, I do much more valuable work.

aj7 7y ago

Wolfram, where are you?

amelius 7y ago

Can these life forms glide at arbitrary angles?

c1ccccc1 7y ago
Yes, from the video it looks like the rule is the same under rotations.

lordleft 7y ago

Give them a lossy mechanism for replication and we can have ourselves a digital Shakespeare in 4 billion years :)

11235813213455 7y ago

Made me think of https://en.wikipedia.org/wiki/Zernike_polynomials https://en.wikipedia.org/wiki/Zernike_polynomials

posterboy 7y ago
That is beautiful. Can't upvote though, as it did not remind me of anything. It's new to me. Wonder what it has to do with optics. the terms of R remind me a bit of the collatz sequence, as 2x^2-1 gives the first branches from the root (times 3).
- 11235813213455 7y ago
  a practical use is for telescope mirrors https://en.wikipedia.org/wiki/Deformable_mirror#Deformable_mirror_parameters https://en.wikipedia.org/wiki/Deformable_mirror#Deformable_m..., the wavefront shape (decomposed in this Zernike basis) is applied to the mirror

georgewsinger 7y ago

Very interesting. Stephen Wolfram discusses continuous cellular automata in New Kind of Science, and basically concludes (IIRC) that they don't give many advantages over discrete automata for study. That said, the continuous cellular automata sure look very beautiful!

jessriedel 7y ago
I thought the word "cellular" referred to discrete space? (Wikipedia also suggests that cellular automata are discrete by definition.) If not, what distinguishes continuous cellular automata from general dynamical systems?
- drongoking 7y ago
  I thought that cellular referred to each point (cell) having its own neighborhood and reacting individually. IIRC, cellular automata have been generalized (made continuous) in both space and time by various researchers, making them (as you point out) less "cellular". As for how they are different from general dynamical systems, the GDSs I've seen have a small set of differential equations that describe the whole system; a cellular automaton has the same rule for each cell but the system comprises a large number of cells. In other words, locality and massive parallelism. But this isn't my field so correct me if I'm wrong...
  - jessriedel 7y ago
    That definition of cellular automata would still include all local dynamical systems in physics, e.g., the wave equation, the heat equation, etc.
    - posterboy 7y ago
      except those aren't automata in the chomsky hierarchy
      - jessriedel 7y ago

posterboy 7y ago

the pertinent question is, can it simulate a cellular grid?