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Lenia – Mathematical Life Forms (github.com/chakazul)
154 points by leephillips on Dec 31, 2019 | hide | past | favorite | 22 comments


This has been submitted before. I found this discussion really interesting:

https://news.ycombinator.com/item?id=18754433


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)


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

[1] https://www.complex-systems.com/abstracts/v28_i03_a01/


In which it was credibly explained that mimimi why do I not get more credit, I do much more valuable work.


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


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!


I don’t know whether continuous automata have advantages, but Wolfram is fairly well known for self-promotion and over-stating the power and importance of his own version of discrete cellular automata. https://en.wikipedia.org/wiki/A_New_Kind_of_Science#Receptio...


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?


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...


That definition of cellular automata would still include all local dynamical systems in physics, e.g., the wave equation, the heat equation, etc.


except those aren't automata in the chomsky hierarchy


But no continuous systems are in the Chomsky hierarchy, right? Isn't that just support for my suggestion that cellular automata are by definition discrete?


The simulation is still using floating point. The fundamental Floating point arithmetic is regular in principle. It's the rules and algorithms that can potentially achieve higher order.

And even classical game of live is turing complete. They built a TM inside GoL!

But it can be modeled by a finite state automaton (if the grid is finite), I suppose, so the rules are just a regular grammar.

A regular machine can output the grammar of a context sensitive language, but not accept the corresponding programms. In the same sense, the turing machine in GoL is ...

you know what, I have no idea.


PS: I'm not sure how Lenia is implemented. If the model is that the points move, you can nevertheless think of each point as a cell on a regular grid, that holds a n-ary variable, that encodes the color (or hight or what) and the position in a x*y=n-1 dimensional coordinate sytem, with one dimension per cell.

In other words, each cell would encode its distance to all other cells. Which seems a bit redundant.


What's the difference between discrete and continuous in this instance if they're both being modelled in a computer? Are the continuous entities represented by functions?



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).


a practical use is for telescope mirrors https://en.wikipedia.org/wiki/Deformable_mirror#Deformable_m..., the wavefront shape (decomposed in this Zernike basis) is applied to the mirror


Can these life forms glide at arbitrary angles?


Yes, from the video it looks like the rule is the same under rotations.


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


Wolfram, where are you?




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