
Lenia – Mathematical Life Forms - leephillips
https://github.com/Chakazul/Lenia
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Quequau
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)

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stareatgoats
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))

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vanderZwan
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/)

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

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georgewsinger
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!

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jessriedel
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?

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drongoking
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...

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

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posterboy
except those aren't automata in the chomsky hierarchy

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jessriedel
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?

~~~
posterboy
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.

~~~
posterboy
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.

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11235813213455
Made me think of
[https://en.wikipedia.org/wiki/Zernike_polynomials](https://en.wikipedia.org/wiki/Zernike_polynomials)

~~~
posterboy
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).

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11235813213455
a practical use is for telescope mirrors
[https://en.wikipedia.org/wiki/Deformable_mirror#Deformable_m...](https://en.wikipedia.org/wiki/Deformable_mirror#Deformable_mirror_parameters),
the wavefront shape (decomposed in this Zernike basis) is applied to the
mirror

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amelius
Can these life forms glide at arbitrary angles?

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

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

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aj7
Wolfram, where are you?

