Lenia


Synopsis

Lenia is a system of continuous cellular automata, a form of artificial life.
It was derived from Conway's Game of Life by making everything smooth, continuous and generalized.

The project started in 2015 by experimenting with Game of Life variations, led to the discovery of continuous glider Orbium, and 400+ more species.
These digital creatures show lifelike features like self-organization, self-repair, bilateral and radial symmetries, locomotive dynamics, and sometimes chaotic nature.
In 2018, investigations on Lenia accumulated into a video and a paper, attracted some attention on the internet and academia.
Once a coding exercise, Lenia has now evolved into an art and science research project, sparking international collaborations with universities and research labs.

In 2020, further extentions of Lenia led to more emergent phenomena, like interesting 3D/4D patterns, self-replication, pattern emission, self-boundary/individuality, aggregated patterns, polymorphism, intercommunicating colonies, etc.
Is there a limit on this digital universe? What kind of new pattern or emergent property will appear next? And what kind of questions or answers can we get from it?
Collaborations

Research:
  • ๐Ÿ‘จโ€๐Ÿ”ฌ Study of sensorimotor capabilities in differentiable Lenia (with Flowers team @ Inria ๐Ÿ‡ซ๐Ÿ‡ท) [PDF] [Team]
  • ๐Ÿ‘จโ€๐Ÿ”ฌ Study of swarm cognition and primitive agency in Lenia (with Allen Discovery Center @ Tufts U ๐Ÿ‡บ๐Ÿ‡ธ) [Team]
  • ๐Ÿ‘จโ€๐Ÿ”ฌ Study of alternative formulations of Lenia (with Arita-Suzuki ALife Lab @ Nagoya U ๐Ÿ‡ฏ๐Ÿ‡ต) [Team]
Software:
  • ๐Ÿ‘จโ€๐Ÿ’ป As a target system in Automated Discovery software (with Flowers team @ Inria ๐Ÿ‡ซ๐Ÿ‡ท) [Team]
  • ๐Ÿ‘จโ€๐Ÿ’ป "Vitrual creature" module in Artbreeder.com (with Joel Simon ๐Ÿ‡บ๐Ÿ‡ธ, etc.) [Website]
  • ๐Ÿ‘จโ€๐Ÿ’ป Continuous cellular automata simulation on GPU (with Slakermanz ๐Ÿ‡ณ๐Ÿ‡ฟ, etc.) [Github]
Art & Education:
  • ๐Ÿ‘จโ€๐Ÿซ Interactive demo in Complexity Explorables (with Dirk Brockmann @ HU Berlin ๐Ÿ‡ฉ๐Ÿ‡ช) [Preview] [Website]
  • ๐Ÿ‘จโ€๐ŸŽจ Appearance in film "Thoughts on Life" (with Will Cavendish @ Princeton / IAS ๐Ÿ‡บ๐Ÿ‡ธ, & team) [Website]
  • ๐Ÿ‘จโ€๐ŸŽจ Appearance in art project "Codex Virtualis _" (with Interspecifics ๐Ÿ‡ฒ๐Ÿ‡ฝ @ Ars Electronica ๐Ÿ‡ฆ๐Ÿ‡น) [Website]
Media

  • ๐Ÿ“ฐ List of tweets (project progress) [Twitter]
  • ๐ŸŽฌ List of videos (movies, talks) [YouTube]
  • ๐ŸŽฌ Asymptotic Lenia (2021-07) [YouTube]
  • ๐ŸŽฌ Lenia: Expanded Universe (2020-07) [YouTube] [Vimeo]
  • ๐ŸŽฌ Lenia: Mathematical Life Forms (2018-07) [YouTube] [Vimeo]
    • ๐Ÿ… Winner, Virtual Creature Contest @ GECCO 2018 Kyoto (2018-07) [Website]
    • ๐Ÿ… Honorable Mention, ALife Art Award @ ALIFE 2018 Tokyo (2018-07) [Website] [Photo @kyrre2000]
Papers

Bert Chan
  • ๐Ÿ“„ Lenia and Expanded Universe (ALIFE 2020) [arXiv] [Proceedings]
    Chan, Bert Wang-Chak (2020). Lenia and Expanded Universe. Artificial Life Conference Proceedings, (32), 221–229. arXiv:2005.03742.
  • ๐Ÿ“„ Lenia: Biology of Artificial Life (Complex Systems 2020) [arXiv] [Journal (Appendix)]
    Chan, Bert Wang-Chak (2019). Lenia: Biology of Artificial Life. Complex Systems, 28(3), 251–286. arXiv:1812.05433.
    • ๐Ÿ… Outstanding Publication of 2019, by the International Society for Artificial Life (ISAL) (2020-07) [Cert] [Tweet]
    • ๐Ÿ”ฅ Front page @ Hacker News, ๐Ÿ”ฅ Top hype #1 @ Arxiv Sanity, ๐Ÿ”ฅ Top trending #1 @ Papers With Code
Inria
  • ๐Ÿ“ Lenia in Minecraft Open-Endedness Challenge (GECCO 2021) [Website] [Code]
    Etcheverry, Mayalen, Chan, Bert, Moulin-Frier, Clรฉment, & Oudeyer, Pierre-Yves (2021). Meta-Diversity Search in Complex Systems, A Recipe for Artificial Open-Endedness?. [Website]
  • ๐Ÿ“„ Lenia with IMGEP-HOLMES (NeurIPS 2020) [arXiv] [Website] [Code] [Official] [Review (Feedback)]
    Etcheverry, Mayalen, Moulin-Frier, Clรฉment, & Oudeyer, Pierre-Yves (2020). Hierarchically Organized Latent Modules for Exploratory Search in Morphogenetic Systems. NeurIPS 2020 - 34th Conference on Neural Information Processing Systems, Dec 2020, Vancouver / Virtual, Canada. arXiv:2007.01195.
  • ๐Ÿ“„ Lenia with IMGEP (ICLR 2020) [arXiv] [Supplemental] [Website] [Code] [Official] [Review]
    Reinke, Chris, Etcheverry, Mayalen, & Oudeyer, Pierre-Yves (2020). Intrinsically Motivated Discovery of Diverse Patterns in Self-Organizing Systems. International Conference on Learning Representations (ICLR), Apr 2020, Addis Ababa, Ethiopia. arXiv:1908.06663.
Nagoya U
  • ๐Ÿ“„ Asymptotic Lenia (ALIFE 2021) [Proceedings]
    Kawaguchi, Takako, Suzuki, Reiji, Arita, Takaya, & Chan, Bert (2021). Introducing asymptotics to the state-updating rule in Lenia. The 2021 Conference on Artificial Life.
  • ๐Ÿ“„ Asymptotic Lenia (AROB 2021)
    Kawaguchi, Takako, Suzuki, Reiji, & Arita, Takaya (2021). Replacement of the state-updating rule in the continuous cellular automaton model Lenia. Proceedings of the 26th International Symposium on Artificial Life and Robotics, 90–95.
  • ๐Ÿ“„ Asymptotic Lenia (JSMB 2020) [Record]
    Kawaguchi Takako, Suzuki Reiji, & Arita Takaya (2020). Searching for self-organizing lifelike patterns in Lenia model with asymptotic state-updating. The 2020 (30th) annual meeting of the Japanese Society for Mathematical Biology, 30, o21p2–2.
  • ๅทๅฃ่ฒดๅญ, ้ˆดๆœจ้บ—็’ฝ, ๆœ‰็”ฐ้š†ไนŸ. (2020). ็Šถๆ…‹ๆผธ่ฟ‘ๆ›ดๆ–ฐๅž‹LeniaใซใŠใ‘ใ‚‹ใ€Œ็”Ÿ็‰ฉใ€ใฎๆŽข็ดข ๆ—ฅๆœฌๆ•ฐ็†็”Ÿ็‰ฉๅญฆไผšๅนดไผš, 30, o21p2–2.
Code & Web Demo

Coding tutorial: Lenia on GPU:
  • ๐ŸŽจ WebGL testing — species: [One] [Two], gradient: [Linear] [Radial]
  • ๐ŸŽจ Shader demo @ Shadertoy [List]
  • ๐ŸŽจ Shader demo @ Smoothstep.io [#1] [#2]
Lenia on web / Python:
  • ๐ŸŽฎ (upcoming) Lenia educational demo @ Complexity Explorables [Preview] [Website]
  • โŒจ๏ธ Lenia source — Python, R, Jupyter, Matlab, JavaScript [GitHub]
    • Current version: v3.5 LeniaNDKC.py (see Timeline below)
  • ๐ŸŽฎ Lenia web demo [Play now!]
    • Version: v1.3 Lenia.html
Primordia (precursor of Lenia):
  • ๐ŸŽฎ Primordia web demo [Play now!] [GitHub]
    • Version: v1.0 Primordia.html
Talks

  • ๐Ÿ—ฃ Tutorial session @ ALIFE 2021 Prague/cyberspace (2021-07) [Website] [Slides] [Teaser] [ALIFE]
  • ๐Ÿ“ข TV talk show about Lenia and Artificial Life @ RTHK Talk Show Hong Kong (2021-07, cancelled)
  • ๐Ÿ—ฃ Plenary speech @ AROB 2021 Beppu/cyberspace (2021-01-23) [Website]
  • ๐Ÿ“ข Invited live @ Cross Labs Tokyo (2020-08-21) [YouTube] [Website] [Slides]
  • ๐Ÿ—ฃ Presentation @ ALIFE 2020 Montrรฉal/cyberspace (2020-07-16) [YouTube] [Website] [Slides] [Photo @HirokiSayama]
  • ๐Ÿ“ข Invited seminar @ Stanford University (2020-01-15) [YouTube] [Website] [Slides] [Photo]
  • ๐Ÿ—ฃ Presentation @ Hong Kong Code Conf (2018-11-24) [Website] [Slides] [Photo @hkcodeconf]
  • ๐Ÿ—ฃ Presentation @ PyCon Hong Kong (2018-11-24) [YouTube] [Website] [Slides] [Photo @jolliffe]
  • ๐Ÿ—ฃ Presentation @ GECCO 2018 Kyoto (2018-07-15) [Photo @kyrre2000]
Mentions

  • ๐Ÿ“ฐ The Lasting Lessons of John Conwayโ€™s Game of Life - Siobhan Roberts @ New York Times (2020-12) [Website]
  • ๐Ÿ“ Hierarchically-Organized Latent Modules for Exploratory Search in Morphogenetic Systems - Mayalen Etcheverry (2020-06) [Website]
  • ๐Ÿ“ The Recursive Universe - Amanda Ghassaei blog (2020-05) [Website]
  • ๐Ÿ“ฐ Introduction to Artificial Life for People who Like AI - Lana Sinapayen @ The Gradient (2019-11) [Website]
  • ๐Ÿ“ Intrinsically Motivated Discovery of Diverse Patterns in Self-Organizing Systems - Mayalen Etcheverry (2019-11) [Website 1] [Website 2]
  • ๐Ÿ“ Artificial Life, Constraint-Closure and Deep Learning - Carlos E. Perez @ Intuition Machine (2018-07) [Website]
  • ๐Ÿ“ (Japanese) ไบบๅทฅ็”Ÿๅ‘ฝใ‚’ใคใใ‚ŠใŸใ„ - ๆ€ใ†ใจใ“ใ‚ใจใ‚ขใƒ—ใƒญใƒผใƒใฎใƒกใƒข | ALife - BioErrorLog (2020-01) [Website]
  • ๐Ÿ“ (Japanese) ไบบๅทฅ็”Ÿๅ‘ฝใ€€๏ฝž็”Ÿๅ‘ฝใ‚’ไฝฟใ‚ใชใ„็”Ÿๅ‘ฝใฎ็ ”็ฉถ๏ฝž - kuromunoriโ€™s diary (2019-12) [Website]
  • ๐Ÿ“ (Chinese) ็ฎ—ๆณ•ๆ็ป˜็š„โ€œไบบ้€ ็”Ÿๅ‘ฝโ€๏ผŒ่ฟๅŠจๆต็•…่‡ช็„ถ๏ผŒๅฆ‚ๅŒๆ˜พๅพฎ้•œไธ‹็š„ๅฎžๆ™ฏ | Demoยทไปฃ็  - ้‡ๅญไฝ @ ๅพฎๅš (2019-01) [Website]
  • ๐Ÿ“ (Russian) ะ’ั€ะตะผั ะฒ ะบะปะตั‚ะพั‡ะฝะพะผ ะฐะฒั‚ะพะผะฐั‚ะต - Closius @ Habr (2020-02) [Website]
  • ๐Ÿ“ (Spanish) Lenia: los coloridos automรกtas celulares de Bert Chan - ALVY @ Microsiervos (2018-07) [Website]
Timeline (chronological)

  • ๐Ÿœ ca. 1990 - Conway's Game of Life in Pascal + Assembly
  • ๐Ÿ 2015-03 - Primordia in JavaScript (v1.0 JSLife.html โ†’ Primordia.html)
  • ๐Ÿ› 2015-04 - Using real numbers and large neighborhoods (v1.1 PrimordiaReal.html)
    • ๐Ÿ› 2015-04-15 - Discovered Orbium [Photo] [Photo]
    • ๐Ÿ› 2015-05 - Automatic data collection (v1.2 PrimordiaPetri.cs)
    • ๐Ÿ› 2015-07 - Using convolution with FFT (v1.3 PrimordiaFFT.html โ†’ Lenia.html)
    • ๐Ÿ“„ 2015-07 - First draft "Zoology of Smooth Cellular Automata"
  • ๐Ÿฆ‹ 2017-12 - Lenia in MATLAB (v2.0 Lenia.m)
    • ๐Ÿฆ‹ 2018-05 - Lenia in Python (v3.0 Lenia.py)
    • ๐Ÿ“„ 2018-12 - Preprint "Lenia - Biology of Artificial Life" in arXiv
  • ๐ŸŸ 2019-12 - Lenia extensions
    • ๐ŸŸ 2019-12 - Discovered 3D/4D patterns in multi-dimensional extension (v3.1 Lenia3D.py, v3.2 Lenia4D.py) [Tweet] [Tweet]
    • ๐ŸŸ 2020-01 - Generalized dimensions (v3.3 LeniaND.py)
    • ๐Ÿ  2020-01 - Discovered self-replicators in multi-kernel extension (v3.4 LeniaNDK.py) [Tweet]
    • ๐Ÿ  2020-02 - Discovered aggregated patterns in multi-channel extension (v3.5 LeniaNDKC.py) [Tweet] [Tweet]
    • ๐Ÿ  2020-07 - Discovered bizarre cells [Tweet]
  • ๐Ÿก 2020-11 - More discoveries
    • ๐Ÿก 2020-11 - Asymptotic update, discovered smooth glider gun [Tweet]
    • ๐Ÿก 2021-03 - Softclip [Tweet]
    • ๐Ÿฆˆ 2021-05 - Object detection [Tweet]
  • ๐Ÿฆ 2021-05 - Lenia on GPU
    • ๐Ÿฆ 2021-05 - Shader demo @ Shadertoy & Smoothstep.io
    • ๐Ÿฆ€ 2021-06 - WebGL testing, multi-species, gradient
Research Directions

A list of topics that are currently or potentially related to Lenia.
If you are interested in exploring these ideas, feel free to chat on Twitter @BertChakovsky or email albert.chak@gmail.com!
(This is also a self reminder of what can/should be done next)

  • Artificial Life
    • Lenia is an example of continuous cellular automata (CCA), a less explored type of cellular automata within artificial life.
    • As an artificial life system, it is a useful tool in studying emergence, complexity, self-organization, morphogenesis, autopoiesis, etc.
    • Its exploding complexity may provide insights on how to achieve open-ended evolution (OEE) on the road to artificial general intelligence (AGI).
  • Artificial Intelligence
    • Searching of new patterns has been utilizing interactive evolutionary computation (IEC) and genetic algorithms (GA).
    • Further automation will need exploratory algorithms, e.g. intrinsically motivated goal exploration (IMGEP), quality diversity (QD).
    • The extended CA architecture approaches a recurrent residual convolutional neural network (RRCNN), which can be evolved through neuroevolution (e.g. NEAT) and possibly trained using machine learning techniques.
    • There are also suggestions to incorporate with generative adversarial network (GAN) for pattern generation, reinforcement learning (RL) for agent training, multi-agent reinforcement learning, etc.
  • Theoretical Biology
    • Lifelike phenomena being observed in this purely digital system may have implications to astrobiology and the origin of life (OoL).
    • The rise of individuals/agents in this grid-based system could be a subject of integrated information theory (IIT), information theory of individuality (ITI), and swarm cognition.
  • Computer Science
    • Implementation of Lenia is accelerated by fast Fourier transform (FFT) and parallel computing (e.g. GPGPU), and potentially using more advanced hardware like field-programmable gate array (FPGA), software frameworks like web assembly (WASM), open graphics library (OpenGL), web graphics library (WebGL) and the next generation WebGPU and Vulkan.
    • It is an open question whether Lenia is Turing complete and thus able to construct universal Turing machines (UTM), or is capable of other exotic kinds of collision-based computation.
    • Lenia as a dynamical system could be studied using arithmetic information dynamics (AID).
  • Mathematics & Physics
    • The structures of Lenia patterns have been studied for their geometric symmetries (polygonal and polyhedral).
    • Their dynamics have been studied using time series analysis (e.g. recurrence plot, periodogram), and possibly chaos theory.
    • Certain variation of Lenia (e.g. asymptotic Lenia) can be studied as a partial integro-differential equation (PIDE).
    • The self-propagating nature of Lenia patterns may be related to soliton theory.
  • Digital Art
    • Lenia is a source of cool art in computer graphics.
    • Its software is a good exercise in user interface and experience (UI/UX), high-dimensional data visualization, and aesthetics e.g. color schemes.
    • Lenia may also be implemented in virtual reality (VR) or interactive mechanical displays.


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