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alife Comprehensive Artificial Life skill combining ALIFE2025 proceedings, classic texts (Axelrod, Epstein-Axtell), ALIEN simulation, Lenia, NCA, swarm intelligence, and evolutionary computation. 337 pages extracted, 80+ papers, 153 figures.
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name alife description Comprehensive Artificial Life skill combining ALIFE2025 proceedings, classic texts (Axelrod, Epstein-Axtell), ALIEN simulation, Lenia, NCA, swarm intelligence, and evolutionary computation. 337 pages extracted, 80+ papers, 153 figures.
ALIFE: Artificial Life Comprehensive Skill
Status : ✅ Production Ready
Trit : +1 (PLUS - generative/creative)
Sources : ALIFE2025 Proceedings + Classic Texts + Code Repos
Quick Reference
Resource Content ALIFE2025 337 pages, 80+ papers, 153 figures, 100+ equations Axelrod Evolution of Cooperation, TIT-FOR-TAT, Prisoner's Dilemma Epstein-Axtell Sugarscape, Growing Artificial Societies ALIEN CUDA 2D particle engine (ALIFE 2024 winner) Lenia Continuous cellular automata Concordia DeepMind generative agent-based models
Core Concepts
1. Evolutionary Dynamics
% Fitness-proportionate selection
P(i) = \frac{f_i}{\sum_{j=1}^{N} f_j}
% Replicator dynamics
\dot{x}_i = x_i \left[ f_i(x) - \bar{f}(x) \right]
2. Prisoner's Dilemma & Cooperation
Cooperate Defect
Cooperate R,R S,T
Defect T,S P,P
where T > R > P > S (temptation > reward > punishment > sucker)
TIT-FOR-TAT Strategy (Axelrod):
Cooperate on first move
Then do whatever opponent did last round
Properties: Nice (never defects first), Retaliatory , Forgiving , Clear
3. Cellular Automata Rule 110: [111→0] [110→1] [101→1] [100→0] [011→1] [010→1] [001→1] [000→0]
A^{t+\Delta t} = \left[ A^t + \Delta t \cdot G(K * A^t) \right]_0^1
G_{\mu,\sigma}(x) = 2e^{-\frac{(x-\mu)^2}{2\sigma^2}} - 1
Flow-Lenia (Mass-conserving, arXiv:2506.08569):
% Velocity field from kernel convolution
\vec{v}(x) = \nabla G(K * A^t)
% Mass-conserving update via continuity equation
A^{t+1} = A^t - \nabla \cdot (A^t \cdot \vec{v})
% With multispecies extension
A_i^{t+1} = A_i^t - \nabla \cdot \left(A_i^t \cdot \sum_j w_{ij} \vec{v}_j\right)
\left[\left[A_i^t + \Delta t G(K * A_i^t)\right]_0^1 + \sum_{j \in N(i)} k_{ji} \cdot E_{ji}^t\right]_0^1
4. Neural Cellular Automata def nca_step (grid, model ):
perception = perceive(grid)
delta = model(perception)
mask = torch.rand_like(delta) < 0.5
return grid + delta * mask
5. Agent-Based Models Sugarscape (Epstein-Axtell):
class Agent :
def __init__ (self ):
self .sugar = initial_sugar
self .metabolism = random.randint(1 , 4 )
self .vision = random.randint(1 , 6 )
def move (self, landscape ):
best = max (visible_sites, key=lambda s: s.sugar)
self .position = best
self .sugar += best.sugar - self .metabolism
6. Swarm Intelligence \vec{v}_{new} = w_s \cdot \text{separation} + w_a \cdot \text{alignment} + w_c \cdot \text{cohesion}
7. Chemical Computing BZ Oscillator (Belousov-Zhabotinsky):
Universal computation at linear-bounded automaton level
Coupled oscillators outperform single for complex tasks
8. Active Inference \mathcal{F} = \underbrace{D_{KL}[q(\theta)||p(\theta)]}_{\text{complexity}} + \underbrace{\mathbb{E}_q[-\log p(y|\theta)]}_{\text{accuracy}}
Key Papers (ALIFE2025) Page Title Equations 1 Chemical Computer BZ reservoir 49 Hummingbird Kernel Chaotic LV 73 Neural Cellular Automata NCA rules 99 Language Cellular Automata NLP + CA 103 Lenia Parameter Space Growth functions 107 Evolvable Chemotons Autopoiesis 111 Category Theory for Life CT formalization 127 Swarm2Algo Swarm → Algorithms 135 Open-Ended Evolution in Binary CA Emergence 173 H-Lenia Hierarchical CA 195 Neural Particle Automata Particles 251 Autotelic RL for CA RL + CA 301 Gridarians: LLM-Driven ALife LLM + ALife
Classic Texts
Axelrod - Evolution of Cooperation (1984)
TIT-FOR-TAT wins iterated PD tournaments
Nice strategies dominate in evolution
Cooperation can emerge without central authority
Don't be envious (relative vs absolute success)
Don't be the first to defect
Reciprocate both cooperation and defection
Don't be too clever
Epstein-Axtell - Growing Artificial Societies (1997)
Resource distribution → wealth inequality
Trade → price equilibrium
Combat → territorial patterns
Disease → epidemic dynamics
Culture → group formation
Skewed wealth distributions (power law)
Migration waves
Carrying capacity oscillations
Code Resources
ALIEN (CUDA Particle Engine) /Users/bob/ies/hatchery_repos/bmorphism__alien/
├── source/ # CUDA kernels
├── resources/ # Simulation configs
└── GAY.md # Gay.jl integration
Winner: ALIFE 2024 Virtual Creatures Competition
Lenia Implementations
Python: github.com/Chakazul/Lenia
Julia: github.com/riveSunder/Lenia.jl
Web: chakazul.github.io/Lenia
Concordia (DeepMind GABMs)
from concordia.agents import entity_agent
from concordia.agents.components.v2 import memory_component
from concordia.agents.components.v2 import observation
from concordia.agents.components.v2 import action_spec_ignored
from concordia.associative_memory import associative_memory
from concordia.associative_memory import importance_function
from concordia.clocks import game_clock
from concordia.environment import game_master
from concordia.language_model import gpt_model
clock = game_clock.MultiIntervalClock(
start=datetime.datetime(2024 , 1 , 1 ),
step_sizes=[datetime.timedelta(hours=1 )]
)
mem = associative_memory.AssociativeMemory(
embedder=embedder,
importance=importance_function.ConstantImportanceFunction()
)
agent = entity_agent.EntityAgent(
model=language_model,
memory=mem,
clock=clock,
components=[
observation.Observation(clock=clock, memory=mem),
memory_component.MemoryComponent(memory=mem),
]
)
gm = game_master.GameMaster(
model=language_model,
players=[agent],
clock=clock,
memory=mem
)
Equations Index
Evolution % Mutation-selection balance
\hat{p} = \frac{\mu}{s}
% Wright-Fisher drift
\text{Var}(\Delta p) = \frac{p(1-p)}{2N}
Reaction-Diffusion % Gray-Scott
\frac{\partial u}{\partial t} = D_u \nabla^2 u - uv^2 + f(1-u)
\frac{\partial v}{\partial t} = D_v \nabla^2 v + uv^2 - (f+k)v
Information Theory % Information synergy
I_{\text{syn}}(X \rightarrow Y) = I_{\text{tot}} - \sum_{i=1}^{n} I_{\text{ind}}(X_i)
Lotka-Volterra \frac{dx_i}{dt} = x_i\left(r_i + \sum_{j=1}^{n} A_{ij} x_j\right)
File Locations /Users/bob/ies/paper_extracts/alife2025/
├── ALIFE2025_full.md # 925KB markdown
├── ALIFE2025_tex.zip # 11MB LaTeX
├── tex_extracted/
│ └── fed660c6-.../
│ ├── *.tex # 7283 lines
│ └── images/ # 153 figures
└── conversion_status.json
/Users/bob/ies/
├── axelrod-evolution-of-cooperation.md
├── epstein-axtell-growing-artificial-societies.txt
├── wooldridge-multiagent-systems.txt
└── hatchery_repos/bmorphism__alien/
Gay.jl Integration using Gay
# Theme colors for ALife domains
ALIFE_THEMES = Dict(
:evolution => Gay.color_at(0xEV0L, 1), # Warm
:emergence => Gay.color_at(0xEMRG, 1), # Neutral
:cellular => Gay.color_at(0xCA11, 1), # Cool
:swarm => Gay.color_at(0x5ARM, 1), # Dynamic
:chemical => Gay.color_at(0xCHEM, 1), # Reactive
)
# GF(3) classification
# -1: Structure (CA rules, genomes)
# 0: Process (dynamics, transitions)
# +1: Emergence (patterns, behaviors)
Commands just alife-toc
just alife-paper 42
just alife-equation "lenia"
just alife-axelrod
just alife-sugarscape
just alife-alien
just alife-lenia "orbium"
Executable Commands (bash/python)
python -c "
import jax.numpy as jnp
from leniax import Lenia
lenia = Lenia.from_name('orbium')
state = lenia.init_state(jax.random.PRNGKey(42))
for _ in range(100): state = lenia.step(state)
print(f'Final mass: {state.sum():.2f}')
"
python -c "
from cax import NCA
import jax
nca = NCA(hidden_channels=12)
params = nca.init(jax.random.PRNGKey(0), jnp.zeros((64, 64, 16)))
grid = jax.random.uniform(jax.random.PRNGKey(1), (64, 64, 16))
new_grid = nca.apply(params, grid)
print(f'Grid shape: {new_grid.shape}')
"
python -c "
import axelrod as axl
players = [axl.TitForTat(), axl.Defector(), axl.Cooperator(), axl.Random()]
tournament = axl.Tournament(players, turns=200, repetitions=10)
results = tournament.play()
print(results.ranked_names[:3])
"
python -c "
import numpy as np
class Agent:
def __init__(self): self.x, self.y, self.sugar = 0, 0, 10
def move(self, grid):
neighbors = [(self.x+dx, self.y+dy) for dx,dy in [(-1,0),(1,0),(0,-1),(0,1)]]
best = max(neighbors, key=lambda p: grid[p[0]%50, p[1]%50])
self.x, self.y = best[0]%50, best[1]%50
self.sugar += grid[self.x, self.y]
grid = np.random.rand(50, 50) * 4
agent = Agent(); [agent.move(grid) for _ in range(100)]
print(f'Final sugar: {agent.sugar:.1f}')
"
External Libraries Library Purpose Install Leniax Lenia simulation (JAX, differentiable) pip install leniaxCAX Cellular Automata Accelerated (ICLR 2025) pip install caxLeniabreeder Quality-Diversity for Lenia GitHub ALIEN CUDA particle engine (5.2k⭐) alien-project.org EvoTorch Evolutionary algorithms (PyTorch+Ray) pip install evotorchneat-python NEAT neuroevolution pip install neat-pythonJaxLife Open-ended agentic simulator GitHub
Research Themes Graph graph TB
subgraph Evolution
GA[Genetic Algorithms]
OEE[Open-Ended Evolution]
NS[Natural Selection]
end
subgraph Emergence
CA[Cellular Automata]
NCA[Neural CA]
Lenia[Lenia]
end
subgraph Agents
ABM[Agent-Based Models]
Swarm[Swarm Intelligence]
GABM[Generative ABM]
end
subgraph Chemistry
BZ[BZ Reaction]
Auto[Autopoiesis]
Chem[Artificial Chemistry]
end
GA --> OEE
CA --> NCA --> Lenia
ABM --> Swarm --> GABM
BZ --> Auto --> Chem
OEE --> Emergence
Lenia --> Agents
GABM --> Chemistry
See Also & Skill Interop Primary Interop Skills (load together for full capability):
Skill Interop Command gay-mcpDeterministic coloring of all ALife entities mcp gay palette 12 seed=0x4C454E49acsets-algebraic-databasesLenia/NCA as C-Set schemas @acset_type LeniaGrid(SchLenia)glass-bead-gameCross-domain morphisms (CA↔music↔philosophy) Morphism.new(:lenia, :timbre)self-validation-loopPrediction/observation for CA dynamics validate_ca_step(grid, kernel, seed)algorithmic-artp5.js visualization with Gay.jl palettes just art-lenia seed=0x4C454E49world-hoppingBadiou triangle for parameter space LeniaWorld.hop_to(target)
epistemic-arbitrage - Knowledge transfer across ALife domainshatchery-papers - Academic paper patterns (ALIEN, Lenia papers)bmorphism-stars - Related repositoriestriad-interleave - Three-stream parallel CA updatesbisimulation-game - Skill dispersal with GF(3) conservation
Citations @proceedings{alife2025,
title = {ALIFE 25: Ciphers of Life},
editor = {Witkowski, O. and Adams, A.M. and Sinapayen, L.},
year = {2025},
pages = {337}
}
@book{axelrod1984,
title = {The Evolution of Cooperation},
author = {Axelrod, Robert},
year = {1984},
publisher = {Basic Books}
}
@book{epstein1996,
title = {Growing Artificial Societies},
author = {Epstein, Joshua M. and Axtell, Robert},
year = {1996},
publisher = {MIT Press}
}
Skill Name : alife
Type : Research Reference / Algorithm Library / Simulation Toolkit
Trit : +1 (PLUS - generative)
Mathpix : PDF ID fed660c6-4d3d-4bb6-bb3c-f9b039187660
Exa-Refined Research Index (2025-12-21)
Breakthrough Papers (2024-2025) Theme Paper arXiv Key Innovation Flow-Lenia Emergent evolutionary dynamics 2506.08569 Mass conservation + multispecies Leniabreeder Quality-Diversity for Lenia 2406.04235 MAP-Elites + AURORA ARC-NCA Developmental Solutions 2505.08778 EngramNCA matches GPT-4.5 DiffLogic CA Differentiable Logic Gates 2506.04912 Discrete learnable CA Active Inference Missing Reward 2508.05619 FEP for autonomous agents CT Autopoiesis Autonomy as Closure 2305.15279 Monoid = operational closure
New Equations % Flow-Lenia mass conservation
A^{t+1} = A^t + \nabla \cdot (A^t \cdot \vec{v}(K * A^t))
% EngramNCA hidden memory
h^{t+1} = \sigma(W_h \cdot [v^t, h^t] + b_h)
% DiffLogic gate probability
p(g) = \text{softmax}(\theta_g) \quad g \in \{\text{AND}, \text{OR}, \text{XOR}, ...\}
% Monoid operational closure
\text{Aut}(S) \cong \text{Mon}(\mathcal{C}), \quad |\text{Ob}| = 1
Performance Benchmarks System Task Score vs GPT-4.5 ARC-NCA ARC public 17.6% comparable EngramNCA v3 ARC public 27% 1000x less compute Leniabreeder OEE metrics unbounded N/A
Extended See Also Exa Index : /Users/bob/ies/ALIFE_EXA_REFINED_INDEX.md
ALife atlas Part of: alife-commons. Family: open-ended-evolution. Canonical: alife.
