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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Status: ✅ Production Ready Trit: +1 (PLUS - generative/creative) Sources: ALIFE2025 Proceedings + Classic Texts + Code Repos
| 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 |
% 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]
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):
Properties: Nice (never defects first), Retaliatory, Forgiving, Clear
Elementary CA (Wolfram):
Rule 110: [111→0] [110→1] [101→1] [100→0] [011→1] [010→1] [001→1] [000→0]
Lenia (Continuous CA):
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)
H-Lenia (Hierarchical):
\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
def nca_step(grid, model):
# Perceive: Sobel filters for gradients
perception = perceive(grid) # [identity, sobel_x, sobel_y, ...]
# Update: Neural network
delta = model(perception)
# Apply with stochastic mask
mask = torch.rand_like(delta) < 0.5
return grid + delta * mask
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):
# Look in cardinal directions up to vision
best = max(visible_sites, key=lambda s: s.sugar)
self.position = best
self.sugar += best.sugar - self.metabolism
Boid Rules (Reynolds):
\vec{v}_{new} = w_s \cdot \text{separation} + w_a \cdot \text{alignment} + w_c \cdot \text{cohesion}
BZ Oscillator (Belousov-Zhabotinsky):
\mathcal{F} = \underbrace{D_{KL}[q(\theta)||p(\theta)]}_{\text{complexity}} + \underbrace{\mathbb{E}_q[-\log p(y|\theta)]}_{\text{accuracy}}
| 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 |
Key Results:
Tournament Lessons:
Sugarscape Phenomena:
Emergent Properties:
/Users/bob/ies/hatchery_repos/bmorphism__alien/
├── source/ # CUDA kernels
├── resources/ # Simulation configs
└── GAY.md # Gay.jl integration
Winner: ALIFE 2024 Virtual Creatures Competition
github.com/Chakazul/Leniagithub.com/riveSunder/Lenia.jlchakazul.github.io/Lenia# Full import paths for Concordia generative ABM
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 # or gemini_model
# Initialize clock and memory
clock = game_clock.MultiIntervalClock(
start=datetime.datetime(2024, 1, 1),
step_sizes=[datetime.timedelta(hours=1)]
)
# Associative memory with embeddings
mem = associative_memory.AssociativeMemory(
embedder=embedder, # sentence-transformers or similar
importance=importance_function.ConstantImportanceFunction()
)
# Create LLM-driven agent with components
agent = entity_agent.EntityAgent(
model=language_model,
memory=mem,
clock=clock,
components=[
observation.Observation(clock=clock, memory=mem),
memory_component.MemoryComponent(memory=mem),
]
)
# Game master orchestrates environment
gm = game_master.GameMaster(
model=language_model,
players=[agent],
clock=clock,
memory=mem
)
% Mutation-selection balance
\hat{p} = \frac{\mu}{s}
% Wright-Fisher drift
\text{Var}(\Delta p) = \frac{p(1-p)}{2N}
% 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 synergy
I_{\text{syn}}(X \rightarrow Y) = I_{\text{tot}} - \sum_{i=1}^{n} I_{\text{ind}}(X_i)
\frac{dx_i}{dt} = x_i\left(r_i + \sum_{j=1}^{n} A_{ij} x_j\right)
/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/
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)
just alife-toc # Full table of contents
just alife-paper 42 # Get paper at page 42
just alife-equation "lenia" # Find Lenia equations
just alife-axelrod # Axelrod summary
just alife-sugarscape # Sugarscape patterns
just alife-alien # ALIEN simulation info
just alife-lenia "orbium" # Lenia creature lookup
# Run Lenia simulation (via leniax)
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}')
"
# Run NCA step (via cax)
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}')
"
# TIT-FOR-TAT simulation
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])
"
# Sugarscape-style agent (simplified)
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}')
"
| Library | Purpose | Install |
|---|---|---|
| Leniax | Lenia simulation (JAX, differentiable) | pip install leniax |
| CAX | Cellular Automata Accelerated (ICLR 2025) | pip install cax |
| Leniabreeder | Quality-Diversity for Lenia | GitHub |
| ALIEN | CUDA particle engine (5.2k⭐) | alien-project.org |
| EvoTorch | Evolutionary algorithms (PyTorch+Ray) | pip install evotorch |
| neat-python | NEAT neuroevolution | pip install neat-python |
| JaxLife | Open-ended agentic simulator | GitHub |
See: LIBRARIES.md for full documentation and code examples
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
Primary Interop Skills (load together for full capability):
| Skill | Interop | Command |
|---|---|---|
gay-mcp | Deterministic coloring of all ALife entities | mcp gay palette 12 seed=0x4C454E49 |
acsets-algebraic-databases | Lenia/NCA as C-Set schemas | @acset_type LeniaGrid(SchLenia) |
glass-bead-game | Cross-domain morphisms (CA↔music↔philosophy) | Morphism.new(:lenia, :timbre) |
self-validation-loop | Prediction/observation for CA dynamics | validate_ca_step(grid, kernel, seed) |
algorithmic-art | p5.js visualization with Gay.jl palettes | just art-lenia seed=0x4C454E49 |
world-hopping | Badiou triangle for parameter space | LeniaWorld.hop_to(target) |
Secondary Skills:
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) conservationSee: INTEROP.md for full integration patterns
@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
| 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 |
% 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
| 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 |
Exa Index: /Users/bob/ies/ALIFE_EXA_REFINED_INDEX.md
Part of: alife-commons. Family: open-ended-evolution. Canonical: alife.
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