Alife

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):

1. Cooperate on first move
2. Then do whatever opponent did last round

Properties: Nice (never defects first), Retaliatory, Forgiving, Clear

3. Cellular Automata

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

4. Neural Cellular Automata

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

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):
        # 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

6. Swarm Intelligence

Boid Rules (Reynolds):

\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)

Classic Texts

Axelrod - Evolution of Cooperation (1984)

Key Results:

• TIT-FOR-TAT wins iterated PD tournaments
• Nice strategies dominate in evolution
• Cooperation can emerge without central authority

Tournament Lessons:

1. Don't be envious (relative vs absolute success)
2. Don't be the first to defect
3. Reciprocate both cooperation and defection
4. Don't be too clever

Epstein-Axtell - Growing Artificial Societies (1997)

Sugarscape Phenomena:

• Resource distribution → wealth inequality
• Trade → price equilibrium
• Combat → territorial patterns
• Disease → epidemic dynamics
• Culture → group formation

Emergent Properties:

• 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)

# 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
)

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)

External Libraries

See: LIBRARIES.md for full documentation and code examples

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):

Secondary Skills:

• epistemic-arbitrage - Knowledge transfer across ALife domains
• hatchery-papers - Academic paper patterns (ALIEN, Lenia papers)
• bmorphism-stars - Related repositories
• triad-interleave - Three-stream parallel CA updates
• bisimulation-game - Skill dispersal with GF(3) conservation

See: INTEROP.md for full integration patterns

r2con Speaker Resources

Malware evolution and binary analysis from r2con speakers relevant to ALife:

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)

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

Extended See Also

• Distill Thread: Differentiable Self-Organizing Systems
• Growing Neural CA
• DiffLogic CA Demo
• Concordia GitHub
• ALIEN Project

Exa Index: /Users/bob/ies/ALIFE_EXA_REFINED_INDEX.md

End-of-Skill Interface

Commands

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

Executable Commands (bash/python)

# 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}')
"

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 10. Adventure Game Example

Concepts: autonomous agent, game, synthesis

GF(3) Balanced Triad

alife (−) + SDF.Ch10 (+) + [balancer] (○) = 0

Skill Trit: -1 (MINUS - verification)

Secondary Chapters

• Ch8: Degeneracy
• Ch7: Propagators
• Ch3: Variations on an Arithmetic Theme
• Ch4: Pattern Matching
• Ch5: Evaluation
• Ch6: Layering
• Ch2: Domain-Specific Languages
• Ch1: Flexibility through Abstraction

Connection Pattern

Adventure games synthesize techniques. This skill integrates multiple patterns.