Grid-Based Cellular Automata (Nutrient-Driven Growth)

A 2D grid-based cellular automata written in modern C++, modeling cell growth, quiescence, necrosis, and division driven by a diffusing nutrient field.
The simulation is rendered in real time using MiniFB.

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Overview

The simulation consists of two coupled grids:

• Cell Grid — discrete cell states (Empty, Alive, Quiescent, Necrotic)
• Nutrient Grid — continuous scalar field in the range [0.0, 1.0]

At each simulation step:

1. Nutrients diffuse across the grid
2. Cells update their state based on local nutrient levels
3. Alive cells may divide into neighboring empty cells
4. The grid is rendered to a window

The model is inspired by tumor-like growth dynamics and reaction-diffusion systems.

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Grid Configuration

Parameter	Value
Grid size	512 × 512
Neighborhood	Von Neumann (up, down, left, right)
Boundary condition	Nutrient source (fixed maximum)

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Cell States

enum class CellState
{
    Empty,
    Alive,
    Quiescent,
    Necrotic
};

State	Description
Empty	No cell present
Alive	Actively dividing, well-fed
Quiescent	Alive but nutrient-limited
Necrotic	Dead tissue (irreversible)

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Nutrient Diffusion

Nutrients spread through the grid via discrete diffusion.

Diffusion Rule

For each non-boundary cell:

new_value = current + diffusionSpeed × (neighbor_average − current)

Only direct neighbors are considered:

• Top
• Left
• Bottom
• Right

Constraints

• Nutrient values are clamped to [0.0, 1.0]
• Boundary cells are continuously refilled to MAX_NUTRIENT
• Diffusion is applied before cell updates

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State Transitions

Cells react to the local nutrient concentration using two thresholds:

• divideThreshold
• deathThreshold

Transition Rules

Current State	Condition	New State
Alive	nutrient < divideThreshold	Quiescent
Quiescent	nutrient ≥ divideThreshold	Alive
Quiescent	nutrient < deathThreshold	Necrotic
Alive	nutrient < deathThreshold	Necrotic
Necrotic	always	Necrotic
Empty	always	Empty

Notes

• Necrotic cells never recover
• Empty cells do not change state
• Only Alive cells are eligible for division

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Cell Division (Mitosis)

Alive cells can divide stochastically.

Division Conditions

A cell may divide if:

• State is Alive
• Nutrient ≥ divideThreshold
• At least one neighboring cell is Empty

Division Process

1. Collect all empty neighboring cells
2. Choose one at random
3. Place a new Alive cell there
4. Reduce parent cell nutrient by divideCost

Constraints

• Maximum one division per cell per step
• Division is probabilistic, not deterministic
• Nutrient cannot go below 0.0

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Visualization

Rendering is handled via MiniFB in real time.

Color Mapping

Cell State	Color
Empty	Black
Alive	Bright Green
Quiescent	Yellow
Necrotic	Blue

Cells fully override the nutrient field visually.

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Simulation Builder

The simulation uses a builder pattern for clean configuration:

CellularAutomata sim =
    SimulationBuilder(cells, nutrients)
        .setDiffusionSpeed(0.08f)
        .setDeathThreshold(0.18f)
        .setDivideThreshold(0.58f)
        .setDivisionCost(0.20f)
        .build();

Tunable Parameters

Parameter	Meaning
diffusionSpeed	Rate of nutrient diffusion
deathThreshold	Nutrient level causing necrosis
divideThreshold	Nutrient level required to divide
divideCost	Nutrient lost during division

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Initial Conditions

Several initialization helpers are provided in main.cpp:

• Sparse random noise
• Central disk
• Multiple clusters
• Small random cluster

Example:

generate_sparse_noise(cells, nutrients, 0.002f, 0.8f);

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Build Instructions

Compile

./comp.sh

Run

./build/cellular_automata

Close the window to terminate the program.

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Dependencies

• C++20
• MiniFB

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Planned Extensions (TODO)

• Custom diffusion models
• Metabolic nutrient consumption
• Nutrient visualization overlay

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License

MIT