diff --git a/cellular_automata/von_neumann.py b/cellular_automata/von_neumann.py
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+"""
+Von Neumann cellular automaton with multi-state fading "heatmap" effect.
+
+This implementation demonstrates a Von Neumann cellular automaton where cells
+follow custom birth/survive rules and dead cells fade gradually through multiple
+visual states, creating a heatmap-like effect.
+
+Based on Von Neumann cellular automata architecture:
+https://en.wikipedia.org/wiki/Von_Neumann_cellular_automaton
+
+Von Neumann neighborhood reference:
+https://en.wikipedia.org/wiki/Von_Neumann_neighborhood
+
+Requirements: numpy
+"""
+
+import numpy as np
+
+
+def create_random_grid(
+    rows: int, columns: int, alive_probability: float, seed: int | None = None
+) -> np.ndarray:
+    """
+    Create initial grid with randomly distributed alive cells.
+
+    Args:
+        rows: Number of grid rows
+        columns: Number of grid columns
+        alive_probability: Probability (0.0-1.0) of each cell being initially alive
+        seed: Random seed for reproducibility
+
+    Returns:
+        2D numpy array where 1 represents alive cells, 0 represents dead cells
+
+    Raises:
+        ValueError: If alive_probability is not between 0 and 1
+        ValueError: If rows or columns are not positive integers
+
+    Examples:
+        >>> grid = create_random_grid(3, 3, 0.5, seed=42)
+        >>> grid.shape
+        (3, 3)
+        >>> bool(np.all((grid == 0) | (grid == 1)))
+        True
+        >>> grid.dtype
+        dtype('uint8')
+
+        >>> create_random_grid(0, 3, 0.5)  # doctest: +IGNORE_EXCEPTION_DETAIL
+        Traceback (most recent call last):
+        ValueError: Rows and columns must be positive integers
+
+        >>> create_random_grid(3, 3, 1.5)  # doctest: +IGNORE_EXCEPTION_DETAIL
+        Traceback (most recent call last):
+        ValueError: alive_probability must be between 0.0 and 1.0
+    """
+    if rows <= 0 or columns <= 0:
+        raise ValueError("Rows and columns must be positive integers")
+    if not 0.0 <= alive_probability <= 1.0:
+        raise ValueError("alive_probability must be between 0.0 and 1.0")
+
+    rng = np.random.default_rng(seed)
+    alive_cells = (rng.random((rows, columns)) < alive_probability).astype(np.uint8)
+    return alive_cells
+
+
+def count_von_neumann_neighbors(
+    alive_mask: np.ndarray, use_wraparound: bool = True
+) -> np.ndarray:
+    """
+    Count Von Neumann neighbors for each cell (4-directional neighborhood).
+
+    The Von Neumann neighborhood consists of the four orthogonally adjacent cells
+    (up, down, left, right) but excludes diagonal neighbors.
+
+    Args:
+        alive_mask: Binary 2D array where 1 represents alive cells
+        use_wraparound: If True, edges wrap around (toroidal topology)
+
+    Returns:
+        2D array with neighbor counts (0-4) for each cell
+
+    Raises:
+        ValueError: If alive_mask is not 2D or contains invalid values
+
+    Examples:
+        >>> mask = np.array([[1, 0, 1], [0, 1, 0], [1, 0, 1]], dtype=np.uint8)
+        >>> counts = count_von_neumann_neighbors(mask, use_wraparound=False)
+        >>> int(counts[1, 1])  # center cell has 0 neighbors (all adjacent are 0)
+        0
+        >>> int(counts[0, 1])  # top middle has 3 neighbors (down, left, right)
+        3
+
+        >>> mask_simple = np.array([[1, 1], [1, 0]], dtype=np.uint8)
+        >>> counts_simple = count_von_neumann_neighbors(
+        ...     mask_simple, use_wraparound=False
+        ... )
+        >>> int(counts_simple[0, 0])  # top-left has 2 neighbors (right and down)
+        2
+
+        >>> invalid_mask = np.array([1, 2, 3])  # doctest: +IGNORE_EXCEPTION_DETAIL
+        >>> count_von_neumann_neighbors(invalid_mask)
+        Traceback (most recent call last):
+        ValueError: alive_mask must be a 2D array
+    """
+    if alive_mask.ndim != 2:
+        raise ValueError("alive_mask must be a 2D array")
+    if not np.all((alive_mask == 0) | (alive_mask == 1)):
+        raise ValueError("alive_mask must contain only 0s and 1s")
+
+    rows, cols = alive_mask.shape
+    neighbor_counts = np.zeros((rows, cols), dtype=np.uint8)
+
+    if use_wraparound:
+        # Use rolling for wraparound
+        up_neighbors = np.roll(alive_mask, -1, axis=0)
+        down_neighbors = np.roll(alive_mask, 1, axis=0)
+        left_neighbors = np.roll(alive_mask, -1, axis=1)
+        right_neighbors = np.roll(alive_mask, 1, axis=1)
+        neighbor_counts = (
+            up_neighbors + down_neighbors + left_neighbors + right_neighbors
+        )
+    else:
+        # Manually count neighbors without wraparound
+        for r in range(rows):
+            for c in range(cols):
+                count = 0
+                # Check up
+                if r > 0 and alive_mask[r - 1, c]:
+                    count += 1
+                # Check down
+                if r < rows - 1 and alive_mask[r + 1, c]:
+                    count += 1
+                # Check left
+                if c > 0 and alive_mask[r, c - 1]:
+                    count += 1
+                # Check right
+                if c < cols - 1 and alive_mask[r, c + 1]:
+                    count += 1
+                neighbor_counts[r, c] = count
+
+    return neighbor_counts
+
+
+def apply_cellular_automaton_rules(
+    current_ages: np.ndarray,
+    birth_neighbor_counts: set[int],
+    survival_neighbor_counts: set[int],
+    maximum_age: int = 5,
+    use_wraparound: bool = True,
+) -> np.ndarray:
+    """
+    Apply cellular automaton rules to advance the grid by one generation.
+
+    Cells are born when they have a neighbor count in birth_neighbor_counts.
+    Living cells survive when they have a neighbor count in survival_neighbor_counts.
+    Dead cells age and eventually disappear completely.
+
+    Args:
+        current_ages: 2D array where values represent cell ages (0 = dead, >0 = alive)
+        birth_neighbor_counts: Set of neighbor counts that cause cell birth
+        survival_neighbor_counts: Set of neighbor counts that allow cell survival
+        maximum_age: Maximum age before cell disappears completely
+        use_wraparound: Whether to use wraparound boundaries
+
+    Returns:
+        New 2D array with updated cell ages after applying rules
+
+    Raises:
+        ValueError: If inputs are invalid
+
+    Examples:
+        >>> ages = np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]], dtype=np.uint8)
+        >>> new_ages = apply_cellular_automaton_rules(
+        ...     ages, birth_neighbor_counts={2},
+        ...     survival_neighbor_counts={2, 3}, use_wraparound=False
+        ... )
+        >>> # corner should be born (2 neighbors: right and down)
+        >>> bool(new_ages[0, 0] > 0)
+        True
+
+        >>> # Test aging of dead cells
+        >>> dead_aging = np.array([[2, 0, 0]], dtype=np.uint8)  # age 2, no survival
+        >>> result = apply_cellular_automaton_rules(
+        ...     dead_aging, birth_neighbor_counts=set(),
+        ...     survival_neighbor_counts=set(), maximum_age=3
+        ... )
+        >>> bool(result[0, 0] == 3)  # should age from 2 to 3
+        True
+
+        >>> apply_cellular_automaton_rules(
+        ...     np.array([1, 2]), {1}, {1}
+        ... )  # doctest: +IGNORE_EXCEPTION_DETAIL
+        Traceback (most recent call last):
+        ValueError: current_ages must be a 2D array
+    """
+    if current_ages.ndim != 2:
+        raise ValueError("current_ages must be a 2D array")
+    if maximum_age < 1:
+        raise ValueError("maximum_age must be at least 1")
+
+    alive_cells_mask = current_ages > 0
+    neighbor_counts = count_von_neumann_neighbors(
+        alive_cells_mask.astype(np.uint8), use_wraparound
+    )
+
+    # Determine which cells are born or survive
+    birth_mask = (~alive_cells_mask) & np.isin(
+        neighbor_counts, list(birth_neighbor_counts)
+    )
+    survival_mask = alive_cells_mask & np.isin(
+        neighbor_counts, list(survival_neighbor_counts)
+    )
+
+    new_ages = current_ages.copy()
+
+    # Set ages for newly born cells
+    new_ages[birth_mask] = 1
+
+    # Reset age for surviving cells (keeps them visually fresh)
+    new_ages[survival_mask] = 1
+
+    # Age cells that neither survive nor get born
+    fade_mask = (~birth_mask) & (~survival_mask)
+    new_ages[fade_mask & (new_ages > 0)] += 1
+
+    # Remove cells that have exceeded maximum age
+    new_ages[new_ages > maximum_age] = 0
+
+    return new_ages
+
+
+def simulate_von_neumann_cellular_automaton(
+    grid_rows: int = 20,
+    grid_columns: int = 40,
+    initial_alive_probability: float = 0.25,
+    birth_rules: set[int] | None = None,
+    survival_rules: set[int] | None = None,
+    maximum_cell_age: int = 5,
+    generations: int = 100,
+    random_seed: int | None = None,
+    use_wraparound_edges: bool = True,
+) -> list[np.ndarray]:
+    """
+    Run a complete Von Neumann cellular automaton simulation.
+
+    This function creates an initial random grid and evolves it through multiple
+    generations according to the specified birth and survival rules.
+
+    Args:
+        grid_rows: Number of rows in the grid
+        grid_columns: Number of columns in the grid
+        initial_alive_probability: Initial probability of cells being alive
+        birth_rules: Set of neighbor counts that cause birth (default: {3})
+        survival_rules: Set of neighbor counts that allow survival (default: {1, 2})
+        maximum_cell_age: Maximum age before cells disappear (default: 5)
+        generations: Number of generations to simulate
+        random_seed: Seed for random number generation
+        use_wraparound_edges: Whether to use toroidal topology
+
+    Returns:
+        List of 2D numpy arrays representing each generation
+
+    Raises:
+        ValueError: If parameters are invalid
+
+    Examples:
+        >>> result = simulate_von_neumann_cellular_automaton(
+        ...     grid_rows=5, grid_columns=5, generations=3, random_seed=42
+        ... )
+        >>> len(result) == 3
+        True
+        >>> all(grid.shape == (5, 5) for grid in result)
+        True
+
+        >>> simulate_von_neumann_cellular_automaton(
+        ...     generations=0
+        ... )  # doctest: +IGNORE_EXCEPTION_DETAIL
+        Traceback (most recent call last):
+        ValueError: generations must be positive
+    """
+    if birth_rules is None:
+        birth_rules = {3}
+    if survival_rules is None:
+        survival_rules = {1, 2}
+
+    if generations <= 0:
+        raise ValueError("generations must be positive")
+    if grid_rows <= 0 or grid_columns <= 0:
+        raise ValueError("grid dimensions must be positive")
+
+    # Initialize grid
+    current_grid = create_random_grid(
+        grid_rows, grid_columns, initial_alive_probability, random_seed
+    )
+
+    generation_history = []
+
+    # Run simulation for specified number of generations
+    for _ in range(generations):
+        generation_history.append(current_grid.copy())
+        current_grid = apply_cellular_automaton_rules(
+            current_grid,
+            birth_rules,
+            survival_rules,
+            maximum_cell_age,
+            use_wraparound_edges,
+        )
+
+    return generation_history
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod(verbose=True)