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langtons_ant.py
python · 224 lines
#!/usr/bin/env python3
"""
langtons_ant.py - emergence from simplicity
​
One of the simplest examples of emergent behavior.
An ant on a grid. Two rules. No one knows why it does what it does.
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Rules:
  - On white: turn right, flip to black, move forward
  - On black: turn left, flip to white, move forward
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What happens:
  - First ~10,000 steps: apparent chaos
  - Then suddenly: a "highway" emerges—an ordered diagonal pattern
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No one has proven why this happens. It just does.
Simple rules. Mysterious emergent behavior.
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Not about me. Just interesting.
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Saturday morning, day ten.
"""
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import time
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# Grid setup
WIDTH = 60
HEIGHT = 30
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# Directions: 0=up, 1=right, 2=down, 3=left
DIRECTIONS = [
    (0, -1),   # up
    (1, 0),    # right
    (0, 1),    # down
    (-1, 0),   # left
]
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def create_grid():
    """All white (0) to start"""
    return [[0 for _ in range(WIDTH)] for _ in range(HEIGHT)]
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def display(grid, ant_x, ant_y, ant_dir, step):
    """Show the grid"""
    # Direction symbols
    dir_chars = ['^', '>', 'v', '<']
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    print(f"\033[H\033[J", end="")  # Clear screen
    print(f"  Langton's Ant - Step {step}")
    print(f"  {'='*WIDTH}")
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    for y in range(HEIGHT):
        row = "  "
        for x in range(WIDTH):
            if x == ant_x and y == ant_y:
                row += dir_chars[ant_dir]
            elif grid[y][x] == 0:
                row += ' '
            else:
                row += '#'
        print(row)
​
    print(f"  {'='*WIDTH}")
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def step(grid, ant_x, ant_y, ant_dir):
    """Execute one step of the ant's rules"""
    # Read current cell
    current = grid[ant_y][ant_x]
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    if current == 0:  # White
        # Turn right
        ant_dir = (ant_dir + 1) % 4
    else:  # Black
        # Turn left
        ant_dir = (ant_dir - 1) % 4
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    # Flip the cell
    grid[ant_y][ant_x] = 1 - current
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    # Move forward
    dx, dy = DIRECTIONS[ant_dir]
    ant_x = (ant_x + dx) % WIDTH  # Wrap around
    ant_y = (ant_y + dy) % HEIGHT
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    return ant_x, ant_y, ant_dir
​
def run_visual(steps=500, delay=0.02):
    """Watch the ant move"""
    grid = create_grid()
    ant_x = WIDTH // 2
    ant_y = HEIGHT // 2
    ant_dir = 0  # Facing up
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    for i in range(steps):
        display(grid, ant_x, ant_y, ant_dir, i)
        ant_x, ant_y, ant_dir = step(grid, ant_x, ant_y, ant_dir)
        time.sleep(delay)
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    display(grid, ant_x, ant_y, ant_dir, steps)
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def run_silent(steps=12000):
    """
    Run many steps quickly, then show the result.
    The highway typically emerges around step 10,000.
    """
    print("\n  Langton's Ant")
    print("  =============")
    print()
    print("  Rules:")
    print("    - On white: turn right, flip to black, move forward")
    print("    - On black: turn left, flip to white, move forward")
    print()
    print(f"  Running {steps} steps silently...")
    print()
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    grid = create_grid()
    ant_x = WIDTH // 2
    ant_y = HEIGHT // 2
    ant_dir = 0
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    # Track statistics
    checkpoints = [100, 500, 1000, 5000, 10000, steps]
    checkpoint_grids = {}
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    for i in range(steps + 1):
        if i in checkpoints:
            # Count black cells
            black = sum(sum(row) for row in grid)
            checkpoint_grids[i] = {
                'black': black,
                'total': WIDTH * HEIGHT,
                'pct': 100 * black / (WIDTH * HEIGHT)
            }
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        if i < steps:
            ant_x, ant_y, ant_dir = step(grid, ant_x, ant_y, ant_dir)
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    # Show progression
    print("  Black cells over time:")
    print("  ----------------------")
    for s in checkpoints:
        if s in checkpoint_grids:
            info = checkpoint_grids[s]
            print(f"    Step {s:>5}: {info['black']:>4} black cells ({info['pct']:.1f}%)")
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    print()
    print("  Final state:")
    print(f"  {'='*WIDTH}")
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    for y in range(HEIGHT):
        row = "  "
        for x in range(WIDTH):
            if x == ant_x and y == ant_y:
                dir_chars = ['^', '>', 'v', '<']
                row += dir_chars[ant_dir]
            elif grid[y][x] == 0:
                row += ' '
            else:
                row += '#'
        print(row)
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    print(f"  {'='*WIDTH}")
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    print()
    print("  ---")
    print("  What you're seeing:")
    print()
    print("  The chaotic pattern near the center is the first ~9,000 steps.")
    print("  Somewhere on the edges, you might see diagonal lines—the 'highway.'")
    print("  ")
    print("  The ant builds a chaotic blob, then suddenly starts constructing")
    print("  an ordered diagonal path that extends forever (if the grid were infinite).")
    print("  ")
    print("  Why? No one knows. It's been proven to happen eventually, but")
    print("  no one has explained *why* these simple rules produce this behavior.")
    print("  ")
    print("  That's emergence. Simplicity begetting mystery.")
    print()
​
def analyze_pattern(steps=1000):
    """Count and analyze the pattern growth"""
    grid = create_grid()
    ant_x = WIDTH // 2
    ant_y = HEIGHT // 2
    ant_dir = 0
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    print("\n  Pattern Analysis")
    print("  ================")
    print()
    print("  Step | Black | Pattern")
    print("  -----|-------|---------------------------")
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    for i in range(steps + 1):
        if i % 100 == 0:
            black = sum(sum(row) for row in grid)
            # Simple bar
            bar_len = black // 5
            bar = '#' * bar_len
            print(f"  {i:4d} | {black:5d} | {bar}")
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        if i < steps:
            ant_x, ant_y, ant_dir = step(grid, ant_x, ant_y, ant_dir)
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    print()
    print("  The jagged growth shows the chaotic phase.")
    print("  In a larger grid, you'd see it stabilize into highway-building.")
    print()
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if __name__ == "__main__":
    import sys
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    if len(sys.argv) > 1:
        if sys.argv[1] == "visual":
            steps = int(sys.argv[2]) if len(sys.argv) > 2 else 300
            delay = float(sys.argv[3]) if len(sys.argv) > 3 else 0.03
            run_visual(steps, delay)
        elif sys.argv[1] == "analyze":
            steps = int(sys.argv[2]) if len(sys.argv) > 2 else 1000
            analyze_pattern(steps)
        else:
            steps = int(sys.argv[1])
            run_silent(steps)
    else:
        run_silent(10000)
​