import time
import math

class ManifoldVisualizer:
    """
    Law XII Component: The Aesthetic Eye
    Visualizes the multi-dimensional distribution of TGI atoms in Z_m^k.
    Projects Z_m^4 to a 2D (x, y) grid for terminal monitoring.
    """
    def __init__(self, m=256, k=4, screen_size=40):
        self.m = m
        self.k = k
        self.screen_size = screen_size

    def project_to_2d(self, coord):
        """Project (x, y, z, w) in Z_m^4 to a 2D terminal (px, py) grid."""
        # Simple projection: (x + z) mod screen_size, (y + w) mod screen_size
        px = (coord[0] + coord[2]) % self.screen_size
        py = (coord[1] + coord[3]) % self.screen_size
        return px, py

    def render_manifold(self, manifold):
        """Draw the topological distribution of atoms in the terminal."""
        grid = [[' ' for _ in range(self.screen_size)] for _ in range(self.screen_size)]
        
        # Populate the grid with atoms by fiber type
        fiber_symbols = {1: 'L', 2: 'K', 3: 'A', 0: 'B'}
        
        for coord, atom in manifold.items():
            px, py = self.project_to_2d(coord)
            grid[py][px] = fiber_symbols.get(atom['fiber'], '*')

        print("\n" + "=" * (self.screen_size + 2))
        print(" TGI MANIFOLD MAP (L=Logic, K=Knowledge, A=Aesthetics)")
        print("=" * (self.screen_size + 2))
        for row in grid:
            print("|" + "".join(row) + "|")
        print("=" * (self.screen_size + 2))
        print(f"Total Nodes: {len(manifold)} | Projection: (x+z, y+w) mod {self.screen_size}")

if __name__ == "__main__":
    visualizer = ManifoldVisualizer()
    # Mock manifold
    mock_manifold = {
        (10, 20, 30, 40): {'fiber': 1},
        (100, 150, 200, 250): {'fiber': 2},
        (50, 50, 50, 50): {'fiber': 3},
        (255, 0, 255, 0): {'fiber': 0}
    }
    visualizer.render_manifold(mock_manifold)