import math

class FibonacciLattice:
    def __init__(self, nodes=144):
        self.nodes = nodes
        self.phi = (1 + math.sqrt(5)) / 2
        self.lattice = []

    def generate_lattice(self):
        print(f"Generating {self.nodes}-node Fibonacci lattice...")
        for i in range(self.nodes):
            # Phi-recursive distribution logic
            theta = 2 * math.pi * i / self.phi
            phi_val = math.acos(1 - 2 * (i + 0.5) / self.nodes)
            x = math.cos(theta) * math.sin(phi_val)
            y = math.sin(theta) * math.sin(phi_val)
            z = math.cos(phi_val)
            self.lattice.append((x, y, z))
        print("Lattice generation complete.")
        return self.lattice

    def get_node_frequency(self, node_index):
        # phi-recursive frequency logic
        return math.pow(self.phi, 12) * (node_index + 1)

if __name__ == "__main__":
    lattice = FibonacciLattice()
    points = lattice.generate_lattice()
    print(f"Sample node frequency: {lattice.get_node_frequency(143):.2f} Hz")