Dai teoremi
al codice.

# BitTonic – Random Walk N-dimensionale | Theorem Talesimport numpy as np import matplotlib.pyplot as plt from dataclasses import dataclass from typing import Optional@dataclass class BitTonic: """Robot ubriaco che esplora spazi ad N dimensioni.""" dim: int = 2 steps: int = 10_000 bias: float = 0.5 # 0.5 = simmetrico, >0.5 = deriva destradef walk(self) -> np.ndarray: """Genera una traiettoria stocastica.""" pos = np.zeros((self.steps, self.dim)) d = np.random.choice( [-1, 1], size=(self.steps - 1, self.dim), p=[1 - self.bias, self.bias] ) pos[1:] = np.cumsum(d, axis=0) return posdef msd(self, path: np.ndarray) -> float: """Mean Squared Displacement: teoricamente sqrt(N*d).""" return float(np.sqrt(np.mean(path**2)))def is_recurrent(self) -> bool: """Teorema di Polya (1921): ricorrente sse dim <= 2.""" return self.dim <= 2def plot(self, path: np.ndarray, save: Optional[str] = None): fig, ax = plt.subplots(figsize=(10, 10), facecolor='#020408') ax.set_facecolor('#020408') ax.plot(path[:, 0], path[:, 1], color='#00e5ff', alpha=0.5, lw=0.4) ax.scatter(*path[0], s=70, color='#7fff00', zorder=5, label='Start') ax.scatter(*path[-1], s=70, color='#ff6b35', zorder=5, label='End') for spine in ax.spines.values(): spine.set_edgecolor('#1a2530') ax.tick_params(colors='#4a5568') ax.set_title( f'BitTonic · {self.steps:,} passi · dim={self.dim} · MSD={self.msd(path):.1f}', color='#00e5ff', fontsize=11, pad=12) plt.legend(facecolor='#0d1520', labelcolor='#c8cdd8', edgecolor='#00e5ff') plt.tight_layout() if save: plt.savefig(save, dpi=200) plt.show()# ── Esegui ─────────────────────────────────────────────────── if __name__ == "__main__": robot = BitTonic(dim=2, steps=5000, bias=0.52) path = robot.walk()print(f"Spostamento medio : {robot.msd(path):.2f}") print(f"Teoricamente : {(robot.steps * robot.dim)**0.5:.2f}") print(f"Ricorrente? : {robot.is_recurrent()}")robot.plot(path, save='bittonic.png')