tempCodeRunnerFile.python

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

def compute_zn(n):
    """Calcule les points zn avec z0 = 16 et zn+1 = ((1+i)/2)zn"""
    if n == 0:
        return [16 + 0j]  # z0 = 16
    
    prev_z = compute_zn(n-1)[-1]
    multiplier = (1 + 1j) / 2  # Le nombre complexe (1+i)/2
    zn = multiplier * prev_z
    
    return compute_zn(n-1) + [zn]

def create_animation():
    # Configuration de la figure
    fig, ax = plt.subplots(figsize=(12, 12))
    ax.set_xlabel('Re(z)')
    ax.set_ylabel('Im(z)')
    ax.set_title('Construction des points zn et lignes Ln')
    
    # Points et lignes à animer
    points, = ax.plot([], [], 'bo', label='Points zn')
    line, = ax.plot([], [], 'r-', label='Ligne Ln')
    
    # Ajout des axes
    ax.axhline(y=0, color='k', linestyle='-', alpha=0.3)
    ax.axvline(x=0, color='k', linestyle='-', alpha=0.3)
    ax.grid(True, alpha=0.3)
    ax.set_aspect('equal')
    ax.legend()
    
    # Pré-calcul de tous les points
    all_zn = compute_zn(20)  # On calcule jusqu'à z20
    
    # Calcul des limites du graphique basé sur les points
    max_coord = max([max(abs(z.real), abs(z.imag)) for z in all_zn])
    margin = max_coord * 0.1
    ax.set_xlim(-max_coord - margin, max_coord + margin)
    ax.set_ylim(-max_coord - margin, max_coord + margin)
    
    def init():
        points.set_data([], [])
        line.set_data([], [])
        return points, line

    def animate(frame):
        ax.cla()  # Clear les annotations précédentes
        ax.grid(True, alpha=0.3)
        ax.set_aspect('equal')
        ax.set_xlim(-max_coord - margin, max_coord + margin)
        ax.set_ylim(-max_coord - margin, max_coord + margin)
        ax.set_xlabel('Re(z)')
        ax.set_ylabel('Im(z)')
        
        n = frame  # Commencer avec n=0
        current_points = all_zn[:n+1]
        
        # Conversion des nombres complexes en coordonnées x,y
        x_coords = [z.real for z in current_points]
        y_coords = [z.imag for z in current_points]
        
        # Annotations des points
        for i, (x, y) in enumerate(zip(x_coords, y_coords)):
            ax.annotate(f'z{i}\n({x:.2f}, {y:.2f}i)', (x, y), 
                       xytext=(10, 10), textcoords='offset points',
                       fontsize=8)
        
        ax.plot(x_coords, y_coords, 'bo-', label='Points et ligne Ln')
        ax.set_title(f'Construction jusqu\'à z{n}')
        ax.legend()
        
        return []

    # Création de l'animation
    anim = FuncAnimation(fig, animate, init_func=init, frames=21,
                        interval=1000, repeat=True)
    
    plt.show()
    return anim

if __name__ == "__main__":
    animation = create_animation()