import numpy as np import matplotlib.pyplot as plt from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg, NavigationToolbar2Tk from matplotlib.colors import LinearSegmentedColormap import tkinter as tk from tkinter import ttk, messagebox import time class MandelbrotViewer: def __init__(self, root): self.root = root self.root.title("曼德勃罗集 - 鼠标中心缩放版") self.root.geometry("1200x800") # --- 核心状态变量 --- self.width = 800 self.height = 600 self.max_iter = 200 self.zoom = 1.0 # 初始中心点 (曼德勃罗集主要位于实轴-0.5附近) self.center_x = -0.5 self.center_y = 0.0 # --- UI 初始化 --- self.setup_ui() # --- Matplotlib 设置 --- self.fig, self.ax = plt.subplots(figsize=(8, 6)) self.canvas = FigureCanvasTkAgg(self.fig, master=self.plot_frame) self.canvas.draw() self.canvas.get_tk_widget().pack(fill=tk.BOTH, expand=True) # 绑定鼠标事件 self.canvas.mpl_connect('scroll_event', self.on_scroll_zoom) self.canvas.mpl_connect('button_press_event', self.on_click_pan) # 初始绘制 self.plot_mandelbrot() def setup_ui(self): main_frame = ttk.Frame(self.root) main_frame.pack(fill=tk.BOTH, expand=True) # 左侧控制面板 control_frame = ttk.LabelFrame(main_frame, text="控制中心", padding=10) control_frame.pack(side=tk.LEFT, fill=tk.Y, padx=10, pady=10) # 1. 数字输入控制区 input_frame = ttk.LabelFrame(control_frame, text="数字指令控制", padding=5) input_frame.pack(fill=tk.X, pady=5) ttk.Label(input_frame, text="缩放倍数 (Zoom):").pack(anchor=tk.W) self.zoom_entry = ttk.Entry(input_frame) self.zoom_entry.insert(0, "1.0") self.zoom_entry.pack(fill=tk.X, pady=2) ttk.Label(input_frame, text="最大迭代 (Iter):").pack(anchor=tk.W) self.iter_entry = ttk.Entry(input_frame) self.iter_entry.insert(0, "200") self.iter_entry.pack(fill=tk.X, pady=2) ttk.Button(input_frame, text="应用数字设置", command=self.apply_numeric_settings).pack(fill=tk.X, pady=5) # 2. 快捷操作 btn_frame = ttk.Frame(control_frame) btn_frame.pack(fill=tk.X, pady=10) ttk.Button(btn_frame, text="重置视图", command=self.reset_view).pack( side=tk.LEFT, padx=2) ttk.Button(btn_frame, text="保存图像", command=self.save_image).pack( side=tk.LEFT, padx=2) # 3. 状态显示 self.status_var = tk.StringVar(value="就绪 | 提示: 滚轮以鼠标为中心缩放") ttk.Label(control_frame, textvariable=self.status_var, foreground="green").pack(anchor=tk.W, pady=10) info_text = ("操作指南:\n" "1. 鼠标滚轮: 以指针位置为中心缩放\n" "2. 左键拖拽: 平移视图\n" "3. 左侧输入: 精确控制参数") ttk.Label(control_frame, text=info_text, justify=tk.LEFT, font=("Arial", 9)).pack(anchor=tk.W, pady=10) # 右侧绘图容器 self.plot_frame = ttk.Frame(main_frame) self.plot_frame.pack(side=tk.RIGHT, fill=tk.BOTH, expand=True, padx=10, pady=10) def apply_numeric_settings(self): """根据输入框的数字更新视图""" try: new_zoom = float(self.zoom_entry.get()) new_iter = int(self.iter_entry.get()) if new_zoom <= 0: raise ValueError("缩放倍数必须大于0") if new_iter < 50 or new_iter > 5000: raise ValueError("迭代次数建议在 50-5000 之间") self.zoom = new_zoom self.max_iter = new_iter self.plot_mandelbrot() self.status_var.set( f"已应用: Zoom={self.zoom:.2f}, Iter={self.max_iter}") except Exception as e: messagebox.showerror("输入错误", f"无效的数字输入: {e}") def reset_view(self): self.center_x = -0.5 self.center_y = 0.0 self.zoom = 1.0 self.max_iter = 200 self.zoom_entry.delete(0, tk.END) self.zoom_entry.insert(0, "1.0") self.iter_entry.delete(0, tk.END) self.iter_entry.insert(0, "200") self.plot_mandelbrot() self.status_var.set("视图已重置") def save_image(self): file_path = tk.filedialog.asksaveasfilename( defaultextension=".png", filetypes=[("PNG", "*.png")]) if file_path: self.fig.savefig(file_path, dpi=300, bbox_inches='tight') messagebox.showinfo("成功", "图像已保存") def on_click_pan(self, event): """左键点击平移中心""" if event.inaxes != self.ax: return if event.button == 1: # 左键 self.center_x = event.xdata self.center_y = event.ydata self.plot_mandelbrot() self.status_var.set( f"中心移至: ({self.center_x:.4f}, {self.center_y:.4f})") def on_scroll_zoom(self, event): """ 核心逻辑: 以鼠标位置为中心进行缩放 原理: 1. 获取鼠标在数据坐标系中的位置 (mx, my) 2. 计算缩放前的范围 3. 应用缩放因子 4. 调整中心点，使得 (mx, my) 在缩放后仍然处于屏幕的相同相对位置 """ if event.inaxes != self.ax: return # 获取鼠标在数据坐标中的位置 mx, my = event.xdata, event.ydata if mx is None or my is None: return # 确定缩放因子 scale_factor = 1.1 if event.button == 'up' else 0.9 # 记录旧的缩放比例 old_zoom = self.zoom # 更新缩放比例 self.zoom *= scale_factor # 关键数学推导: 保持鼠标指向的点 (mx, my) 在屏幕上的像素位置不变 # 新中心 = 鼠标点 - (鼠标点 - 旧中心) * (旧缩放 / 新缩放) # 简化理解: 距离鼠标点的偏移量需要随着缩放比例反向调整 ratio = old_zoom / self.zoom self.center_x = mx - (mx - self.center_x) * ratio self.center_y = my - (my - self.center_y) * ratio # 更新UI显示 self.zoom_entry.delete(0, tk.END) self.zoom_entry.insert(0, f"{self.zoom:.4f}") self.plot_mandelbrot() self.status_var.set( f"Zoom: {self.zoom:.4f} | 中心: ({self.center_x:.4f}, {self.center_y:.4f})") def compute_mandelbrot_array(self): """使用 NumPy 向量化计算曼德勃罗集""" # 计算当前视图的边界 # r 是半高对应的复平面半径 r = 2.5 / self.zoom xmin = self.center_x - r * self.width / self.height xmax = self.center_x + r * self.width / self.height ymin = self.center_y - r ymax = self.center_y + r # 生成网格 x = np.linspace(xmin, xmax, self.width) y = np.linspace(ymin, ymax, self.height) X, Y = np.meshgrid(x, y) C = X + 1j * Y # 初始化 Z 和 掩码 Z = np.zeros_like(C) M = np.zeros(C.shape, dtype=int) # 存储发散所需的迭代次数 mask = np.ones(C.shape, dtype=bool) # 标记哪些点还在集合内或未发散 # 迭代 for i in range(self.max_iter): Z[mask] = Z[mask]**2 + C[mask] # 找出本次迭代中发散的点 diverged = np.abs(Z) > 2 # 记录这些点是第几次迭代发散的 M[mask & diverged] = i # 从掩码中移除已发散的点 (不再计算它们) mask &= ~diverged # 未发散的点标记为 max_iter M[mask] = self.max_iter return M, (xmin, xmax, ymin, ymax) def plot_mandelbrot(self): start_time = time.time() self.root.update_idletasks() # 刷新UI显示"计算中" M, extent = self.compute_mandelbrot_array() self.ax.clear() # 使用 imshow 绘制，origin='lower' 使虚轴向上为正 self.ax.imshow(M, extent=extent, cmap='magma', origin='lower') self.ax.set_title(f"Mandelbrot Set (Zoom: {self.zoom:.2f})") self.ax.set_xlabel("Re(c)") self.ax.set_ylabel("Im(c)") # 隐藏刻度以获得更沉浸的体验，或者保留以便观察坐标 # self.ax.set_xticks([]) # self.ax.set_yticks([]) self.canvas.draw() elapsed = time.time() - start_time print(f"Render time: {elapsed:.3f}s") if __name__ == "__main__": root = tk.Tk() app = MandelbrotViewer(root) root.mainloop()