import tkinter as tk from tkinter import ttk, messagebox import math import colorsys class FractalApp: def __init__(self, root): self.root = root self.root.title("020. 最复杂的图形 —— 分形生成器") self.root.geometry("900x700") self.root.resizable(False, False) self.canvas = tk.Canvas(root, width=850, height=600, bg="black") self.canvas.pack(pady=10) # 控制面板 ctrl = tk.Frame(root) ctrl.pack(pady=5) tk.Label(ctrl, text="选择分形：", font=("微软雅黑", 11)).pack(side=tk.LEFT) self.choice = ttk.Combobox(ctrl, width=20, state="readonly") self.choice['values'] = ( "科赫雪花", "谢尔宾斯基三角形", "分形树", "曼德勃罗集", "龙形曲线" ) self.choice.current(0) self.choice.pack(side=tk.LEFT, padx=5) tk.Label(ctrl, text=" 迭代次数：").pack(side=tk.LEFT) self.iter_spin = tk.Spinbox(ctrl, from_=1, to=10, width=4) self.iter_spin.pack(side=tk.LEFT, padx=2) self.iter_spin.delete(0, tk.END) self.iter_spin.insert(0, "4") tk.Button(ctrl, text="生成", bg="#4CAF50", fg="white", font=("微软雅黑", 10), width=10, command=self.generate).pack(side=tk.LEFT, padx=10) tk.Button(ctrl, text="清空", bg="#f44336", fg="white", font=("微软雅黑", 10), width=10, command=lambda: self.canvas.delete("all")).pack(side=tk.LEFT) # 信息标签 self.info = tk.Label(root, text="", font=("Consolas", 10), fg="gray") self.info.pack() def generate(self): self.canvas.delete("all") fractal = self.choice.get() try: n = int(self.iter_spin.get()) except: n = 4 cx, cy = 425, 300 if fractal == "科赫雪花": self.draw_koch(cx, cy, n) elif fractal == "谢尔宾斯基三角形": self.draw_sierpinski(cx, cy, n) elif fractal == "分形树": self.draw_fractal_tree(cx, cy, n) elif fractal == "曼德勃罗集": self.draw_mandelbrot() elif fractal == "龙形曲线": self.draw_dragon(cx, cy, n) # ==================== 科赫雪花 ==================== def koch(self, x1, y1, x2, y2, n): if n == 0: self.canvas.create_line(x1, y1, x2, y2, fill="cyan", width=1) return dx = (x2 - x1) / 3 dy = (y2 - y1) / 3 x3 = x1 + dx y3 = y1 + dy x5 = x1 + 2 * dx y5 = y1 + 2 * dy # 等边三角形的顶点 x4 = (x3 + x5) / 2 - math.sin(math.pi / 3) * (y5 - y3) y4 = (y3 + y5) / 2 + math.sin(math.pi / 3) * (x5 - x3) self.koch(x1, y1, x3, y3, n - 1) self.koch(x3, y3, x4, y4, n - 1) self.koch(x4, y4, x5, y5, n - 1) self.koch(x5, y5, x2, y2, n - 1) def draw_koch(self, cx, cy, n): self.info.config(text="科赫雪花：用不断细分的等边三角形构成的无限边界曲线") r = 250 pts = [] for i in range(3): angle = -math.pi / 2 + 2 * math.pi * i / 3 pts.append((cx + r * math.cos(angle), cy + r * math.sin(angle))) for i in range(3): self.koch(pts[i][0], pts[i][1], pts[(i + 1) % 3][0], pts[(i + 1) % 3][1], n) # ==================== 谢尔宾斯基三角形 ==================== def sierpinski(self, x1, y1, x2, y2, x3, y3, n): if n == 0: self.canvas.create_polygon(x1, y1, x2, y2, x3, y3, fill="", outline="magenta", width=1) return mx1 = (x1 + x2) / 2 my1 = (y1 + y2) / 2 mx2 = (x2 + x3) / 2 my2 = (y2 + y3) / 2 mx3 = (x1 + x3) / 2 my3 = (y1 + y3) / 2 self.sierpinski(x1, y1, mx1, my1, mx3, my3, n - 1) self.sierpinski(mx1, my1, x2, y2, mx2, my2, n - 1) self.sierpinski(mx3, my3, mx2, my2, x3, y3, n - 1) def draw_sierpinski(self, cx, cy, n): self.info.config(text="谢尔宾斯基三角形：不断挖去中心三角形的递归结构") r = 280 h = r * math.sqrt(3) / 2 pts = [ (cx, cy - h * 2 / 3), (cx - r, cy + h / 3), (cx + r, cy + h / 3) ] self.sierpinski(pts[0][0], pts[0][1], pts[1][0], pts[1][1], pts[2][0], pts[2][1], n) # ==================== 分形树 ==================== def fractal_tree(self, x, y, angle, length, n, color): if n == 0 or length < 2: return x2 = x + length * math.cos(angle) y2 = y + length * math.sin(angle) # 根据深度变色 if n > 3: c = "saddlebrown" elif n > 1: c = "forestgreen" else: c = "limegreen" self.canvas.create_line(x, y, x2, y2, fill=c, width=max(1, n)) new_len = length * 0.7 self.fractal_tree(x2, y2, angle - math.pi / 6, new_len, n - 1, c) self.fractal_tree(x2, y2, angle + math.pi / 6, new_len, n - 1, c) def draw_fractal_tree(self, cx, cy, n): self.info.config(text="分形树：模拟自然界中树枝的递归生长模式") self.fractal_tree(cx, cy, -math.pi / 2, 120, n, "brown") # ==================== 曼德勃罗集 ==================== def draw_mandelbrot(self): self.info.config(text="曼德勃罗集：z = z² + c 迭代不发散的复数集合（最著名的分形）") w, h = 850, 600 xmin, xmax = -2.2, 0.8 ymin, ymax = -1.2, 1.2 max_iter = 50 for px in range(0, w, 2): for py in range(0, h, 2): x0 = xmin + (xmax - xmin) * px / w y0 = ymin + (ymax - ymin) * py / h x, y = 0, 0 iteration = 0 while x * x + y * y <= 4 and iteration < max_iter: x_new = x * x - y * y + x0 y = 2 * x * y + y0 x = x_new iteration += 1 if iteration == max_iter: color = "black" else: # 映射到彩色 hue = iteration / max_iter r, g, b = colorsys.hsv_to_rgb(hue, 1.0, 1.0) color = f"#{int(r*255):02x}{int(g*255):02x}{int(b*255):02x}" self.canvas.create_rectangle(px, py, px + 1, py + 1, fill=color, outline="") # ==================== 龙形曲线 ==================== def dragon(self, points, n): if n == 0: return points new_pts = [points[0]] for i in range(len(points) - 1): x1, y1 = points[i] x2, y2 = points[i + 1] # 取中点，然后旋转90度 mx = (x1 + x2) / 2 my = (y1 + y2) / 2 dx = x2 - x1 dy = y2 - y1 # 旋转90度 nx = mx - dy / 2 ny = my + dx / 2 new_pts.append((nx, ny)) new_pts.append(points[i + 1]) return new_pts def draw_dragon(self, cx, cy, n): self.info.config(text="龙形曲线：反复折叠一条线段产生的空间填充曲线") # 初始线段 pts = [(cx - 200, cy), (cx + 200, cy)] for _ in range(n): pts = self.dragon(pts, 0) for i in range(len(pts) - 1): x1, y1 = pts[i] x2, y2 = pts[i + 1] ratio = i / len(pts) r = int(255 * ratio) b = int(255 * (1 - ratio)) color = f"#{r:02x}00{b:02x}" self.canvas.create_line(x1, y1, x2, y2, fill=color, width=1) if __name__ == "__main__": root = tk.Tk() app = FractalApp(root) root.mainloop()