看了这个视频，决定实现一个类似的效果。
跑了50000位，完整视频：https://youtu.be/aHvkQXpwkU0
规则，起始方向向右，奇数左转，偶数右转，经过次数越多颜色越深。
预览：
代码结合AI写成。
使用方法，首先保存pi的前n位为pi.txt（去掉3.），放在下面的python文件的同级文件夹。记得安装引用的库。你也可以直接下载打包好的文件，包含主文件和pi.txt。
import numpy as np
import matplotlib.pyplot as plt
from collections import defaultdict
from matplotlib.animation import FuncAnimation
from matplotlib.widgets import Button
from matplotlib.patches import Rectangle
# 方向向量（初始向右）
directions = [
np.array([2, 0]), # 右
np.array([0, -2]), # 下
np.array([-2, 0]), # 左
np.array([0, 2]) # 上
]
# 颜色映射
COLOR_MAP = {
1: '#a5a5a3', # 1次
2: '#ebd03e', # 2次
3: '#1abf27', # 3次
4: '#2d7f77', # 4次
5: '#832443', # 5次
6: '#49207d', # 6次
7: '#7f7f7d', # 7次
8: '#010103' # ≥8次
}
MAX_COLOR_LEVEL = max(COLOR_MAP.keys())
class PiVisualizer:
def __init__(self, filepath):
self.filepath = filepath
# 初始化状态
self.position = np.array([0, 0])
self.dir_index = 0
self.visit_counts = defaultdict(int)
self.digit_counts = defaultdict(int)
self.total_digits = 0
self.patches = {}
self.bars = None
# 动态加速参数
self.warmup_frames = 500 # 预热帧数
self.current_batch = 1 # 当前批处理量
self.speed_multiplier = 1.0 # 速度倍数
# 初始化界面
self.fig, (self.ax1, self.ax2) = plt.subplots(
1, 2,
figsize=(18, 9),
gridspec_kw={
'width_ratios': [3, 1],
'wspace': 0.3
}
)
self.setup_ui()
self.pi_gen = self.read_pi_file()
self.current_pi = next(self.pi_gen, '')
self.pi_index = 0
# 坐标跟踪
self.min_x = self.max_x = 0
self.min_y = self.max_y = 0
def read_pi_file(self, chunk_size=100000):
"""循环读取π文件"""
while True:
with open(self.filepath, 'r') as f:
while True:
chunk = f.read(chunk_size)
if not chunk:
break
clean_chunk = ''.join(c for c in chunk if c.isdigit())
if clean_chunk:
yield clean_chunk
def setup_ui(self):
"""界面初始化"""
# 主绘图区域
self.ax1.set_aspect('equal')
self.ax1.set_title('π Walk - Initializing')
self.ax1.set_facecolor('white')
# 信息显示
self.info_text = self.ax1.text(
0.98, 0.96, 'Processed: 0 digits\nSpeed: 1.0x',
transform=self.ax1.transAxes,
ha='right', va='top',
fontsize=10,
bbox=dict(facecolor='white', alpha=0.8)
)
# 统计区域
self.ax2.set_ylim(0, 20)
self.ax2.set_xticks(range(10))
self.ax2.set_title('Digit Distribution')
# 控制按钮
btn_ax = plt.axes([0.01, 0.02, 0.1, 0.04])
self.start_btn = Button(btn_ax, 'Start')
self.start_btn.on_clicked(self.start_animation)
def update_ranges(self, x, y):
"""动态更新坐标范围并保持正方形"""
self.min_x = min(self.min_x, x)
self.max_x = max(self.max_x, x)
self.min_y = min(self.min_y, y)
self.max_y = max(self.max_y, y)
# 保持正方形显示
size = max(self.max_x - self.min_x, self.max_y - self.min_y) or 1
self.ax1.set_xlim(self.min_x - 1, self.min_x + size + 1)
self.ax1.set_ylim(self.min_y - 1, self.min_y + size + 1)
def update_plot(self):
"""严格的正方形绘图"""
for pos, count in self.visit_counts.items():
color = COLOR_MAP.get(
min(count, MAX_COLOR_LEVEL), COLOR_MAP[MAX_COLOR_LEVEL])
if pos not in self.patches:
rect = Rectangle(pos, 1, 1,
color=color,
edgecolor='black',
linewidth=0.3)
self.ax1.add_patch(rect)
self.patches[pos] = rect
else:
self.patches[pos].set_color(color)
def update_stats(self):
"""更新统计图表"""
if not self.bars:
self.bars = self.ax2.bar(range(10), [0] * 10,
color=[COLOR_MAP.get(
i + 1, '#010103') for i in range(10)],
alpha=0.7)
total = sum(self.digit_counts.values()) or 1
percentages = [self.digit_counts[d] / total * 100 for d in range(10)]
for bar, h in zip(self.bars, percentages):
bar.set_height(h)
self.ax2.set_ylim(0, max(percentages) * 1.2)
def process_digits(self, batch_size):
"""处理数字逻辑"""
for _ in range(batch_size):
if self.pi_index >= len(self.current_pi):
self.current_pi = next(self.pi_gen, '')
self.pi_index = 0
digit = int(self.current_pi[self.pi_index])
self.pi_index += 1
self.total_digits += 1
self.digit_counts[digit] += 1
new_pos = self.position + directions[self.dir_index]
steps = np.linspace(self.position, new_pos, num=3, dtype=int)
for step in steps:
pos = tuple(step)
self.visit_counts[pos] += 1
self.update_ranges(*pos)
self.dir_index = (self.dir_index - (digit % 2) * 2 + 1) % 4
self.position = new_pos
def animation_frame(self, frame):
"""动画帧更新"""
# 动态加速曲线
if frame < self.warmup_frames:
# 预热阶段：缓慢加速
self.current_batch = 1 + int(frame / 20) # 前100帧从1逐步增加到6
self.speed_multiplier = 1.0 + frame * 0.02
else:
# 正常阶段：平方根加速
progress = (frame - self.warmup_frames) ** 0.5
self.current_batch = min(200, 1 + int(progress * 5))
self.speed_multiplier = min(20.0, 1.0 + progress * 0.3)
self.process_digits(self.current_batch)
self.update_plot()
self.update_stats()
# 更新信息显示
map_size = max(
self.max_x - self.min_x,
self.max_y - self.min_y
) or 1
self.info_text.set_text(
f'Processed: {self.total_digits:,} digits\n'
f'Speed: {self.speed_multiplier:.1f}x\n'
f'Map size: {map_size}x{map_size}'
)
return [self.ax1.patches, self.ax2.patches]
def start_animation(self, event):
"""启动动画"""
self.start_btn.label.set_text('Running')
self.anim = FuncAnimation(
self.fig,
self.animation_frame,
frames=range(100000), # 足够大的帧数
interval=50, # 固定刷新率
blit=False,
cache_frame_data=False
)
plt.show()
# 使用示例
if __name__ == "__main__":
visualizer = PiVisualizer('pi.txt')
plt.show()