深入浅出matplotlib

Matplotlib 是 Python 的一个 2D 绘图库，可以非常方便地创建各种常见或者特殊类型的图形，包括折线图、柱状图、散点图、饼图、等高线图、3D 图等等。同时，Matplotlib 也可以用于动态交互式数据可视化、定制化图形等高级应用。它因为易于学习和使用，而成为 Python 数据可视化工具库中最受欢迎的一种。

相关问题

深入浅出matplotlib(22):实现多边形的颜色填充

要实现多边形的颜色填充，可以使用Matplotlib库中的fill()函数。fill()函数可以指定多边形的顶点坐标，并选择填充的颜色。

首先，我们需要导入Matplotlib库中的pyplot模块，并创建一个图形对象。

接下来，我们需要创建一个包含多边形顶点坐标的列表，例如[(x1, y1), (x2, y2), (x3, y3)]。

然后，使用fill()函数来填充多边形。fill()函数需要传入两个参数：一个包含多边形顶点坐标的列表，和填充的颜色。

最后，调用show()函数来显示图形。

以下是一个示例代码：

import matplotlib.pyplot as plt

# 创建图形对象
fig, ax = plt.subplots()

# 创建多边形顶点坐标列表
vertices = [(0, 0), (1, 0), (1, 1), (0, 1)]

# 填充多边形，颜色为红色
ax.fill(vertices[:, 0], vertices[:, 1], 'r')

# 显示图形
plt.show()

在这个示例中，我们创建了一个包含4个顶点的正方形，并使用红色填充了多边形。

我们可以根据需要修改多边形的顶点坐标以及填充的颜色来实现不同的效果。同时，还可以探索Matplotlib库中其他函数和选项来进一步定制多边形的填充效果。

深入浅出 diffusion

### Diffusion Model Explained Simply

Diffusion models describe how particles spread out over time within a medium due to random motion. This concept can be visualized through everyday phenomena such as adding sugar to water; initially, the sugar molecules are concentrated in one area but gradually disperse throughout the liquid until evenly distributed.

In computational terms, diffusion processes often involve discretizing space into small segments where changes occur incrementally based on predefined rules or parameters like dispersivity values[^1]. For instance, when modeling environmental systems, adjusting these parameters allows researchers to simulate different scenarios accurately[^2].

To further simplify understanding:

- **Particles**: Think of individual entities moving randomly.
- **Medium**: The environment wherein movement occurs (e.g., air, water).
- **Dispersal Rate**: How quickly substances mix within their surroundings depends largely upon properties specific both to substance itself alongside external conditions present during transition period involved.

By breaking down complex mathematical formulations behind diffusion theory into relatable concepts, it becomes easier to grasp fundamental principles without delving too deeply into technical specifics immediately.

import numpy as np
from matplotlib import pyplot as plt

def simple_diffusion_simulation(grid_size=50, steps=100):
    grid = np.zeros((grid_size, grid_size))
    
    # Initial concentration at center
    mid_point = int(grid_size / 2)
    grid[mid_point][mid_point] = 1
    
    for step in range(steps):
        new_grid = grid.copy()
        
        for i in range(1, grid_size - 1):
            for j in range(1, grid_size - 1):
                neighbors_sum = sum([
                    grid[i + di][j + dj]
                    for di in [-1, 0, 1]
                    for dj in [-1, 0, 1]
                    if not(di == 0 and dj == 0)])
                
                average_neighbor_value = neighbors_sum / 8
                
                new_grid[i][j] += (average_neighbor_value - grid[i][j]) * 0.1
        
        grid = new_grid
    
    plt.imshow(grid, cmap='hot', interpolation='nearest')
    plt.colorbar(label="Concentration")
    plt.title(f"Simple Diffusion Simulation after {steps} Steps")
    plt.show()

simple_diffusion_simulation()

This code snippet demonstrates a basic simulation of particle distribution spreading across an empty field starting from its central point towards surrounding areas iteratively according to specified algorithmic logic implemented here.