Plotting $\sin(x^2+y^2)$ for a regular grid with a total of 40,000 points or 20,000 points and on 20,000 random points

We create (x,y) points first and plot a scatter plot on them with gray level given by $\sin(x^2+y^2)$

Importing vector and plotting libraries. %matplotlib inline to see plots in notebook



In [1]:

    
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

First we show the case of a regular grid with a total of 40,000 points

We plot the function between -10 and 10, so for a total of 40,000 points we need a spacing of $0.1=20/\sqrt(40000)$ in a regular grid



In [20]:

    
xlist = np.arange(-10.0, 10.0, 0.1) # vector of x values
ylist = np.arange(-10.0, 10.0, 0.1) # vector of y values
X, Y = np.meshgrid(xlist, ylist) # regular mesh from x and y values

Z = np.sin(X**2 + Y**2) # function to plot

fig, axes = plt.subplots(figsize=(4,4)) # Making fig square
plt.title('Hi res regular grid')
plt.scatter(X, Y, c=Z, s=1) # Scatter plot
plt.gray()

Already at this resolution above one can interference patterns. These patterns are more clear when using less points in the grid, below for 20,000 points, for which the spacing is $0.1414=20/\sqrt(20000)$



In [25]:

    
xlist = np.arange(-10.0, 10.0, 0.1414) # vector of x values
ylist = np.arange(-10.0, 10.0, 0.1414) # vector of y values
X, Y = np.meshgrid(xlist, ylist) # regular mesh from x and y values

Z = np.sin(X**2 + Y**2) # function to plot
fig, axes = plt.subplots(figsize=(4,4)) # Making fig square
plt.title('Lower res regular grid')

plt.scatter(X, Y, c=Z, s=1) # Scatter plot
plt.gray()

Now for 20,000 random points



In [7]:

    
X = np.random.uniform(low=-10, high=10, size=(20000,))
Y= np.random.uniform(low=-10, high=10, size=(20000,))
Z = np.sin(X**2 + Y**2)
plt.figure()

fig, axes = plt.subplots(figsize=(4,4)) # Making fig square
plt.title('random points')
plt.scatter(X, Y, c=Z, s=1)
plt.gray()









    





<matplotlib.figure.Figure at 0x1062e6940>

For random points, there are no interference patterns