VectorOnTwoSticks

For my 28th sketch of Mathober2026 coded in #Python , VectorOnTwoSticks follows a disorganized set of vector fields with the DevilOnTwoSticks equation (Day 23 of Mathober).

Poetry

Vectors dictating the Pattern shown
Showcasing the flow
But what if the fields don’t follow?
What if this zone,
Is a scalar unknown?

Images

Code

import numpy as np
import matplotlib.pyplot as plt

def VectorOnSticks(pos):

    # Meshgrid
    x, y = np.meshgrid(np.linspace(-10, 10, 40), 
                       np.linspace(-10, 10, 40))
    
    b = np.linspace(-10, 10, 40)
    a = np.linspace(-10, 10, 40)
    
    
    u = x/(y**4-x**4+ a*(y**2)+ b*(x**2))
    v = y**4-x**4+ a*(y**2)+ b*(x**2)
    t = y/(y**4-x**4+ a*(y**2)+ b*(x**2))
    
    
    plt.quiver(x, y, u,u, color='green',headwidth = 12,headaxislength = 6)
    plt.quiver(x, y, t,u, color='blue',headwidth = 9,headaxislength = 4)
    plt.quiver(x, y, v,v, color='cyan')
    plt.quiver(y, x, v,u, color='red',headwidth = 6,headaxislength = 3)
    plt.quiver(y, x, t,t, color='orange')
    plt.title('Vector On Sticks')
    
    
    plt.xlim(-pos, pos)
    plt.ylim(-pos, pos)
    
    
    plt.show()

VectorOnSticks(5)
VectorOnSticks(10)
VectorOnSticks(15)
VectorOnSticks(20)