Generate slope fields in R and Python

Here is a short post on how to generate a quick slope field in R and Python.

If you do not know what a slope field is, well I am not the best person to explain it to you since it is a relative new concept for me as well. From what I’ve understood on the subject, a slope field is a graphical way to sort out a first-order differential equation and get a grasp at the solution without having to solve it analytically.

As the Wikipedia’s page says, “it may be used to qualitatively visualize solutions, or to numerically approximate them.”

In general, I feel safe saying that a slope field is some sort of a graphical approach to a differential equation.

Say you have the following differential equation:

drawing the slope field would look something like this:
In Python (without arrows)

and in R (with arrows, x=f and y=h)

Of course these plots are just very quick and can be improved.

Here is the Python code I used to draw them.

	import numpy as np
	from matplotlib import pyplot as plt
	# Differential equation
	# diff = y'= y/x (or say x+y)
	def diff(x,y):
	return y/x # try also x+y
	x = np.linspace(-10,10,50)
	y = np.linspace(-10,10,50)
	# use x,y
	for j in x:
	for k in y:
	slope = diff(j,k)
	domain = np.linspace(j-0.07,j+0.07,2)
	def fun(x1,y1):
	z = slope*(domain-x1)+y1
	return z
	plt.plot(domain,fun(j,k),solid_capstyle='projecting',solid_joinstyle='bevel')
	plt.title("Slope field y'")
	plt.grid(True)
	plt.show()
	print("End of the program")

view raw slope_field_py.py hosted with ❤ by GitHub

And the R code

	# Our differential equation
	diff <- function(x,y)
	{
	return(x/y) #Try also x+y
	}
	# Line function
	TheLine <- function(x1,y1,slp,d)
	{
	z = slope*(d-x1)+y1
	return(z)
	}
	# Domains
	x = seq(-20,20,0.5)
	y = seq(-20,20,0.5)
	# Points to draw our graph
	f = c(-5,5)
	h = c(-5,5)
	plot(f,h,main="Slope field")
	# Let's generate the slope field
	for(j in x)
	{
	for(k in y)
	{
	slope = diff(j,k)
	domain = seq(j-0.07,j+0.07,0.14)
	z = TheLine(j,k,slope,domain)
	arrows(domain[1],z[1],domain[2],z[2],length=0.08)
	}
	}

view raw slope_field_R.R hosted with ❤ by GitHub

Here is a beautiful slope field for the following differential equation:

In Python

If you need a quick tool for drawing slope fields, this online resource is good, click here.

Hope this was interesting.