Python Matplotlib Random Walk Example

Random walk means to walk follow a path in a random direction with a random distance from the start point. It is a mathematics concept. Use the python matplotlib module, you can implement random walks easily. This article will tell you how to implement a random walk graph in python.

1. Python Matplotlib Random Walk Example

1. Below is this random walk example-generated picture. The blue point is the start point, the red point is the endpoint.
   
2. Below is the example source code, save the source code in a python file then execute it.

   '''
   @author: zhaosong
   '''
   
   import matplotlib.pyplot
   import random
   
   # Generate two random point steps based on the random direction and distance.    
   def generate_steps(distance_truple=[1,2,3,4,5,6,7,8,9,10]):
   
       # Get random direction.
       direction = random.choice([-1,1])
   
       # Get random distance.
       distance = random.choice(distance_truple)
   
       step = direction*distance
       return step
   
       
   
   # Generate all random point x, y value numbers.
   def generate_random_walk_list(max_point_numbers):
   
       # Must give a initialize value 0, otherwise the code will throw index out of range error in the while loop.
       x_numbers = [0]
       y_numbers = [0]
   
       # get x value list size.
       x_numbers_size = len(x_numbers)
   
       # Loop to create max_point_numbers point coordinate.
       while(x_numbers_size < max_point_numbers):
           x_step = generate_steps()
           y_step = generate_steps()
           
           # If the new point location is same with original, then calculate next point location.
           if(x_step==0 and y_step==0):
               continue
   
           # Calculate the next x and y by adding new step
           next_x = x_numbers[-1] + x_step
           next_y = y_numbers[-1] + y_step
   
           # Append new x, y value at the list end.
           x_numbers.append(next_x)
           y_numbers.append(next_y)
   
           # Recalculate the number list size.
           x_numbers_size = len(x_numbers)
   
       # Save the generated x, y value number list in a dictionary to return.    
       ret = {}
       ret['x_numbers'] = x_numbers
       ret['y_numbers'] = y_numbers
   
       return ret   
   
   # Draw a random walk graph. Each point represent a random position that the walk pass.
   def draw_randmon_walk(max_point_numbers):
   
       # Get all random walk points with x, y axis values list.
       random_walk_dict = generate_random_walk_list(max_point_numbers)
       x_numbers = random_walk_dict['x_numbers']
       y_numbers = random_walk_dict['y_numbers']
   
       # Get point color list.
       point_color = list(range(max_point_numbers))
   
       # Plot all the point with x, y value based on green colormap.
       matplotlib.pyplot.scatter(x_numbers, y_numbers, s=1, c=point_color, cmap=matplotlib.pyplot.cm.Greens)
   
       # Plot the start point as blue.
       matplotlib.pyplot.scatter(0, 0, c='blue', edgecolors='none', s=100)
   
       # Plot the end point as red.
       matplotlib.pyplot.scatter(x_numbers[-1], y_numbers[-1], c='red', edgecolors='none', s=100)
   
       # Remove all x, y axes.
       matplotlib.pyplot.axes().get_xaxis().set_visible(False)
       matplotlib.pyplot.axes().get_yaxis().set_visible(False)
   
       # Display the graph.
       matplotlib.pyplot.show()
   
   if __name__ == '__main__':
       # Plot 50000 random points graph.
       draw_randmon_walk(50000)

Reference

1. Python 3 Matplotlib Draw Point/Line Example
2. Random walk From Wikipedia