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):
            # 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.
            # 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,
        # 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.
        # Display the graph.
    if __name__ == '__main__':
        # Plot 50000 random points graph.


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

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