Random Walk Simulation

In this project plots with simulations of randomized walks are generated.

Description

"A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers. An elementary example of a random walk is the random walk on the integer number line, which starts at 0 and at each step moves +1 or -1 with equal probability" (Source).

This project aims to simulate a random walk simulation with different options and further implementations. The main implementations are:

1. Simulation of multiple random walkers with different speeds
2. High randomization of speeds, start points, colorization etc.
3. Enabling options to simulate the random walk of your needs like different neighborhood movement patterns (Neumann/Moore), enabling random start points, running the code multiple times, saving the plot and/or results automatically...
4. TBD: 3D walks
5. TBD: impenetrable objects

Getting Started

To run the program every machine having at least Python 3.9 installed is suitable. Your Python environment should additionally include the libraries numpy, matplotlib and pandas. The rest should be included in the python installation. If you are using Linux or Mac, you should check the relative paths beforehand.

Installing

Create your virtual python environment and clone the repository. You should then be ready to execute the program.

Execution

The program is structured as explained below:

• variables for the number of walks and steps are defined (user-generated)
• the user can specify if a plot should be saved and how many times the code should be executed in total
• additionally the movement pattern can be chosen (4 or 8 directions)
• this leads to the definition of two arrays in form of x and y-coordinates with zeros..
• ..that are filled with random generated values through a for-loop for each walker
• the starting point in form of x and y can be randomized for each walk, otherwise all walkers start at 0,0
• the randomized choice of speed is implemented in the loop and is randomized for every walker
• with the definition of the class Walkers a detailed dataframe for every walk is generated which contains information about the type of walker, the starting point and the speed
• finally the dataframe can be saved as a CSV-file and the walks are plotted together in one figure
• if the user specified that there should be multiple runs, this process is automatically repeated

Calling

Call the program without any arguments to access the help within the terminal with information on how to use the optional arguments:

$ python src/main.py

usage: main.py [-h] [-s Steps] [-w Walkers] [-m Movepattern] [-xy Startpoint] [-p Save plot] [-r Runs]

Simulate a random walk with n walkers for n steps. You can use the following options to change the simulation to your needs. Have fun!

optional arguments:
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  -h, --help            show this help message and exit

  -s Steps, integer     Integer | Number of total steps every walker shall take.
                        Default value: 1000
  -w Walkers, integer   Integer | Number of total walkers to be created.
                        Default value: 1
  -m Movepattern, bool  Boolean | Choose neighborhood movement pattern between
                        Neumann (4 directions, false) or
                        Moore (8 directions, true, default)
  -xy Startpoint, bool  Boolean | Do you want different (random) start points for
                        each walker (true, default) or
                        let all plots start at 0,0 (false)?
  -p Save plot, bool    Boolean | Do you want to automatically save the plot locally
                        (in ./data/)? Use true/false. Default: false
  -r Runs, integer      Integer | Total runs of the script (generate multiple plots if
                        wished). Default value: 1
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  -h, --help      show this help message and exit
  -s Steps        Integer | Number of total steps every walker shall take. Default value: 1000
  -w Walkers      Integer | Number of total walkers to be created. Default value: 1
  -m Movepattern  Boolean | Choose neighborhood movement pattern between Neumann (4 directions, false) or Moore (8 directions, true, default)
  -xy Startpoint  Boolean | Do you want different (random) start points for each walker (true, default) or let all plots start at 0,0 (false)?
  -p Save plot    Boolean | Do you want to automatically save the plot locally (./data/)? Use true/false. Default: false
  -csv Save csv   Boolean | Do you want to automatically save the results as csv-file locally (./data/)? Use true/false. Default: false
  -r Runs         Integer | Total runs of the script (generate multiple plots if wished). Default value: 1
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Results

Due to the high randomization of the simulation the following possible results are shown only exemplarily.

Example 1

Options: 25 walkers, 25000 steps, default values and saving the plot

$ python src/main.py -s 25000 -w 25 -p true

Example 2

Options: 10000 steps, 12 walkers, start point at 0,0, movement pattern Neumann and saving the plot

$ python src/main.py -s 10000 -w 12 -xy false -m false -p true

Example 3

With default values only

$ python src/main.py
...
You can run the program with the default values.
Want to run it now? Use y/n: y