random walk

Simulations of various types of random walk.

• Simple random walks

  • Random walk on regular 1D lattice where you can step in any of the two directions {↑, ↓} with the same probability.
  • Random walk on regular 2D lattice where you can step in any of the four directions {↑, ←, ↓, →} with the same probability.
  • Random walk on regular 3D lattice where you can step in any of the six directions {↑, ←, ↙, ↓, →, ↗} with the same probability.

• Restricted random walks

  • Random walk on regular 1/2/3D lattice without immediate return where you can step in three possible directions with the same probability, the first step is in any direction.
  • Random walk on the square lattice without crossing i.e. self-avoiding random walk.

Examples

Simple random walks

Restricted random walks

Random walk statistics

Build and run

All outputs such as data and images are located in output folder. The presented images were produced by Python implementation.

See the source files:

• random_walk.py module
• random_walk.ipynb notebook
• random_walk.f90 module
• random_walk_main.f90 program
• random_walk_main.f90 test

Python

You need Python version 3.10+.

Create a virtual environment.

py -3.10 -m venv .venv
.venv\scripts\activate
pip install matplotlib seaborn numpy pandas

Note: On Ubuntu may need to install venv module as sudo apt-get install python-venv. And invoke the module as python3 -m venv .venv (there is no py.exe as on Windows. Please read the official documentation.

Run the simulations.

python .\source\random_walk.py 1_000_000 3 123321 True # 1D simulation with 100_000 steps
                                                   ^------ Run solution (example) (True | False)
                                           ^-------------- Random seed
                                         ^---------------- Dimension (1 | 2 | 3)
                                ^------------------------- Number of steps per walk

The running simulation looks like this:

Run 2D example with statistics: from 1 to 500 steps and 100 repeats per steps.
trial = 218, walk = 990

… after succes run:

---SUCCESS---

Fortran

Work-in-progress: The Fortran version is almost finished, but data are not at the shape suitable for analysis.

Compile and run main program:

gfortran source\random_walk.f90 source\random_walk_main.f90 -o build\random_walk_main.exe
.\random_walk_main.exe 123 100 1 > data.psv

Compile and run test program:

gfortran source\random_walk.f90 source\random_walk_test.f90 -o build\random_walk_test.exe
.\build\random_walk_test.exe

Also, you can execute the project.bat with build command and then run programs:

.\project.bat build

.\build\random_walk_main.exe 123 100 1
.\build\random_walk_test.exe