This project was developed as part of the Probabilistic Simulation course at LUT University.
The task focused on implementing Iterated Function Systems (IFS) to generate well-known fractals.
We implemented and analyzed:
- Sierpiński Triangle
- Barnsley Fern
- 3D Sierpiński Triangle (extra extension)
The goal was to study how random transformations can produce complex fractal structures and to explore both 2D and 3D cases.
- Apply probabilistic simulation methods to generate fractals.
- Implement affine transformations using different probability distributions.
- Visualize and analyze the self-similarity properties of the resulting fractals.
- Extend the work by adding a 3D version of the Sierpiński Triangle.
- Implemented in MATLAB using a single script (
Task4.m). - Affine transformations were defined as matrices with associated probabilities.
- Random number generation was used to select transformations iteratively.
- Visualization was done with MATLAB plotting functions for both 2D and 3D cases.
- Results were compared and discussed in the accompanying report.
- The Sierpiński Triangle appeared after only a few hundred iterations, with finer detail as iterations increased.
- The Barnsley Fern required more iterations but reproduced the natural fern-like shape successfully.
- The 3D Sierpiński Triangle demonstrated how self-similarity extends naturally into higher dimensions, showing a fractal pyramid structure.
- Across all cases, randomness guided the process, yet the deterministic rules of the transformations ensured the fractal shapes emerged reliably.
Probabilistic-Simulation-Task4/
│
├── Task4.m # MATLAB script (Sierpiński, Barnsley fern, 3D extension)
│
├── docs/ # Report & task description
│ ├── Report.pdf
│ └── practical_assignment.pdf
│
├── README.md # Project documentation
├── LICENSE # MIT License
└── .gitignoreThis project was completed by:
- Nada Rahali
- Tanjuma Haque
- Jash Chalodiya
This project is licensed under the MIT License – see the LICENSE file for details.