## 3 Materials and Methods
### Cellular Automata  
Cellular automata are valuable tools for modeling complex phenomena using simple local rules [30; 31; 32]. They have applications across various fields, including the following:  
* Geosciences: models natural events such as landslides, soil erosion, and fire propagation;
* Biology: employed to simulate cell population growth, disease spread, and ecosystem evolution;
* Physics: helps study complex systems like fluid dynamics and crystal formation;
* Urban Planning: assists in analyzing urban growth, traffic distribution, and resource management;
* Computer Science: applied in cryptography, random number generation, and neural network simulation.  
For instance, in terrain modeling, cellular automata represent the landscape as a grid of cells, where each cell can change its state over time based on predefined rules. This method not only allows for simulating how the terrain evolves in response to extreme weather events, such as heavy rainfall, but it also provides real-time forecasts of landslide susceptibility. By integrating cellular automata with neural networks, predictions can be enhanced further, as neural networks can be trained on historical climate data to recognize patterns and trends. This approach not only helps anticipate risks but also facilitates the analysis of large spatial datasets, enabling the identification of vulnerable areas and the implementation of preventive measures.  
Cellular automata are valued for their simplicity and flexibility. They operate based on local rules, making them suitable for modeling distributed phenomena where interactions primarily occur among neighboring elements. This characteristic is beneficial for simulating natural processes such as the spread of landslides or urban growth. Additionally, the parallel nature of cellular automata allows for the effective use of modern computers' parallel computing capabilities, which speeds up simulations and improves efficiency. Another significant advantage of cellular automata is their spatial accuracy, providing high-resolution data essential for identifying risk zones and planning preventive interventions. The essential components of cellular automata include the following:  
* Cell Grid: A cellular automaton consists of a grid of cells, which can be two-dimensional (like simple squares) or different shapes (such as triangular or hexagonal). Each cell is associated with a state and can assume a finite number of possible states. The state of a cell may change over time.
* Transition Rules: Each cell interacts with its neighboring cells according to a specific set of rules. These rules determine how a cell's state changes over time based on the states of its neighboring cells. The change in a cell's state depends on local rules that consider both the cell's current state and that of its neighbors.  
* Synchronous Evolution: All cells in the grid update their states simultaneously at discrete time intervals, allowing for the simulation of the system's evolution.
* Local Interaction: Cells interact only with their immediate neighbors, making cellular automata well suited for modeling local and distributed phenomena.