1. Modeling Rainfall using a Cellular Automata
Bruce Betancourt, Hunter Davis

2. What is a Cellular Automata?
Cellular Automata: a collection of cells on a grid that evolves over time through a set of rules. The value of each cell is determined by the surrounding cells.
The most popular version of this is Conway’s game of life.

3. Conway’s Game of Life
Any live cell with fewer than two live neighbors dies.
Any live cell with two or three live neighbors lives.
Any live cell with more than three live neighbors dies.
Any dead cell with exactly three live neighbors becomes a live cell.
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4. Informal Problem Statement
Our goal is to forecast storms as accurately as possible using a cellular automata with rules governed by wind, dewpoint, time, and geographic location.
At the certain points throughout the storm’s life, we will measures the amount of raining cells int the storm at those points and subtract that from the actual storm data and use that to measure the accuracy of the algorithm.
This is an optimization problem.

5. Formal Problem Statement
Let the rainfall at cell R at position (m,n) in the 2-dimensional square Cartesian grid of Z^2 size (Z is a fixed, non-negative number that represents the width of the board) such that m,n <= Z.
Let the initial set of rain values S represent the initial conditions of the storm. Model the movement of storm S such that it minimizes:
𝑖=1 3 𝑖=1 𝑛 |𝑋−𝑌| = margin of error.
X is the average amount of raining cells of the initial storm and Y is the amount of rain cells of the simulated storm.

6. Initial Conditions
Initially the system will be fed a storm system from a text file. The program will read the text file and give the values for each cell for the start of the system. The program will then run and move the storm based on the rules of the game. At certain points, the program will read data onto the file to show the data from the storm as it moves through the grid. That data will then be compared to the actual data the storm produced to objectively measure the performance of the algorithm.
The data from the storm will come from weatherundergound.

7. Brute Force
For our brute force algorithm, we changed the rules from the game of life. It changed from determining whether a cell is dead or alive from its neighbors, to determining dispersion of rain and movement of a cell from that cells neighbors to mimic that of a rain storm.
Big O(nm)
Where n is the amount of cells and m is how many times the algorithm repeats until the storm dies

8. Brute Force Formulas
Movement Formula - Take a target cell, gather the wind speed s and wind direction d from all 8 neighbors surrounding the cell and target cell. Based on the wind speed gather a weight w such that if wind speed is higher the weight is higher. Multiply the wind direction and wind speed to find m how much a cell moves in a direction. Find the avg of all neighbors and apply to the cell.
Dispersion Formula - Every cell has a vapor value, v. The vapor value is highest in the center of the storm decreasing at a rate of (-1/16) outward for each cell. Gather the rainfall, r, from surrounding 8 neighbors and the target cell. If the rainfall of a surrounding neighbor is less than the target cell, distribute vapor value into that cell evenly. If a cell is less than ⅛ of its original vapor value it dies.

9. Genetic
Over the course of a certain number of generations, the genetic algorithm will change the rules slightly each generation, and it will make combinations of the “fittest” attempts to reduce the margin of error.
The algorithm will use the training data to make the best rules that reduce the margin of error.

10. Backtracking
Backtracking would seek to find all the possible 2^n conditions of the storm moving in different directions (N, NE, E, SE, S, SW, W, NW).
If the storm cells wind direction is not in that direction it would die off and start at a different direction.
This would eventually find the correct direction, however with these constraints it would take much more time to find the right amount of cells.
Big O: O(2^n)
We could reduce the amount of directions by knowing where the storm is coming from.
For this algorithm we used the same method of finding rainfall as the brute force algorithm

11. Conclusion/Final Thoughts
Brute Force could be modified to take into account more variables to get more accurate
Our algorithms could be modified to predict:
hurricane movement
Measure rainfall
Having rain appear in other places.
Overall the genetic algorithm is the best approach because of how it evolves with each generation. With the amount of data here, backtracking would be a good approach but when adding more data, it could be useless.

12. Questions: What is a Cellular Automata?
A collection of cells on a grid that evolves over time through a set of rules. The value of each cell is determined by the surrounding cells.
2. What kind of problem is this?
Optimization Problem
3. What 3 algorithms did we use?
Brute Force, Genetic, and Backtracking
4. What were we modeling?
Storm movement and rainfall
5. Who made the game of life?
John Conway

13. Sources http://mathworld.wolfram.com/CellularAutomaton.html