This repository is intended to be a simulation of Conway's Game of life. The goal of the project is to obtain a Pygame window in which the evolution of the cellular automaton (i.e. Conway's game of life) is shown state by state in real time. First, it is advisable to create a virtual environment within a new folder in which you want to run the project. In order to use the project, Git must be installed. Then type the following command from the terminal:
"git clone https://github.com/AldoCanfora/Repository-for-the-Software-and-Computing-for-Applied-Physics-Project"
Next, installation of the following libraries is required:
-numpy
-pygame
-sys
-configparser
-random
-pytest
The pytest library is required only for testing functions of testing.
To view the output of the project, with the default configuration file configuration, run the following code from the terminal:
"python cellular_automata_visualization.py"
If you want to view the output of the project, with a different configuration file, run the following code from the terminal:
"python cellular_automata_visualization.py configuration_name_file.txt"
Remember to type [settings] at the top of the configuration_name_file.txt
After entering the name of the configuration file you intend to use from the terminal, the pygame window appears on the screen and you can view the evolution of Conway's game of life with the configuration parameters entered.
To check if the code works properly it's possible to type in the terminal the following command:
"pytest testing.py"
These are the steps in order to start the program and to show the results:
Modify the configuration file to use a different configurations fot the outuput. The parameterts are:
- WIDTH and HEIGHT: for the size of the grid, the minimum selectable values WIDTH and HEIGHT are greater than 20, to have a grid of at least 2 by 2;
- seed_value: for random cells generation;
- border_type: for a different state configuration of the outer edges of the grid.
The allowed border_types are:
- death : cells outside the grid are all considered dead;
- alive : cells outside the grid are considered all alive;
- reflective : cells outside the grid assume the same state as the adjacent cell laterally;
- toroidal : The grid is considered to be wrapped around itself both horizontally and vertically so that there is no real "off grid".
The actual grid used in cellular_automata_visualization is scaled by going to divide both WIDTH and HEIGHT by 10, approximating the result by default to the nearest integer.
This is how I divided my project into blocks:
- In the file cellular_automata I have built the Conway's Game of life functions that randomly initialize the grid, count the number of neighbors in each cell, update the grid state.
- In the file cellular_automata_visualization there is the pygame code to show the window where we can se the updating of the states of the game of life.
- In the file testing I have tested all the cellular_automata functions to ensure that all of them work properly, using differet assert based on border_type parameters. For the other functions to be tested, I used examples of grids on which to make asserts. In addition, I included testing functions for special cases, such as all live cells or all death cells and emergent forms.
- In the file configuration there are the definitions of the parameters imported in the cellular_automata_visualization, there are definitions of WIDTH, HEIGHT, seed_value and border_type.
In the images folder I have included some images to understand Conway's Game of life theory and an example of the output of cellular_automata_visualization.
In the figure below I show a frame of a state of the cellular_automata viewed through the Pygame window.
A cellular automaton is a discrete model of computation studied in automata theory. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off. The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood, is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. The rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously.
In the above figure, this cellular automaton is a grid composed by 25 cells. The set of neighbor- hood is called Moore Neighborhood and it is defined on a two-dimensional square lattice and it is composed of a central cell and the eight cells that surround it, here indicated with initials of cardinal points.
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. It is Turing complete and can simulate a universal constructor or any other Turing machine. The universe of the Game of Life is an infinite, two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, live or dead (or populated and unpopulated, respectively). Every cell interacts with its eight neighbours, which are the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:
- Any live cell with fewer than two live neighbours dies, as if by underpopulation.
- Any live cell with two or three live neighbours lives on to the next generation.
- Any live cell with more than three live neighbours dies, as if by overpopulation.
- Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
These rules, which compare the behavior of the automaton to real life, can be con- densed into the following:
- Any live cell with two or three live neighbours survives.
- Any dead cell with three live neighbours becomes a live cell.
- All other live cells die in the next generation. Similarly, all other dead cells stay dead.
The initial pattern constitutes the seed of the system. The first generation is created by applying the above rules simultaneously to every cell in the seed, live or dead; births and deaths occur simultaneously, and the discrete moment at which this happens is sometimes called a tick. The rules continue to be applied repeatedly to create further generations.
As is a property of complex systems, the operation of these rules produces emergent new forms, with properties that are not predictable from the initial conditions. These new forms and properties do not involve changes in initial conditions, since the counters are unchanged, but in the emergent forms, the configurations that emerge, and their properties.
Conway identifies three distinctive emergent forms.
- “Still life”
- “Blinker”
- “Movers” which include “Gliders”, which move across the grid.
In figure above, an example of a still life. The pattern stabilizes into a fixed form.
There are also other stable forms such as those shown in the figure above.
In figre above an example of a blinker, which is a pattern that oscillates with a fixed period, that is, after n iterations the pattern returns to a previously visited state. In the example this pattern has period 2.
The glider is a repeating pattern that travels across the grid. Their movement is diagonal in cellular grid
and after one period come back to initial pattern and this procedure continues.
Therefore important feature of gliders is their movement in cellular grid. Figure above shows a glider whit period 4.