The objectives of this assignment are

• to become familiar with the use of MPI synchronizing calls (reduction) and with data movement commands.
• to do so on a project that has many features in common with real world models which demand large amounts of computation. Such models discretize an object into cells and model the flow of material, force, energy through the object by formulas dictating transfers between neighboring cells in discrete time steps. Examples of objects to which this may be applied are the atmosphere, an ocean, an airfoil, a bridge, a chemical reaction vessel, etc.

• to produce a better product through combination of knowledge, skills, ideas, effort of two or more people.
• to experience the difficulties of group efforts and find solutions to those problems. Software development is done by teams in the "real world".

Conway's game of life is played on a 2 dimensional grid. Life starts at time zero in a given state in which some of the grid cells are occupied by a life form and some are empty. A cell has 8 neighbors. Four neighbors share a common side with the cell and four touch at a corner. At each time step the living or empty condition of each cell is determined by its neighbors according to the following rules.

1. If a cell is empty but has exactly three living neighbors it becomes live in the next time step.
2. If a cell is alive it remains alive in the next time step if it has 2 or 3 live neighbors. With 0 or 1 live neighbors it dies of neglect. With 4 or more it dies of overcrowding.

You can see examples of the life game for example at the site
http://hensel.lifepatterns.net/
The game has been intensely studied and many interesting patterns have been discovered.

Dr. Bio Logic has a grant to study how life game populations evolve over many time steps. Bio is trying to build evidence that the life game closely models aspects of life around vents in the deep ocean floor. For this purpose Dr. Logic does not need to see a display of the evolving state of the life game, rather she requires a report at each time step of just the triple of numbers:
( number-of-newly-born-cells, number-of-newly-dead-cells, total-current-population ).
However, you may want to write a display function of the grid for debugging purposes. Initially, at time step zero, print on a line the name of the file or "1/3-random" and the total-initial-population.

Some initial configurations will be given and also results are wanted for random patterns in which the initial state is determined by giving each cell life with 1/3 probability. Your program should accept either two or three command line arguments: the grid size, the number of time steps, and a file name containing the initial state. If the third argument is missing, a random initial state is to be used.

Note: it is a rule that only process 0 reads the file or initializes the initial state. Also only process 0 outputs the triple of numbers per step. Many parallel machine environments have this restriction that only a designated process has i/o capability and we want our code to work anywhere MPI is available.

1. Deliverable 1. Due by Friday 2pm, Sept 28. Form a group of 3, 2(favored), or 1(discouraged) people. Be sure you have time in your schedules in which you can meet and work together with computer access. One person from each group email me a list of names and email addresses of the group members. Those I do not hear from will be assigned groups of 2 to work in.
2. Deliverable 2. Due by midnight Friday, Oct 5. Working serial code. For what size n can you do 100 time steps in a few seconds?
3. Deliverable 3. Due by midnight Thursday, Oct 11. Working parallel code. Timing runs on a n by n grid, with n of your choice, 100 time steps, 1 to 7 processors.
4. Deliverable 4. Due at start of class Friday, Oct 19 final writeup. This includes discussion of method, timing plot, speedup plot, efficiency plot, interpretation and explanation of timing results, discussion of the group's collaboration, conclusion.