docs(frontend): adding a Game of Life example

closes #457

docs/SUMMARY.md

@@ -33,6 +33,7 @@
 
 * [Key Value Database](application-tutorial/key\_value\_database.md)
 * [SHA-256](application-tutorial/sha256.md)
+* [Game of Life](application-tutorial/game_of_life.md)
 
 ## How To
 

docs/application-tutorial/game_of_life.md

@@ -0,0 +1,54 @@
+# Game of Life
+
+In the associated [Python file](https://github.com/zama-ai/concrete/blob/main/frontends/concrete-python/examples/game_of_life/game_of_life.py), you can run the Game of Life, written in Concrete Python.
+
+![ Game of Life](../_static/game_of_life.gif)
+
+### Installation
+
+In addition to Concrete, you must install `pygame` in your virtual environment:
+
+- `pip3 install pygame`
+
+Once done, if you go to `frontends/concrete-python/examples/game_of_life`, `python game_of_life.py --help` should give you the manpage:
+
+```
+Game of Life in Concrete Python.
+
+options:
+  -h, --help            show this help message and exit
+  --dimension DIMENSION
+                        Dimension of the grid
+  --refresh_every REFRESH_EVERY
+                        Refresh the grid every X steps
+  --method {method_3b,method_4b,method_5b,method_basic}
+                        Method for refreshing the grid
+  --log2_global_p_error LOG2_GLOBAL_P_ERROR
+                        Probability of correctness issue (full circuit)
+  --log2_p_error LOG2_P_ERROR
+                        Probability of correctness issue (individual TLU)
+  --simulate            Simulate instead of running computations in FHE
+  --show_mlir           Show the MLIR
+  --stop_after_compilation
+                        Stop after compilation
+  --text_output         Print a text output of the grid
+```
+
+### Running
+
+Then, you can play with the different options, and in particular:
+
+- `dimension`, to chose the size of the grid; the larger, the slower
+- `method`, to chose which implementation is used for the grid update
+- `log2_global_p_error` and `log2_p_error`, to chose the probability of correctness issue (see the Concrete documentation for more information)
+- `simulate`, to do computations only in simulation, i.e., not in FHE
+
+### Typical Executions
+
+In simulation: `python3 game_of_life.py --dimension 100 --refresh_every 50 --simulate`
+
+In FHE: `python3 game_of_life.py --dimension 6 --refresh_every 8 --log2_p_error -40 --method method_4b`
+
+### Technical Explanations
+
+A blog is currently being under writening, and a link will be added it here when it's available. In the meantime, some explanations are given in the code.