added more information, refs #3

README.md

@@ -2,15 +2,15 @@
 A python implementation of the MIXMAX PRNG.
 
 ## Description
-In this project we successfully construct a python implementation of the two-parameter family of C-system operators `A(N,s)`, as discussed in this [1] paper.
+In this project we successfully construct a python implementation of the two-parameter family of C-system operators `A(N,s)`, as discussed in this [1] paper. A more general three-parameter family of C-system operators `A(N,s,m)` is calculated too. But our generator doesn't produce all the results of the three parameter family, whereas it works good for the two parameter family. 
 
 ## Code
 There are two implementations. The first attempt was a naive approach, using vanilla python3 for the construction of the operator `A(N,s)`. The second attempt, which is much better and faster is using cython for speeding up the construction process.
 
 ## How to use the python script
 Run: `python3 create_matrix.py` . You'll get instructions then.
 
-An example of correct run: `python3 create_matrix.py 100 0 1`. 
+An example of correct run: `python3 create_matrix.py 128 1 1`. 
 
 ## How to use the cython files
 
@@ -23,10 +23,11 @@ Simply run in your terminal:
 ### Using the create_matrix_new.py script
 Run: `python3 create_matrix_new.py`. You'll get instructions then.
 
-A correct run: `python3 create_matrix_new.py 100 0 1`.
+A correct run: `python3 create_matrix_new.py 128 1 1`.
 
 ## Features
-Both programs plot the distributions of the eigenvalues of the given `A(N,s)` for input variables `N`,`s` on the plane.
+Both programs plot the distributions of the eigenvalues of the given `A(N,s,m)` for input variables `N`,`s,m` on the plane.
+When `m` equals `1` then `A(N,s,m``)` is the same matrix as the matrix `A(N,s)`.
 
 ## Results
 The results agree with the results presented in the paper [1]. The distribution of the eigenvalues in some cases follow the curve of a cardioid as expected. For various other values of `N` and `s` different shapes are being created. See inside the images directory for more examples.