Let us see what happens when we make a PascGalois triangle using the group *Z*_{2}_{ } x* Z*_{2}. Remember that the *multiplication* table for this group is

Now we have to choose which elements to place down the sides of our triangle. Notice that if we chose to place (0,1) down both sides, combining (0,1) with itself gives (0,0) and combining again with (0,1) gives (0,1) again so the element (0,1) cannot *generate* the whole group. Unlike the case of modular addition, where repeated addition of 1's will generate all of the possible results, in this set there is no single element that generates the whole set. Thus we decide to put the element (1,0) down one side of the triangle and the element (0,1) down the other side. In this triangle, pink is (0,1), yellow is (1,0), purple is (1,1), and teal is (0,0).

Here is the same triangle with a few more rows:

Does this triangle remind you of any of the modular arithmetic triangles? In particular does it remind you of the mod 2 triangle, also known as the *Z*_{2} PascGalois triangle? Let's take another look at the *Z*_{2}_{ } x* Z*_{2} triangles with 50 rows. In the following sequence of figures, we begin to change slowly the color corresponding to (1,1) to the color corresponding to (0,0). Then we change the color corresponding to (1,0) until it matches the color corresponding to (0,1). The final triangle is the *Z*_{2} triangle redrawn using teal for zero and pink for one. The colors corresponding to the different elements are displayed in order {(0,0),(0,1),(1,0),(1,1)} to the left of each triangle.

The following animation shows the same identification occurring in the 128-row triangles.