Some Extensions and Conclusion.

There are a number of extensions of this investigation, for example:

• One thing that you can notice when you look at these triangles is that sometimes when you "zoom out" or increase the number of rows you get triangles that look very similar. This behavior is one of the additional things that we have studied. Would you like more explanation and to see some examples?

• There has been considerable interest recently in structures called cellular automata. The most famous example of a cellular automata is probably John Conway's Game of Life. Cellular automata have been used to model a number of natural phenomena including the spread of fires and disease. PascGalois Triangles are examples one-dimensional cellular automata. We can also look at two-dimensional cellular automata with similar constructions and at one-dimensional cellular automata with slightly different constructions. Interested in reading more and seeing some animations?

There are a myriad of other questions one could ask, either spawned by the above investigations or by going in other directions entirely. We have had students interested in computer science, statistics, pure mathematics and applied mathematics work with us on various questions that have spun off of these investigations. A full listing of even the extensions we have begun investigating is beyond the scope of this paper but we refer you to the references for more information. We also invite you to think of your own questions. It seems that every investigation in mathematics leads to more new questions. Thus mathematics is an ever-growing rich field of knowledge. We hope you have enjoyed this small journey into just one of the many accessible niches in mathematics.