## Recognizing Patterns Depends on our ability to Perceive Them.

One interesting sidebar that arose in our study of these patterns has to do with human perception. The patterns that
we are able to find in the * D*_{3} triangles are Much Much more apparent with some color assignments than with others.
This of course leads us to questions about how humans perceive colors, etc. We also wonder how much this might differ from individual
to individual. There are a wealth of interesting questions that could be researched in this area. Some of the questions could probably
be answered with a review of the literature in psychology of perception or in biology. Others could lead to further experimentation in these areas.
We have not had the time to pursue these issues, but we wished to bring these questions to your attention and have constructed a
graphical illustration of the phenomena to which we refer. You can also see the difference between the six triangles in the hexagon below.
All six were generated the same way but using different color assignments. If you read section 2, they are PascGalois triangles for *D*_{3}.

There are also questions about which kinds of patterns people would find aesthetically appealing. An interesting possible study would be to
ask people to choose from Hexagons made with Pascal's Triangles mod n for *n *prime vs.* n* composite and between values of *n* with different
prime factors vs. values with the same prime factors. For example,
see this page.

One other question of interest is: How many different colors can the human eye distinguish in patterns
like these? And then there is the related question: How do we generate the maximum number of distinguishable colors on a computer screen? Interestingly enough,
having once generated colors for the computer screen, it is a non-trivial problem to generate equivalent colors for print. We have a pretty good algorithm for generating
16 colors and can expand to a reasonable set of 64 colors but are not certain that they are all truly distinguishable. There is definitely work to be done in this area.
Those who study art and graphical design struggle with similar issues. There are some interesting projects that
students from a number of disciplines might wish to tackle, trying to address this.