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.