Desert Desideratum Mathematica

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TodayI was able to spend time with Jane Curnutt and Ernesto Gomez and Keith Schubertfrom the Computer Science and Engineering program at San Bernardino working onthe Cellular Automata. We started talking about the radius and theneighborhoods that surrounding each cell, which is represented by a square.Each square has a radius of either 1, 2 or 3, each having a differentneighborhood size. A radius one has a length of a side of a neighborhood squareof 3 squares surrounding it, counting itself and diagonals. A radius of 2 has alength of a side of a square of 5, and a radius of 3 has a length of a side ofthe neighborhood of 7. The cell looks around in the neighborhood and if theyfind a square within their radius neighborhood, then they follow the rules set.For example we set the rules for the neighborhood of 0 to be unchanging. Therule for the neighborhood of 1 for life and the neighborhood of 2 for death.There are more neighborhoods to be set, but for the sake of the example we justset those different. We put one center square in the sea of brown, and clickedthe button for an iteration, and watched the square grow. The space around thesquare grew, all the surrounding squares filled in with green, including thediagonals, creating a 3×3 square. We continued pushing the iteration button tosee what would happen and the patterns that were created were symmetrical. Janepointed out that the square started out with a 1, would create the same patternas a 3×3 starting square as long as the rules for the neighborhoods were thesame.

Inorder to understand the working of the program, we talked about how to bringthe program into a classroom. We created an activity involving chairs andpeople acting like the cells. We talked about how to teach a student to thinkabout the radius and the neighborhoods. The activity would have a set of chairsset up like a square and have a person sit in the middle or somewhere in thesquare of chairs, acting like a cell. They would sit down and reach around tofigure out how big the length of the neighborhood side is based on the rule ofradius. We set it like a radius 1 and had one person sit in the square and lookto see if they can reach out to the chairs that is 1 away. Since all of thechairs can be reached, they count themselves and say that has 1 which meansthat cell grew. We put in people where the squares that were empty. Andcontinued the activity according to the rules we set up.

Ireally enjoyed working with these people. I learned a lot about working in aclassroom and trying to make the program that was designed to mimic patterns ofbacteria or any form of growth pattern, can be taught to first graders inrelation to patterns and counting. The activity we created for the classroomhelped me understand how the program works. I was able to continue playing withthe program itself and figure out some more patterns just by playing aroundwith the neighborhood rules.

Cassandra Guido, California Polytechnic University San Luis Obispo