Thursday was our fourth day of CAMP and for our morning activity we played an observational game entitled “Find the Chief.” We sat in the auditorium in an ellipse, per the students’ request, and learned how to play this exciting game! A detective was picked and then asked to leave the room. While the detective was away we picked a chief who would serve as our leader. When the detective returned, the chief would begin performing a motion of their choice (a common favorite is to clap) and then the rest of the group would follow the chief. The chief’s job is to repeatedly change their motions while trying to make sure the whole group can follow them; the detective’s, to pick out the chief from the rest of the group. One of our student’s observantly pointed out that a great strategy would be to pick fake chiefs, who could watch the real chief, while the rest of the group could watch the fake chiefs to throw the detective off! After this fun game we started our classes of the day.
Our fractal lamp shades continued to be individualized as we accumulated our art projects from the week into our final art piece as we pleased. Alexis (one of our superb TAs) even taught us how to cut paper in simple ways resulting in intricate and gorgeous radial fractals! Some of us even added these radial fractals to our lamps!! Other students found more ways to incorporate the marbled paper they had created in the beginning of the week. In addition to working on our lamps we watched a video of a dancer who choreographed dances on sand that would result in geometric patterns drawn in the sand!
In math class we were able to apply our recently obtained knowledge of how we can use geometry to create and draw fractals! We experimented with applying planar transformations—specifically scaling and translating—onto the unit square to begin to make the Sierpinski triangle. We developed a set of rules that would transform the figure between stage 0 and stage 1, and then observed how the figure would change after multiple iterations of the rules we found together. Through this exercise, we were able to better understand how fractals are created using planar transformations. Frances, our lovely math instructor, then gave us a worksheet from the Yale Fractal Lab to work through in order to attempt to look at fractals, that had already gone through multiple iterations of a set of rules, and be able to discover these sets of rules on our own.
Our math class showed us the geometry behind making fractals, which connected fluidly to our computer science class where these brilliant mathematicians learned how to program our computers to make the fractals for us. We programmed commands that essentially perform the equivalent of scaling and translating, but instead of performing these planar transformations on points on a graph written on paper, the transformations were applied to our turtles in the world that we created in NetLogo. The students were able to see the program they created forming these fractals, and be grateful for the computers because they had personal experience with how complex and difficult it can become to compute and create fractals by hand!
Following lunch we held the much anticipated game of capture the flag: Team Team versus Team Mystic!! Both teams defended their flags admirably, but Team Team was able to capture Team Mystic’s flag and return safely to their side without being caught! The teams then united again to hear about options for their afternoon activities: finishing tessellation art, continuing work on their stunning lamp shades, or learning about the Physics of Chaos Theory from one of our excellent TAs Victoria!
And to end the day we hosted another game of Bard Math Circle CAMP Jeopardy! Today we achieved a new wonderful accomplishment: we were able to have a Jeopardy game that was not only filled with excitement, but also was filled with listening to other teams answer each question. We learned that, instead of planning an answer in case another group misses the questions,
it actually is beneficial to listen as other teams guess because then it helps us understand the questions better and also makes it less likely to restate a wrong answer if the questions gets to your team! Another exciting part of this day’s Jeopardy was that during the game we all got our CAMP shirts to wear on the last day! So at the end of the fourth day of camp everyone left with more than they had when they came in that morning: a little extra knowledge and a fun shirt!