Symmetry through (Programmed) Motion
For this project, we had to learn how to use the computer program StarLogo, and use it to create a kaleidoscope. StarLogo is a program which allows you to use agents and program them to create shapes, play games, and much more. There were several steps to learning how to use the program and create the kaleidoscope. First, we did some simple activities in StarLogo such as play games, learn how to make simple shapes, and maneuver the agents. Once we had a good idea of how to use StarLogo and were familiar with the coding, we had to come up with a simple sketch on what we wanted our agents to do (what shapes we wanted created) in our kaleidoscope, and write a brief description of what each agent will do and how or if it will affect the terrain. For our second benchmark, we programmed an example of translation. In "setup" we had to create and x and y axis as well as a line that went through 3 quadrants and in "run" we had to have our agent run back and forth along that line from one side of "spaceland" to the other. For our third benchmark, we were to create an example of rotation in StarLogo. In setup, we had to have our agent draw the x and y axis, and in run, we had to have one agent spin on some spot in spaceland, one agent rotate in a circle clockwise around a point, one agent rotate in a circle counterclockwise around a point, and the last agent would run back and forth in a semi circle around a point. For our fourth benchmark, we had to create an example of glide reflection. In setup, we had to have one agent create the x and y axis, and in tun we had to have one agent run back and forth through the first and second quadrants and have another agent mirror that movement in quadrants three and four (reflected over the x axis). In another StarLogo file, we had to have one agent draw the x and y axis in setup, and then, in quadrants two and three, run back and forth to both sides of spaceland, and have another agent reflecting the motion over the y axis in quadrants one and four. In another StarLogo file, we had to have one agent create and run along the line y=-x and another agent mirror the movement below that line. In the last StarLogo fie for this benchmark, we had to have one agent create and run along the line y=x and another agent mirror the movement below that line. For our fifth benchmark, we used a graphing application to revise our fist benchmark, and more accurately portray the trajectories of our agents for our kaleidoscope. In this benchmark, we had to figure out how many lines of symmetry we were going to use in our kaleidoscope, how may agents we would be using in our kaleidoscope, the type of rigid motion, each agent's original and final position, each agent's speed and trajectory. For our sixth benchmark, we had to create the lines of symmetry in StarLogo, and create the shapes from benchmark 5 in the first sector. The last thing we had to do was reflect the shapes from the first sector into all of the other sectors.
Symmetry is described when one shape becomes exactly like another if you flip, slide or turn it. Symmetry is exhibited in my kaleidoscope because the shapes in the first sector are reflected over lines of symmetry into 7 other sectors. Rigid motion is any transformation as a translation or rotation, where the distance between the vertices remains the same. Rigid motion is exhibited in my kaleidoscope because the same motions displayed in the first sector, are also displayed in all of the other sectors. This project was really long, but it was also really interesting and I think I took a lot away from it. One challenge I faced in this project was that during the process of me making my seventh benchmark, the computer I was using froze and none of the work I had done in that time was saved. I overcame this challenge simply by persevering and redoing all of the coding over again. It wasn't as hard and didn't take me as long as it did the first time because I already knew how to do it, but it was still very tedious and not fun. Another challenge I faced during this project was that when I was working on my sixth and seventh benchmarks, I realized that the trajectories I had originally planned were not going to work with the canvas of spaceland because they would overlap into other sectors, or reach the edge of the map and throw them off course. I overcame this challenge by using the graphing app Geogebra to redefine my trajectories so that they would work with spaceland. A success I had with this project was my finished product. I am so happy with the way it turned out and I am very proud of myself for doing it because I never would have thought that I would be able to learn that much coding. Another success I had was the first shape that I was able to reflect from the first sector into all of the other sectors because I had been struggling with it and it took along time to do it it paid off once I saw that I actually did it.
Symmetry is described when one shape becomes exactly like another if you flip, slide or turn it. Symmetry is exhibited in my kaleidoscope because the shapes in the first sector are reflected over lines of symmetry into 7 other sectors. Rigid motion is any transformation as a translation or rotation, where the distance between the vertices remains the same. Rigid motion is exhibited in my kaleidoscope because the same motions displayed in the first sector, are also displayed in all of the other sectors. This project was really long, but it was also really interesting and I think I took a lot away from it. One challenge I faced in this project was that during the process of me making my seventh benchmark, the computer I was using froze and none of the work I had done in that time was saved. I overcame this challenge simply by persevering and redoing all of the coding over again. It wasn't as hard and didn't take me as long as it did the first time because I already knew how to do it, but it was still very tedious and not fun. Another challenge I faced during this project was that when I was working on my sixth and seventh benchmarks, I realized that the trajectories I had originally planned were not going to work with the canvas of spaceland because they would overlap into other sectors, or reach the edge of the map and throw them off course. I overcame this challenge by using the graphing app Geogebra to redefine my trajectories so that they would work with spaceland. A success I had with this project was my finished product. I am so happy with the way it turned out and I am very proud of myself for doing it because I never would have thought that I would be able to learn that much coding. Another success I had was the first shape that I was able to reflect from the first sector into all of the other sectors because I had been struggling with it and it took along time to do it it paid off once I saw that I actually did it.