Though you may not realize it, you see patterns everywhere in your day to day life. Before this unit, I didn’t realize how much of our world is made up of beautiful, complex patterns. A good example of this is the patterns in flowers, plants, and many organic structures. I first became interested in learning about the patterns in natural structures when we watched a video in class called “Doodling in math: Spirals, Fibonacci, and being a plant.”- A three part series about the complex patterns in things like pine cones, sunflowers, even cauliflower. The creator of the video, Vihart, explains what the Fibonacci sequence is, and how it’s important for the beautiful design of these objects. The Fibonacci sequence is a sequence of numbers that can be found in many naturally created objects. We can also see patterns in things like art. As an artist myself, I can assure you that i use patterns in almost all of my work. If it’s something as simple as proportions, to something more complicated like eye focus, rule of thirds, protecting your eyes, or the shapes used to sketched out a portrait, they’re all constructed of patterns! One where pattern stand out in particular, is shading. Shading is the opposite of light, and the forms it takes on the face are usually similar. Following a pattern, when a face is angled at a different position the shading will create different shapes. For POW #2, ( Section A) we had a problem including shapes, patterns, and graphic design. For this assignment we were given a 8x8 square. 8 cubes upwards, and 8 cubes sideways, making 64 smaller cubes in the square as a whole. Our job was to find out not only how many 1x1 cubes there were, but how many 2x2, 3x3, 4x4, 5x5, 6x6, 7x7, and 8x8 ones there were as well. One of the key things I figured out while working on this problem was that squares can overlap, and a new square can be formed by moving the cube over one line, adding one line and removing one, instead of not reusing any squares previously counted. Through exploring this, I found a pattern. I saw that starting with the 1 x 1 cube, I’d multiply 8 x 8 to find the amount of cubes. Then, moving to 2 x 2 , I’d multiply 7 x 7 to find the amount of 2 x 2 cubes. You keep going down until you get to 8 x 8 cubes, which turns to 1 x 1, which is one large cube. After you've gotten the answer to every single - x -, then you add them all together. Once I was finished adding all of this together, I came out with the answer of 204.
How do we represent them?Part A.) Now that we know what patterns are, how do we represent them? Patterns can be represented and exemplified in multiple ways, but in my opinion the easiest way is through in and out tables. In and out tables are charts with two sides, one being x, and the other being y. Of course, x and y are substituted in for things. The purpose of an in and out table is to see what happens to the x, to turn it into the y. You can think of it almost as a machine, you put a number in the x, and you get the y back out. While the number is in the machine, an equation is being applied to it. For example, the equation for this in and out table is x times 2 equals y. X being our “input”, and y being our “output.” One time that we used in and out tables to show our work, was in our 8-26 homework, (Section B.) In this homework, we were given in and out tables similar to the one in the picture. Our task was to figure out the equation for each of the tables. We had to explain what to do to x, to turn it into y. A problem I liked in specific was C. In problem C, the in was simple words. Such as “house,” or “Cup.” This problem might seem weird to the normal viewer, because it isn’t a numeric table. However the out, was normal numbers. Cup = 2, writer = 5, elephant = 7, and so on. When I looked closer into this, I noticed a pattern. The pattern I found was that Y is equal to the amount of letters in the word before, (x) minus 1. So cup, 3 letters, minus 1 = 3. Writer, 6 letters, minus 1 = 5. This shows that in and out tables can show patterns, not only numerically but in the real world too! Part B.) Another way to represent patterns in through spirals! As I was talking about before, the Fibonacci sequence is a great way to show this. The Fibonacci pattern is created by adding the two numbers before the next together. The numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. We can see the pattern when we add the number up together ourselves. 0 plus 1 equals 1. 1 plus 1 equals 2. 1 plus 2 equals 3, 3 plus 2 equals 5 and so on. So why are all these numbers important? Well, they all reflect the spirals found in nature. How petals wrap around flowers, how many spirals / times does something wrap around a plant, it’s all the Fibonacci sequence numbers. Why are They Important? Part A.) But Patterns aren’t just random numbers used for math class. They have deeper meaning. Now that we know that they are found in things like art and nature, imagine those things without any patterns to them. They’d be completely chaotic and random. Now, I want you to think of the last time you were playing a game. Chances are, that game has a pattern to it making it playable. Even if this is as simple as something like monopoly, where the players go in a pattern to roll the rice, it makes the game function. This also works for things like sports! Time periods are all patterns put into every sport game that you play to keep balance and order- to keep things flowing. Part B.) If we didn’t have patterns, we wouldn’t live a regular life. Things from our sports, to even our sleep schedule are managed by patterns. Whether they're subtle, or very obvious, they impact our lives without them. It’d be hard to imagine a world without patterns, if there would even be one…?