In class on Wednesday, we talked about the universe and if we thought it was infinite or finite. There were obviously different views and opinions on the subject. When we began to do our arts and crafts with the paper cutting and twisting creating cylinders and Mobius Bonds, I began to make a connection to the real world. As we kept tracing lines and cutting I began to realize that as we started with the Mobius Bond and ended with knots I recognized the shape and thought it looked like the infinity knot. This is often scene in women’s jewelry and other sorts of crafts. It also resembled a so called figure 8 which is seen in dancing. Oddly enough, that is also what my final project is going to be about, the mathematics behind dancing. As I was twisting and observing the shape made with the paper, a friend sitting next to me in class also made another observation of the paper that resembled something that we played with in our childhood. As I know she is going to post about it, I will leave it for her to share about but it was astonishing to see how a piece of paper resembling what we were learning about can relate and remind us of so many other aspects in the outside world.
After talking about higher dimensions in class including our beliefs in the universe, is is infinite versus finite? Is there aliens? Other worlds? All I could think about during this conversation is the show called Stranger Things. I recently binge watched the first season after hearing how good it is, and I would totally suggest it as a must watch. In this show they have another world, “the upside down”. It is not easy to get to, and it is not the same as our world. The upside down is creepy, and evil. It’s cold and lacks human life but is filled with over grown root like structures and life related membranes. It is so hard to get to you need a stronger magnetic force than anything available on this planet. I’m not saying this is what I believe but the crazy thing is, we don’t know! This show is just an example of how many types of worlds or creatures there possibly could be in higher dimensions.
I think snowflakes are a good example of fractals. Because of their repetition shown by their arms, it looks like it could repeat forever. Here is what I’m talking about:
This snowflake reminds me of what we did in class, where we pick a spot on the fractal and zoom in forever. To me, it looks like we can zoom in to the middle of the snowflake, and have it do just that.
This snowflake has a fractal repetition in its arms. It looks like the tree branch fractal–
You add 5 lines stemming out of a singular line, and do the same to each of the 5 lines. Add 5 more. So in a way, if you really think about it, tree branches are like snowflakes! (When we talk about fractals)
Fractals in nature reach skin deep within this video. It discusses that nature displays many fractals, even within our anatomy. The video lists off these various examples including: our veins, kidneys, lungs, etc. All of which, having the self-similar (never ending) pattern of a fractal. I admire this video because of its mixture of both biology and mathematics. It actually made me realize the significance behind these patterns and how intricate they are. Also, the idea of how they came to be and the various forms of repetition to create them. The video acknowledges Mandelbrot and how he issues his idea on the limits of mathematics.
One example being the Mandelbrot set, in which brought to life the idea of mathematics many have not seen before. Thus, showing the intricate structure of fractals. I would definitely give this video a watch! It brings to light the many examples of where fractals are alive where we would never think to find them.
As soon as we started talking about fractals in class I immediately thought about something I love, flowers. I have always had a love for flowers since I was little. I find them beautiful but interesting. When you really look at them you see so much. They are all so unique and different. There are certain flowers that have a few fractals and then others that have tons! Below are some pictures that I found online that are different shapes and sizes. When discussing fractals I think of flowers because to me they are easiest to relate to!
So when Dr. Plante was showing us the many different types of fractals this past week, my mind instantly went to a toy I loved playing with as a child. The kaleidoscope! I was and still am so intrigued by how the device manages to take an ordinary image and superimpose/distort itself to look larger or smaller than what you originally looked in upon.
For those who don’t know how one works, a kaleidoscope is a tube with two or more reflecting surfaces that are positioned on one another at an angle to form symmetrical patterns that can be seen when you look into the lense. Most kaleidoscopes allow you to twist the tube, which allows you to alter the shape’s size and sometimes even the color. Some of the pictures that you can see are very closely related to mandalas and maybe even prisms.
Here are a few examples of what I’m talking about
It honestly took me a few minutes to find kaleidoscope images with fractals inside it, but hopefully these provide an idea of what I was thinking about during our lectures. This intriguing toy of my childhood, definitely not something I ever thought I would instantly think of in a math class.
When we were talking about fractals, I actually wrote in my notes “like spongebob’s hands on hands” because that is what I instantly though of. For those of you not familiar with what I am talking about, the image in my head is of hands on each of spongebob’s fingers when the image is zoomed on spongebob’s hand. I could not find that image, but I could find an image of a glove from gloveworld that follows the same pattern. I have said glove a lot, so I will show you a picture to depict what I am trying (and failing) to explain:
Because I could not find the exact picture I was looking for, you will have to imagine gloves on every finger, and on the finger of every finger.
Update: a better example of what I am trying to show, just not in Spongebob:
Research that attempts to use fractal mathematics to make sense of natural complex systems has been shown to yield more precise prediction capabilities than previous prediction models that relied on statistical analysis. This work, done by the “Father of Fractals,” Dr. Benoit Mandelbrot, yields a deeper level of information that greatly increases the potential for earth scientists to understand and predict natural disasters. By studying past events in terms of order and scale, scientists are able to calculate more accurate probabilities of future natural disasters. This application of data analysis is increasingly more valuable as we combat global warming and the increased frequency and intensity of these events. Better prediction allows for increased preparedness and potential evacuation which saves lives.
I am the son of a Greek immigrant and when I was 10 years old I was fortunate enough to take a trip to Greece during the summer for a few months with my family. I have these ongoing and aged memories from childhood of exploring caves rooted deep into the sides of mountains right by the Aegean Sea. Traveling down these thorn-encrusted and lavishly green 105 degree angled hill into a dark sea cave. On the ground, rocks, pebbles, dust, the skeletal jaw of a goat which my brother collected and brought back. I remember him hol
ding it out of the car window as the air brushed by it. On the top of the cave though, stalagmites. These beautiful rock formations that are created due to the accumulation of ceiling drippings. After doing some googling of the fractals in nature, I came across this image. It fits the criteria of a fractal as you can see from the repeating branches coming off each main dripping. These are beautiful to me. Both in natural beauty and the beauty of nostalgia.
/end pretentious post of childhood reminiscence/
What do ya’ll think?
I saw fractals this morning, but was in too much of a rush to take a photo. On a cold morning, it’s common to see ice on your car windows and this is what I saw this morning. When you look closely you, beautiful snowflake-like patterns become apparent. I found a great example of this in a photo I took last year.
Probably the only perk of living in an old house with un-insulated windows is that on especially cold mornings I wake up and see these sparkly works of art. I know it’s a low quality photo, so zooming in doesn’t really work the way I want it to. But you can still see the fractals in the ice!