Course Final Reflection - Blog Response #18

It has certainly been a wonderful semester and getting to know great people. The structure and nature of the course was collaborative and refreshing, which was completely different when comparing it to my math undergraduate classes that I took alongside this course. There was a lot about math history that I didn't know of before this taking this class like base 60 number systems and the exact origins of Pythagoras theorem. I also knew very little about the contributions that ancient civilizations like Babylonians and Egyptians made to current mathematics. Some of the in-class activities involving solving ancient math word problems are definitely one of my favourite memories. Even seeing the glimpse of the origins of modern mathematics through Euclid's Elements was extremely interesting to me!

Overall, listening to my peers' discussions and presentations were the most valuable to me. Everyone is so passionate and intelligent about their ideas which makes learning from each other extremely enjoyable. The structure of this course further supports and fosters environments like this, which I'm sure that Susan will continue to maintain! 

I look forward to continue learning about more math history, story-telling, and art as I take more courses, participate in classrooms, and engage with the community. I hope to implement in my own class someday and pass all these fun ideas to my future students.

Until next time,

JJ Kim

Assignment 3 Reflection - Blog Response #18

Cellular automata was a fun topic to research about. The first time I learned about it was during a computer science undergraduate course about a year or two ago. When I realized that the project could be presented as a digital piece of media, I immediately thought that this topic would be suitable. Other than John Conway's Game of Life, there was very little that I knew of related to its history. It's quite interesting to find out that the origins started with a theoretical concept of populating other planets with self-replicating machines. 

While I figured that this topic would have interesting historical backgrounds due its modernity and implications, I was worried about how we could implement it to showcase to the class. My knowledge of coding is not very extensive, after all, I study mainly math and not computer science! Regardless, we decided to stick with the idea and figure out things along the way. Thankfully, I knew about the existence of Pygame which allowed the creation of the art piece to be possible in the first place. Another challenge came about when it came to implementing the rules for some of the cellular automata. Initially, the "Reaction" one would become static and lose its mesmerizing patterns after a few generations, but a solution to this problem was to add some slight randomness to continuously shake up the state of the cells. Since Pygame isn't a very robust software, our board sizes were finite and relatively small. I dealt with this issue by allowing the cells to wrap around the edges, which is possible thanks to our favourite modulo operator! I still have questions regarding on how I can create cellular automata with even more complex rules and patterns, or how it would like like in higher dimensions.

Our presentation slides looked amazing, especially due to Carson's contributions and his drawing expertise! We didn't realize how fast 20 minutes could go by during the presentation so we should have been more mindful.  There was a lot of historical details despite it being popularized in about the last 50 years. If we managed our time better, maybe it would have been nice to go over a bit more in detail on how some of the algorithms ran; I'm not entirely sure but maybe some people were curious about how the code runs. Overall, I was very happy with our presentation and glad that the project turned out the way it did. The mathematics involving cellular automata is very interesting and it is capable of producing some amazing artistic pieces!

Assignment 3 - Blog Response #17

Carson and I worked on the history of Cellular Automata. It originates from the field of computer science, which is a branch of mathematics that has garnered a lot of popularity in the last 50 years! Our presentation will feature 4 pieces of digital art. 

The first one is Stephen Wolfram's "Rule 30". This is a 1-dimensional cellular automata with elementary rules that are encoded by binary representation. We wanted to start with this to introduce the basics of what cellular automata looks like. It utilizes Python packages "numpy" and "matplotlib" to allow us to store the rule as an array with 1's and 0's as elements and subsequently plot to show the outcomes of the iterations. Here, the vertical axis represents time and any horizontal cross-section of the image represents the state of all the cells in the array at a specific point in the pattern's evolution. The rules are simple but it produces a complex and chaotic pattern! 

The next three examples utilize pygames, which is an open-source cross-platform library for the development of multimedia applications like video games using Python. It makes programming 2-D cellular automata intuitive thanks to the implementation of certain convenient functions. 

The second one is the classic "Game of Life" by John Horton Conway. We wanted to show it off as it represents a pivotal moment in cellular automaton history, representing the moment when the concept flew into mainstream and wasn't just exclusive to academia. This inspired many others to create their own rules and creative designs. The specifics of how Game of Life works will be expanded on during the presentation. We will showcase it with colours and various patterns like glider, gosper  glider gun, block, and switch engine. 

The third one is called "Reaction". This type of cellular automata is inspired by research done in chemistry, particularly the Belousov-Zhabotinsky reaction. Due to its spiraling and oscillating patterns, it is commonly studied through a mathematical lens through models and simulations. We hope to show it off in a cellular automaton context!

The last one is called "Brian's Brain". This is a particular rule set discovered by Brian Silverman. We thought it would be a great addition to our collage as it produces beautiful patterns. We wanted to capture history, mathematics, art, and philosophy through this creation. There is background music as well, so hopefully it's enjoyable to experience!

Here is the link to the slides:

https://docs.google.com/presentation/d/1e4g0f9ziMtitHs39ReJUr_33CCBnJ21u1PiqiHKduo8/edit?usp=sharing

Here are some snippets of our artwork. To fully visualize the animation, a suitable source code editor like VS Code is convenient for running the .py files.

Here are the associated .py files:

https://drive.google.com/drive/folders/14WwBmJ-hpqTB0CyzKBXLSdpdYtixIvWh?usp=sharing

Assignment 3 Draft - Blog Response #16

 I will be partnered with Carson, and we will be working with the history of cellular automata. The format of our artistic piece will be electronic/digital art through the use of code (most likely Python).

Draft reference list:

Berto, F., & Tagliabue, J. (2017). Cellular Automata (E. N. Zalta, Ed.). Stanford Encyclopedia of Philosophy; Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/entries/cellular-automata/ 

Poundstone, W. (2024, October 24). John von Neumann. Encyclopedia Britannica. https://www.britannica.com/biography/John-von-Neumann

Sarkar, P. (2000, March 1). A brief history of cellular automata. ACM Computing Surveys, 32(1), 80–107. https://doi.org/10.1145/349194.349202

Schiff, J. L. (2008). Cellular Automata: A discrete view of the world. Wiley-Interscience. https://doi.org/10.1002/9781118032381 

Wolfram, S. (2002). A new kind of science (pp.876-878). Wolfram Media. 

Assignment 2: Math History Reflection - Blog Response 15

My presentation was focused on the history of limits to infinity. It was really interesting to research on how it all started, especially before a time of mathematics where Arabic numerals and algebraic notation were absent. The majority of my presentation was focused on the findings of Archimedes and the area of a circle via infinitesimals. It incorporated a clever use of a proof by contradiction method, which somewhat surprised me as I thought that would have been more of a modern notion. Due to time constraints, it was impossible to cover the entire history of limits with every detail. It stretches over a millennia and the most interesting part is that the order of development started with integrals, then derivative, and finally limits. This is the opposite order of what is being taught in schools! 

One of the main things I want to take away from this and show students is that infinity is not mere value that we plug in the limits notation. It seems like due to the extensive amount of analytic work that students have to in a calculus class, they get desensitized to the concept of the idea and ignore the beauty and complications that come with it. Infinity was deemed as beast by mathematicians, and even the very best failed to wrestle with such concepts. Perhaps by presenting these historical moments, students will be able to relate and realize why it's okay to find calculus confusing. We have prime examples of moments of epic collaboration and battles between pairs of mathematicians like Kepler and Galileo, and Leibniz and Newton. And we can't forget that none of their work wouldn't occur without the work of Ancient Babylonians, Greek, Egyptian, and Indian mathematicians that pioneered the early foundations.