Well, this was an interesting project, to say the least.
I definitely had to think a little bit about how I could implement the functions covered this year and turn them into a Christmas card of sorts. All in all, I believe I did a good job, and I know for a fact that my understanding of the implementation of the functions in a graph has improved.
I’d say overall, the most difficult function to use would have been the logarithmic functions as their shape was difficult to manipulate into my design, but with some creative restrictions, I managed to make a nice Christmas stocking out of them. However, the heavy lifting was done by the polynomials and the radicals, simply because they created such excellent starting blocks to create an image from. With functions using trigonometric values, for instance, they create fairly complex graphs, which in turn create harder to manipulate images.
Though some parts were arduous, one strategy that helped was to go over pieces of functions in steps. Coordinates and plotting, restrictions, color, and if necessary, animation. Ticking off a checklist like this enabled me to move at a quicker pace and to keep my sanity intact a little while longer. This was definitely a challenge, and mostly because of unfamiliarity with the software. I’ve never used demos for something this in-depth, so it took a little time to get comfortable with the mechanics provided. It’s like learning lightroom or photoshop. They can be slightly intimidating, to begin with, but with practice, all the tools make sense and can be used to create pretty much anything.
For a bit of inspiration, I checked out the Demos page of user-created images on graphs and I was blown away by what some people are capable of. Most notably, a portrait of Simba from The Lion King was put together incredibly well, and I was even able to draw inspiration from certain equations used there to create specific shapes on my graph.
All in all, I believe my understanding of the correlation between graph and formula has increased drastically and I think this exercise has helped massively in my general comprehension of the graphing of formulas. I now feel much more confident using demos and will be able to use its tools in the future to better myself, and my understanding of mathematical principles.
Here is the final image and here is the link : https://www.desmos.com/calculator/1kzbasuk2z to check out the formulas I used!
Owen