Week 2. Art + Math

This week's post is devoted to math as one of the most fundamental knowledge of the whole universe. Math is all around us: starting from the shape of the flower and a snowflake and going to the architecture design. I believe that nature is the best architect, and we should learn from it.

Two fractal scales of phi spiral overlapping in opposite directions

Take a look at these fractal images. Although they are visual representations of the mathematical equations, they are aesthetically pleasing to our eye. They are like a piece of art by itself.

 

Equations and their visual representations

In addition, artists have been using golden ratio since the dawn of time. From the lecture, I found out that the golden ratio is found to be aesthetically appealing. No wonder the most famous pieces of art were created in reference to the golden ratio. It brings order and understanding. Artists use different aspects of math all the time: fractals, spatial perspective, balance, and symmetry. 

Under the wave off Kanagawa

As creatures living in 3D, it is impossible for us to see the fourth dimension and very difficult to imagine - our perception of space is limited by the laws of Euclidean geometry. As Linda Henderson mentioned the fourth dimension was treated as freedom from established laws and exploration beyond what we can see or understand. In addition to that, Adwin Abbott pushes our limits of understanding the space in his book “Flatland”. My personal perception of 4D is probably the same as A Square’s confusion when he found out that there is a third dimension. As a math major student, representation of the fourth dimension always interested me, and I believe that Art and Math cannot go without each other. Art is a visual representation of Math. Everything can be described by mathematical equations. I think that these disciplines cannot exist without each other as both require spatial recognition skills, feel of shape, proportion, symmetry, and so on. To finish off, I would like to show some ideas how gave designers see, interpret, and use the fourth dimension in their works. Think it is a great way to incorporate math and art in computer science project like the one in the video.

Sources:

Abbott, Edwin Abbott. “Flatland.” Flatland, by E. A. Abbott, 1884, http://www.ibiblio.org/eldritch/eaa/FL.HTM. 

Bernard, Luc. “ Luc Bernard.” Luc Benard, https://virtualmathmuseum.org/mathart/ArtGalleryluc/lucindex.html. 

CodeParade. Non-Euclidean Worlds Engine - YouTube. https://www.youtube.com/watch?v=kEB11PQ9Eo8. 

Henderson, Linda Dalrymple. “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion.” Leonardo, vol. 17, no. 3, 1984, pp. 205–10, https://doi.org/10.2307/1575193. Accessed 9 Apr. 2022.

“Learn the Golden Ratio for Your Artworks on Canvas.” Upper Canada Stretchers | Art Canvas Stretcher Bars | Serving USA & Canada, https://www.ucsart.com/learn/blog/learn-the-golden-ratio-for-your-artworks-on-canvas. 

“Multi-Frequency Phi Double Spirals.” Cosmometry, https://cosmometry.net/multi-frequency-phi-double-spirals.html.