Mathematics of Symmetry and Art: Week 6

This week represented the culmination of my project. I finally set up my still life and went to work. Setting up a still life for a project is never easy and I think I made it even harder for myself by trying to make it fit a certain grid. I wanted to explore how symmetrical patterns helped make a composition more effective, and I think that thinking about the patterns as a guide was helpful, but difficult to think past. In the end I had an idea of the pattern that I wanted to achieve, but I also started with a composition that I liked and then tweaked it to fit the symmetric type I wanted to explore. Another difficult thing to manage was my exploration of color symmetry. This art piece was done with grey-tone pastels because I really wanted to explore the value shifts of the still life and in the end I grouped them into three color types, light, mid-tone, and dark and described the symmetries I fond in terms of three-fold symmetry types.

This is my still life set up:

Screen Shot 2019-07-12 at 3.30.31 PM

I also took pictures of my drawing as I made changes. It started with a pencil plan and then I started to add value be mapping in the darkest parts and the lightest to divide up the drawing. After that I added some more values keeping it to only 5 different pastels to keep the value range pretty close and got progressively more detailed.

This is the progression of the piece:

Screen Shot 2019-07-12 at 3.34.44 PM

The largest picture in the bottom right is the final product. Using this final product I explored the symmetry of the composition focussing on the plane repeating patterns that I saw.

Final symmetric composition

This design shows a *442 plane repeating pattern and how that pattern maps out the composition. You can see that there are strong diagonals in the composition. Ex: The line that starts at the top of the wine bottle, meets the lip of the vase, and follows the angle of the plaster sculpture. There are numerous other lines that mathematically describe the scene and I like that the composition feels solid and has an explanation routed in math.

Final *333:o option 2

Color Key: 0: lightest 1: mid range 2: darkest

This design is a *333//o. This means that the pattern is made by three intersections of three mirror lines. The o represents the kernel of the homomorphism of the symmetry group into the group which permutes the colors of the artwork. The colors are not a perfect match, but they are pretty close!

There are a few other color maps that I though were pretty close. These are:


Final *632::*333

*333//o (variation 2)

Final *333::o

I will spend my last week putting together my presentation. I will officially tie together the math I studied and the art I created.


  1. eclawrence says:

    Wow, very cool how much there is to unpack in just that one still-life. You said you set up the things you drew to achieve the symmetry and patterns you wanted. Now that you are so familiar with them do you also see these patterns randomly in your daily life? Also, similar to what you did, I would be interested to see a drawing where arrangements that did not fit these patterns were distorted to do so (kind of like how cubism made people into rectangles). With such a strong base of mathematics and so many avenues to explore with this topic I hope you continue your research. Good luck!

  2. arvanessendelf says:

    Thanks for the interest in my project! I definitely catch myself diagraming patterns and things in day to day life trying to figure out their symmetry patterns. It is pretty funny how the brain can be taught to see things in a whole new way. I really like your idea about the distortion of objects to make art. I think that there are limitless avenues that could still be explored and I hope that I get to look into more.