Creation Process

Phase 1: Exploration

In the initial stages, I spent time trying to visualize GL(2, F₂) using MATLAB figures and came up with the following images.

The initial black and white figure represents GL(2, F₂) by showing the matrices' elements of 1 and 0 with the colors white and black, respectively.

The following figures represent each element of GL(2, F₂) with a distinct color. The second displays the elements in the same order as the black and white figure, while the third is an attempt at creating a more striking visual pattern by grouping warm and cool colors.

Phase 2: Insect Collection

After creating the initial MATLAB figures, the next step was determining how to organize insect specimens in a way that would reflect the six elements in the group. Naturally (no pun intended), taxonomy came to mind, and the rank of order was the most distinctive in terms of arranging similar insects.

From there, insect specimens belonging to the following orders were collected:

Lepidoptera (butterflies and moths)
Hymenoptera (wasps, bees, and ants)
Orthoptera (grasshoppers and crickets)
Diptera (flies)
Hemiptera (cicadas, wheel bugs)
Coleoptera (beetles)

Additionally, to represent the number 0, black beetles (coleoptera) were selected as they resembled the black squares in the original MATLAB figure.

Note: The insect specimens featured in this piece were generously provided by the Clemson University Entomology Department.

Part 3: Rehydrating and Rearranging Insect Specimens

Before placing the specimens in the arrangement of the group, they needed to be rehydrated in order to rearrange their limbs, wings, etc. This was done by placing the specimens in an airtight container along with a paper towel soaked in water along with isopropyl alcohol to avoid mold growth. These were left for a several days before removing them from the containers and using insect pins to rearrange the desired parts in a way they could dry and remain in that orientation. After allowing the specimens to dry for around two weeks, the pins were removed.

Part 4: Exploring Materials

After establishing the orientations of the insects, the next step was selecting a medium to convey each element through color. Card stock was chosen for its strong visual contrast and cut into 1.5×1.5 inch squares, with each matrix constructed from four individual squares.

With the elements arranged, I observed the orientations and color relationships, and felt that the group structure could be shown more clearly by reorganizing the layout. In particular, grouping the warm-colored elements (corresponding to the subgroup of order 3) separately from the cool-colored elements made this structure more visually apparent. I then rearranged the composition to better highlight these relationships, especially the distinction between the subgroup and the remaining elements.

During this process, I also played around with different color combinations. I eventually landed on the one shown to the right. In this orientation, the colors move from lightest to darkest from left to right.

Based on feedback from a mentor, I was encouraged to reconsider the choice of materials. This led to the use of watercolor in place of card stock, allowing for visible brushstrokes that give the work a more natural and unpolished quality, echoing the organic nature of the insects. This shift was inspired in part by examples of early African quilts, whose patterns reflected similar structural arrangements.

Initially, I attempted to paint each square individually with watercolor. However, I ended up adopting a similar approach to the one used with card stock: painting sheets of watercolor paper and then cutting them into 1.5×1.5 inch squares.

Before placing the insect specimens onto the board, I also tested some arrangements with smaller black squares on top of the colored paper to create some contrast. I ended up discarding this idea since I thought it removed from the prominence of each color.

Part 5: Final Composition

The final composition brings together the mathematical structure, material choices, and visual design developed throughout the process. The arrangement highlights the underlying group structure, with color and placement emphasizing the distinction between the subgroup of order 3 and the remaining elements. The use of watercolor introduces subtle variations and visible brushstrokes, giving the piece a more natural quality that complements the insect imagery.

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