Hyperbolic Beehive: Upcycled in Folds, Hanging Beehive Art

Nature’s precision has always captivated me, a notable example of which is the perfect hexagonal geometry of beehives. In my latest project, I sought to transform this natural perfection through the lens of hyperbolic geometry, creating a piece that challenges our perception of organic forms. This exploration into the intersection of natural patterns and mathematical distortion has led to insights about both artistic process and the underlying structures that shape our world.

The Concept: Bee-Core Meets Non-Euclidean Space

My vision merged two distinct visual languages: the structured beauty of honeycomb patterns and the mind-bending world of hyperbolic geometry. While beehives represent nature’s mathematical precision with their perfect hexagonal repetition, hyperbolic geometry introduces an element of controlled chaos—a mathematical framework where parallel lines diverge exponentially and shapes curve inward infinitely.

The inspiration for this fusion came from multiple sources I came across in my undergrad studies. During my research, I discovered the fascinating work of mathematician Dr. Diana Davis, whose visualizations of hyperbolic planes helped me understand how to transform regular patterns into curved spaces. Additionally, the writings of D’Arcy Thompson in “On Growth and Form” revealed how natural structures often follow mathematical principles, yet can be transformed through systematic distortion while maintaining their essential character.

The hexagonal pattern of honeycomb isn’t just aesthetically pleasing—it’s mathematically optimal. Bees create these structures to maximize storage space while minimizing material usage, a principle that guided my own material choices and construction methods. By introducing hyperbolic distortion to this optimized pattern, I aimed to create tension between natural efficiency and mathematical abstraction.

Sustainable Creation Process: Materials and Methods

Sustainability being the theme of the assignment, drove my design and material choices. I worked near exclusively with second hand art materials, reflecting both practical constraints and ecological consciousness.

Material Selection

• Black craft paper from my personal art supplies, handed down sister’s art supplies nearly a decade ago
• Second-hand gold leaf scraps and pearl pigments from Art Parts, selected for their light-interactive qualities
• Paper cement from my existing collection, Excellent for creating strong paper bonds

The selection of these materials wasn’t just about sustainability—each component brought unique properties that enhanced the final piece. The black craft paper, for instance, proved ideal for creating sharp creases while maintaining structural integrity. Its dark color adds depth to the piece and enhances the pop from the gold embellishments, creating additional layers of visual interest.

Technical Development

The fabrication process combined traditional origami techniques with modern technology, a fusion that proved essential for achieving precise results. I based my design on Herng Yi Cheng’s honeycomb crease pattern, which I modified by expanding the angles 15 degrees. This modification was crucial—it allowed for a more dramatic hyperbolic effect while maintaining structural stability. For the much requested bee, I followed a tutorial by Tadashi Mori for an origami wasp (close enough).

 

The development process included several key stages:

1. Pattern Modification
   • Digital adaptation of the base pattern using Adobe Illustrator
   • Mathematical calculations to ensure proper angle relationships
   • Creation of test patterns at various scales
2. Prototyping
   • Multiple iterations testing different fold sequences
   • Curvature assessments
   • Glue tests and pearl pigment medium tests
3. Final Construction
   • Laser engraving for precise crease patterns
   • Nearly 6 hours of folding
   • Painting on gold elements

 

After prototyping multiple iterations, I used the BTU lab’s laser cutter to engrave the final pattern—a step that ensured precise folding while maintaining the organic feel I sought. This technology proved invaluable for achieving consistent results across the entire piece, especially in areas where multiple folds intersect.

 

 

 

 

Where Mathematics Meets Art: The Final Form

The resulting piece hangs from my ceiling, creating an ethereal floating effect that captures both the rigid structure of beehives and the fluid distortion of hyperbolic space. The golden hues catch light differently throughout the day, bringing the mathematical patterns to life in unexpected ways.

The gentle rotation of the piece became a crucial element I hadn’t fully anticipated. As the sculpture slowly spins from air currents in the room, the gold leaf elements create an ever-changing dance of reflections that amplify the sense of dimensional distortion. The black paper base appears to shift between solid and void as the piece turns, creating a mesmerizing effect that makes the structural geometry seem to flux and flow in space.

The gentle air currents of the room also makes it possible to observe the full complexity of the hyperbolic distortion as it rotates. From any given angle, the honeycomb appears to curve and warp in a specific way, but as the piece spins, these curves seem to transform and flow into one another. What looks like a gentle bend from one viewpoint suddenly reveals itself to be a dramatic fold from another, creating an ever-changing landscape of geometric distortion. The rotation allows viewers to understand the true three-dimensional nature of the hyperbolic plane, as each turn exposes new relationships between the hexagonal cells and shows how they connect across curved space.

An Ecological Future

While this piece currently adds mathematical intrigue to my apartment (and thankfully remains untouched by my cats), its journey isn’t over. I plan to recreate the pattern using organic, non-toxic materials and introduce it to my mother’s beehive this summer. This next iteration will test how my mathematical interpretation of honeycomb structure interacts with actual bees—a fascinating intersection of artificial and natural geometry.

The future ecological experiment raises intriguing questions:

• How will bees respond to the hyperbolic distortion of their natural patterns?
• Can this geometric exploration inform our understanding of bee behavior?
• What modifications might be necessary to make the structure more appealing to its intended inhabitants?

Reflection and Continuation

This project represents more than just an artistic exploration; it’s a meditation on how mathematical principles underpin natural structures, and how we can distort and reimagine these patterns while maintaining their essential beauty. Through sustainable materials and precise execution, I’ve created a piece that honors both the complexity of nature and the elegance of mathematical abstraction.

The process has opened new avenues for exploration:

• Further investigations into geometric distortion patterns
• Experiments with different materials and scales
• Potential collaborations with biologists studying bee behavior
• Development of educational models demonstrating geometric principles

As this project evolves, it continues to reveal connections between mathematical theory, natural structure, and artistic expression. Each iteration brings new insights and possibilities, suggesting that the intersection of these disciplines holds rich territory for continued exploration.

Citations:

• Thompson, D’Arcy W. 1942. On Growth and Form. Cambridge: Cambridge University Press.
• Davis, D. 2023. “Visualization of Hyperbolic Geometry through Surface Patterns.” Journal of Mathematics and the Arts 17 (1): 44–61. [DOI]

• Aesthetic0ly-Pleasing, “????????? ??????? ??? ???????,” Tumblr, July 14, 2021, https://www.tumblr.com/aesthetic0ly-pleasing/653853556916502528.

• Naiad’s Eye, “The Use of Non-Euclidean Geometry in Art,” Naiad’s Eye Blog, November 13, 2014, https://naiadseye.wordpress.com/2014/11/13/the-use-of-non-euclidean-geometry-in-art/.

• Tadashi Mori. Origami Wasp. YouTube video, 20:37. January 10, 2024. https://youtu.be/eewG05yjL_k.

•  OpenAI, Grammar Assistant ChatGPT (January 5, 2025), https://chat.openai.com.

•  Herng Yi Cheng, “Flexing Honeycomb Origami Design,” Herng Yi Cheng Blog, 2023, https://www.herngyi.com/blog/flexing-honeycomb-origami-design.