Gallery Exhibition

Encoding-Decoding
Constellations

Wiesner Student Art Gallery · Stratton Student Center · W20 Room 209 · 84 Massachusetts Avenue · Cambridge, MA

Wiesner Gallery Polyglot Geometry

Opening Reception

Dec 10 · 5:30PM–7PM

About

Our choice of representation shapes what we can create.

This exhibition explores a translation between constellation patterns of Islamic art and mathematical graphs. By moving between these representations, we gain access to new vocabularies that let us revisit classical patterns and uncover new expressive forms. Central to this work is a method by Rebecca Lin and Craig S. Kaplan that "encodes" constellations as graphs—stars as vertices and their connections as edges—and then "decodes" them back into interlocking stars through circle packing and classical construction techniques.

The designs are crafted computationally in custom-built software and refined through careful manual intervention. They are then grounded in physical making across a range of media, including light, wood, and textiles, often through a dialogue between handcraft and machine processes such as laser cutting. Together, these works trace the interplay between mathematical abstraction, computation, and craft, and the expanded space that emerges when constellations move between these worlds.

By

Rebecca Lin (PhD in EECS, G'27)

In Collaboration With

Ben Weiss (MSc in MAS, G'27)
Yufeng Zhao (MSc in MAS, G'27)

About section image (left wall) About section image (right wall)

Works

Background Videos

Video I: Constellation Patterns

Islamic geometric patterns are a rich and venerable ornamental tradition, their interlocking stars woven through precise geometric rules. While four- and six-fold constellations rest naturally on square or hexagonal grids, any departure from these symmetries—with stars of five, seven, nine, or eleven points, and countless others—unravels into a far more complex puzzle. Artists have met this challenge with inventive geometries and artful distortions, yet the crafting of nonstandard constellations has remained painstaking, uncertain, and underexplored.

Video II: Encoding-Decoding Scheme

Intrigued by constellations that mix or depart from classical symmetries, Rebecca Lin and Craig S. Kaplan proposed an encoding–decoding scheme for generating star-based designs. A planar graph encodes the pattern: vertices represent stars, and edges specify how they meet. From this graph, a circle packing—guaranteed by the circle packing theorem—provides a geometric scaffold, upon which classical construction techniques are adapted to produce the interlocking motifs.

This translation between combinatorial and geometric representation opens new expressive possibilities. By crafting the connections between vertices, one controls each star's points and how stars relate. The rest of the exhibition features many new designs—some classical-looking, others more freeform—created with this approach.

Video III: Computational Design Tool

Lin and Kaplan developed a computational design tool that renders the graphical and geometric objects of their encoding–decoding scheme as graphical and programmable structures. It supports a new mode of reasoning about the method and the expanded design space it creates, bridging the gap between mathematical abstraction and craft.

Projections

Projection I: Patterns / Circles / Graphs

Year: 2025

Collaborator: Yufeng Zhao

Three constellation forms, traced in white, appear alongside animations of their circle-based scaffolds (yellow) and the corresponding contact graphs (blue), where each vertex represents a circle and each edge marks a tangency.

These constellations are traced via Euler tours, each covering every segment once. Different heuristics—such as taking the smallest turn or the longest next edge—produce distinct tracings, hinting at a broader idea: representing constellations as graphs gives us access to the language and tools of graph theory, and exploring them through code reveals new ways to see and understand them.

Projection II: Discovery

Year: 2025

Collaborator: Yufeng Zhao

A collection of structured graphs that, when reinterpreted through our mathematical–computational framework, generate classical-looking patterns that, to the best of our knowledge, are distinct from known examples.

Laser Engravings

After Schotter

After Schotter

Year: 2025

Medium: Laser engraving on acrylic

This piece nods to Georg Nees's Schotter (1968), an early computer-generated artwork where a grid of squares unravels through controlled, parametrized randomness encoded in a computer program. The work visually articulates the relationship between order and disorder. In our reinterpretation, each square is replaced by a rosette—a petaled star that recurs in Islamic constellation patterns and serves as the fundamental unit interpreted and woven throughout this exhibition.

Disintegrating (State of Mind)

Disintegrating (State of Mind)

Year: 2024

Medium: Laser engraving on printmaking paper

An expression of order and chaos emerging from "decoding" a graph designed with controlled randomness. The stars, although scattered in shape, size, and combination, are woven into structure, all at once integrated and unraveling.

Also: 2025 JMM Mathematical Art Exhibition
(Honorable Mention)

Press: New York Times
American Mathematical Society

Yearning (for a Fantasy)

Yearning (for a Fantasy)

Year: 2025

Medium: Laser engraving on printmaking paper

Against structure, a stretch toward freedom. A gap between what is and what could be.

Two pieces on the wall
Photo: Esther Lin

Sculptures

Textile Studies

Textile Studies

Year: 2025

Medium: Polyester cotton blend

These pieces explore a translation of digital patterns into the physical world. Mathematics and computation—often seen as abstract or distant—can become embodied through dialogue with handcraft, which carries care and closeness. In this form, the patterns are lived-in and intimate: draped on the body.

Also: 2026 JMM Mathematical Art Exhibition

i couldn't find myself (in your cosmic presence)
Photo: Esther Lin
i couldn't find myself (in your cosmic presence) i couldn't find myself (in your cosmic presence)

i couldn't find myself
(in your cosmic presence)

Year: 2025

Medium: Engraved plywood, acrylic paint, and light

Shadowed and fragmented,
yet widening—
a field of rosettes blooms,
a nod to kintsugi.

Sculpture Study

Sculpture Study

Year: 2025

Medium: Nylon 12 (SLS 3D print) and Gypsophila

Collaborator: Ben Weiss

The piece begins with a circle packing on a freeform surface, followed by our motif construction atop that scaffold. It demonstrates the possibility of entering the framework at a different point in the translation—working directly from circle packings instead of starting from graphs—and explores the new forms unlocked when this approach is extended into 3D.

Opening reception
Photo: Esther Lin

Prints

Spiraling

Spiraling

Year: 2025

Medium: Digital print

This piece explores the interplay of curiosity, compulsion, and overwhelm—the mind-numbing sensation at the cusp of countless rabbit holes, each a vortex of possibility. Which one to choose? It hardly matters. Linger on any, and become lost (again) in a spiraling, looping imagination.

Also: "Intersections", Group Exhibition, Seattle Universal Math Museum (SUMM) & MercerIsland Visual Arts League (MIVAL), Mercer Island, WA.

Press: KING 5 News

How it appeared in my dreams - Image 1
How it appeared in my dreams - Image 2
How it appeared in my dreams - Image 3
How it appeared in my dreams - Image 4

How it appeared in my dreams

Year: 2025

Medium: Photography

Two pieces on the wall

Process

Research Notes collage
Photo: Esther Lin

Research Notes

Year:2021, 2023

Medium: Collage

A collection of snapshots revealing Lin and Kaplan’s development of their encoding–decoding scheme.

Laser Engraving Experiments

Laser Engraving Experiments

Year: 2024-2025

Medium: Laser engraving on printmaking paper

A series of tests using different laser cuttings to understand how their parameters interact with printmaking paper.

Acknowledgements

I’m grateful for the support of many individuals and communities across campus and beyond. This exhibition was made possible through the generosity of MIT MAD, whose freedom and support enabled this season of work, and the MIT Office of the Arts for the opportunity, thoughtful curation, and a lovely write-up. I’m also thankful to the communications teams at MIT Arts, the Media Lab, CSAIL, MAD, and SA+P for helping share this work, and to the folks at the CBA and CSAIL machine shops for their thoughtful advice.

I owe special thanks to my advisors, Erik D. Demaine and Zach Lieberman, for their guidance. I'm also grateful to Craig S. Kaplan for being one of my early mentors and advocates, and to my collaborators Ben Weiss and Yufeng Zhao, who were a joy to work with.

A heartfelt thank you to Sarah Hirzel, the gallery’s curator, and Katherine Higgins from MAD for being steadfastly in my corner throughout this process. Finally, thank you to my family and friends for their constant love and support—especially my sister Esther Lin, my biggest supporter, an incredible event planner and photographer, and a powerful researcher.

Opening reception