Interactive Geometry
Visualizing Lissajous curves through interactive shape transformations
Designed an interactive parametric system translating Lissajous oscillatory motion into real-time geometric transformations within a user-driven grid.
Research Project · Harvard MDE
Role: Computational Design · Interaction Design · Parametric Geometry
Team: Hana Khurshid, Liz Wu
Awarded Jurors Choice Award
Lissajous Grid is an interactive computational project that explores oscillatory motion through geometric constraint. Inspired by Lissajous curves, the project translates mathematical relationships into a user-driven visual system.
A 10×10 grid serves as the interactive field, where users can toggle boundary geometries such as circles, triangles, and squares. While the underlying oscillatory logic remains constant, the internal tracing adapts in real time to each geometry, revealing how spatial constraints reshape motion.
By combining parametric geometry and interaction design, the project makes abstract mathematical behavior legible and engaging, offering a platform for future exploration in data-driven and multisensory systems.
What are Lissajous Curves?
Lissajous curves are the graphical representation of two oscillating systems interacting in perpendicular directions, creating beautiful looping patterns.
It traces a trajectories of points whose coordinates follow sinusoidal movements.
Concept
This project visualizes the mathematical elegance of Lissajous curves through interactive shape transformations, blending motion, geometry, and user engagement.
Project Overview
We use a grid where users can interact with the shapes. The outer geometry changes between a circle, triangle, or square, and the inner tracing follows Lissajous curve logic, adjusted based on the selected shape.
Each shape transforms individually upon user interaction, creating personalized geometric patterns.
Purpose
The project is about experiencing the harmony of oscillations and geometry through interaction.
It’s a playful tool for understanding mathematical patterns visually and interactively.
