JIAYIN (KAY) LU 卢嘉茵
Applied Mathematician & Computational Artist & Freelance Photographer
Here, I put together my pursuit of artistic expression inspired and enabled by mathematics and computation.
Many of these are 3D printing designs. Personally, I view 3D printing as a great way to make art. It provides a "hands-on" opportunity to explore the beauty of mathematical art and to examine its complexity, patterns and symmetry.
All the designs I made can be downloaded for free on Thingiverse.
Highlights
Computational Design: Series of Perforated Lamps
Course project: SCI 6338, Introduction to Computational Design, Harvard
• Implemented a C++ code to create 3D models of perforated lamps, where the lamps can take any shapes, and can project light on surrounding walls with pre-designed patterns
• Investigated computer graphics techniques in creation of the code, such as voxelization, ray tracing, boolean operations, and the marching cube algorithm
• Designed example demo models, 3D printed them and prepared a setup with LED lights and cut-out foams, to showcase in the final project demo day in class
Computational Design: Series of Perforated Lamps
Documentation GitHub code Video demo
I have always liked light. Light is romantic; Light is imaginative; light is colorful; light is mysterious; light represents hope; light is a world of unbounded dreams.
In this project, I developed a C++ program that generates perforated lamps based on pre-designed wall projection patterns.
The program takes in two kinds of inputs: a lamp shape STL model, and pre-designed light projection patterns on the 6 surrounding walls of the lamp. The program will then generate holes at the corresponding places on the lamp model and output a perforated lamp STL model.
The perforated lamp, when put in a light source inside, will then project the desired patterns on the walls.
I made three demo pieces, where each of them is an artwork of a theme. The program is made available on my GitHub for anyone to use for their own design purposes.
Introduction to Generative Art and Scientific Visualization
Instructor for January@GSAS Mini Course
• Instructed a course at the intersection of computation, mathematics, and art for a diverse audience
• Collaborated with co-instructors to formulate course objectives and curriculum
• Developed teaching materials for “Voronoi art” and “3D printing art”
• Conducted hybrid workshops, combining online and in-person formats, which included explanations of mathematical concepts, coding demonstrations, art demonstrations, and creative design idea suggestions
• Engaged a wide-ranging audience, including Harvard SEAS students and post-docs, as well as participants from various Harvard departments (Medical School, Economics) and external institutions like MIT
Mathematical Art: Rose Tea-light holder
Selected design I created for the mini-course Introduction to Generative Art and Scientific Visualization.
A tea light holder with patterns of the mathematical rose.
Enjoy ! :D
Mathematical Art: the ultimate Triangular Bipyramid
Selected design I created for the mini-course Introduction to Generative Art and Scientific Visualization.
By joining two regular tetrahedron together, we have a triangular bipyramid.
I named this "the ultimate triangular bipyramid" XD Since it not only has all six faces being equilateral triangles (one of Johnson solids), but also each face features a Sierpinski triangle design or a Delaunay triangulation design! XD
I love the shape and the shadow it casts! :D
Mathematical Art:
Tetrahedron Delaunay Triangle Lamp +
Sierpinski-Triangle Tetrahedron-Shaped Lamp
Two selected designs I created for the mini-course Introduction to Generative Art and Scientific Visualization.
1. A regular tetrahedron shaped lamp with Delaunay triangulation designs on the sides~ Each side features a Delaunay triangulation with different particle density.
2. Regular tetrahedron shaped lamp with Sierpinski triangle pattern! Each side features a different iteration/depth of the Sierpinski triangle.
Mathematical Art: Voronoi photo art
Created for the mini-course Introduction to Generative Art and Scientific Visualization.
On the second day of the course, in the "Voronoi Art" session, I taught making image art using Voronoi tessellation/Delaunay triangulation to the class.
Other Artworks
Mathematical Art: earrings 032024
First 3D printing design since after I passed the defense!
Mathematical Art: [2D] Delaunay triangulation heart shape earrings
Delaunay triangulation heart shape earring!
The Delaunay triangulation on the heart shape is generated by the code I wrote in my research project with my advisor Professor Christopher Rycroft!
Mathematical Art: [3D] Delaunay triangulation heart shape earrings
Delaunay triangulation heart shape earring/necklace!
3D version. :)
Mathematical Art: Flowery Lamp
I just like lamps so much :D
Actually this was a design from a year ago, but I finally made it and put on the lights...
I am so happy to see the effect of the lamp with three different colors of LED lights (white, green, blue), against the background of my half-finished painting... I think they match quite well!
-Dec 12th, 2019
Mathematical Art: Bookmark with Delaunay Triangulation
Bookmark with Delaunay Triangulation: Good for gifting!
Mathematical Art: Koch Snowflake Puzzle
A fun set of puzzle designed for my advisor Christopher Rycroft's public library talk on fractal!
His library talk aims at promoting mathematics and science ideas to the general public, in a way that's both educational and fun/interesting.
This is a demo to use to show some ideas of fractal (self-similarity, simple rules).
Mathematical Art: Delaunay Triangulation Dream Catcher Design: "Dreaming of the Stars"
Last time I bought a beautiful little dream catcher during my travel in Ecuador... This time I made a (giant) one for myself! Even better ^_^ It has Delaunay triangulation patterns, generated from the code I am developing in my current research project with my advisor Chris Rycroft! :D I am glad that my research aligns with/contributes to my interests in art and my pursuit of creativity and the freedom that comes with it ⭐️ -Oct 29th, 2019
Mathematical Art: (Fractal Art) Moore Curve Lamp
A lamp with the space filling Moore curve design:
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Inspired by Markellov's Maze Lamp design
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I used the L-algorithm of generating fractals to generate the moore curve; I used the 5th iteration of the Moore curve and used half of it in my design.
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Since a large part of the curve is not connecting, after the print some parts are not supported. To fix the issue, I glue the pattern design on a sheet of paper inside to stabilize it (as seen in the photos, which is the red sheet paper, with a cutted heart shape :) ).
Mathematical Art: (Fractal Art) Menger Sponge Puzzle
A fun set of puzzle designed for my advisor Christopher Rycroft's public library talk on fractal!
His library talk aims at promoting mathematics and science ideas to the general public, in a way that's both educational and fun/interesting. This is a demo to use to show some ideas of fractal (self-similarity, simple rules).
In this case, we made a Menger Sponge puzzle! If you assemble them in a certain way... They will turn out to be a bigger Menger Sponge!
Mathematical Art: Vector Norm Hanging
Decoration
Vector Norm Design! Inspired by a lecture in my AM 205 class, where professor Chris Rycroft showed us some cool animation that you can do to visualize different vector norms (i.e. different ways of comparing the magnitude of a vector).
Here, I took vectors in R^3, and made some variations of 3D designs to visualize the 1, 2 and 4-norm of the vectors. 😊
The last photo is a sketch I did in class, when the idea emerged at the time 😃It is magical to see you idea came true in the end!
Mathematical Art: Flower Ball
Magical to see my imagination coming to life (2/2)
<Necklace>
Mathematical Art: Crumpled Circle
Magical to see my imagination coming to life (1/2)
<Earrings>
Mathematical Art: Light Tower
Inspired by an applied complex variables class! :D
Specifically, inspired by w = sin(z), z=x+iy, x,y are real numbers.
This function maps horizontal lines in the z-plane to ellipses in the w-plane.
My naive idea is to visualize this mapping (although impossible since it is 4-dimensional) by setting the z-plane and w-plane just parallel to each other, and then draw horizontal lines on the z-plane and corresponding ellipses in the w-plane, and then sample some points of z and connect them to their corresponding points of w with straight lines.
Notice that as the horizontal lines (in the bottom) are further away from iy=0 (the center line), the corresponding ellipses become rounder and rounder. As the horizontal lines are closer to iy=0, the corresponding ellipses are thinner and thinner. The focus of all the ellipses in the w-plane are (-1, 0) and (1, 0).
Playing around with it and add some random thoughts in the modeling I got this shape that I like a lot!
I put it next to my scented candle, and with the LED lights added on, it is a perfect decoration that makes a romantic / nice atmosphere at night!
Differential Equation Class Inspired Candle Lamp Holder
After I took a differential equations class, I used laser cutting to make a lamp with patterns designed from the phase plane of linear differential equation systems, to illustrate their different stability of solutions.
Mathematical Art: Seashell
It may be used for home-decor. You could simply put it on the table or hang it up by the windows. :)
The process of making this model was fun. I was just playing around with Mathematica, trying out different functions and graphing commands.
When I got the interesting seashell shape, I used several programs to edit it for a elegantly looking pattern. Softwares used: Meshmixer, Meshlab, 3Ds Max and NetFabb.
Now it sits quietly by my wine and candle on the wooden table, giving a serene and modern feeling in an antiquated surrounding. (I live in one of the oldest building in the area. ;) )
Mathematical Art: Geometric Earings
These three pairs of earrings represent Euclidean Geometry, Non-Euclidean Geometry - including Hyperbolic Geometry & Spherical Geometry.
Motivation: I was thinking of designing a set of earrings that have very simple designs, yet representing some important mathematical phenomenon, especially the ones I learned last semester in my MATH 402 Non-Euclidean Geometry class.
Things to notice: the triangles' interior angles sum; the definition of "straight line" or "line" in different geometries; the look of the triangles; the perpendicular lines...
Fun fact: They were designed in my winter break of 2016: One night during my shower, the idea came to me suddenly and I used the steam from the hot shower water to sketch the earring designs on the mirror... :)
Mathematical Art: Necklace "The Future"
Co-designed with Richard Southwell - a master in Mathematica shaping.
The idea for the necklace is to convey a feeling of the future using geometry shapes, it doesn't look like things in real life, so it could give a feeling of uncertainty, limitlessness and possibilities in the future.
(PS. The very pretty dress which is light up with LED lights in the first picture, is made by Jessica Nelson, who is an expert in dress making and bag making with beautiful designs and different technologies. The photo was took in State Fair with CUC Fab Lab. I think she and her dress look perfectly with the necklace!! )
(PSS. My chopstick hair was made by costume expert Duncan Baird without a hair tie, He knows a lot of artistic style hair-doing and he is awesome!!)
Mathematical Art: Tealight Cover "Colors of Light"
Co-designed with Richard Southwell - a master in Mathematica shaping.
The idea is to explore different ways of expressing colors- Here, it is to express it as flame-like lights with an elegant-looking tealight cover.
Mathematical Art: Flowerpot "Jetzt ist Sommer"
Co-designed with Richard Southwell - a master in Mathematica shaping.
The idea comes from the beautiful summer season, when there are green and colorful flowers everywhere. :)
Mathematical Art: Surprise Box
My very first big 3D printing design project!
I used Mathematica to model a heart shape using the cartesian expression of cardioid and some flowers by modifying online open codes Virtual Flowers with Crispate Petals by János Karsi, an applied mathematician at the University of Szeged.