# Yongquan Lu

Mathematical Artist; Computer Science Student
CSAIL, MIT
Cambridge, MA, USA

I am a paper artist and am currently completing my Bachelor's in Mathematics and Computer Science at the Massachusetts Institute of Technology.

I love working with paper and have in particular been making paper sliceform artwork since 2010. This is a medium in which paper strips are cut, folded, and slotted together to form geometric configurations. These configurations have traditionally been inspired by Islamic star patterns but in theory there is no restriction.

Since 2014 I have been working with my advisor Erik Demaine to develop computational tools to aid in the design of such pieces. The two pieces show the breadth of possibilities of this type of artwork.

Royalty
25 x 25 x 1 cm
Paper
2016

Royalty is a sliceform based on a traditional Islamic motif, where a symmetrical 12-sided motif is tiled in a square grid. Traditionally, such designs would be drawn via compass-and-straightedge constructions. This piece, however, is significant because it was built declaratively with an approach developed by Erik Demaine and me: I drew the approximate pattern digitally with a mouse, and applied numerical optimization techniques to "clean it up" (for example, make sure parallel lines were exactly parallel).

This piece is hence a proof of concept that traditional designs could be constructed via our numerical optimization technique, with visually indistinguishable results from traditional compass-and-straightedge constructions.

Sunflower
27 x 27 x 10 cm
Paper
2016

Sunflower is inspired by the spirals naturally occuring in plant phyllotaxis. I used Mathematica to plot two families of logarithmic spirals, one clockwise and one counter-clockwise. By plotting the intersection points of each curve, I was able to compute the arc length of each segment and generate strips of paper with slits in the correct locations. Every strip is unique since the two families are mutually prime. As in phyllotaxis, the number of spirals in each direction form consecutive Fibonacci numbers.

This piece is unexpectedly dynamic -- it can lie flat as a disk or contract up into a cylinder. The picture shows an intermediate state, where it is curved and opening like an umbrella.