2015 Bridges Conference

# Yongquan Lu

## Statement

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 below demonstrate these techniques; while they were hand-assembled, their dimensions were derived via a computer program.

## Artworks

Girih II is an instance of paper sliceform artwork. The central structure is derived from a traditional Islamic motif, which is noted for its quasiperiodicity (like Penrose tilings!) and is discussed in Lu and Steinhardt's 2007 paper "Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture". I have opted to surround the motif with a border of pentagonal stars for aesthetic reasons. Observe that this pattern has 10-fold radial symmetry. There are 6 strips which are closed loops and circle around the piece before closing up; the others all extend radially from the center. The assembly of this piece from the constituent paper strips took 8 hours.
Brimstone is an instance of paper sliceform artwork and has an underlying 12-12-3 semiregular tiling. Each dodecagon's center contains a traditional rosette motif, but I have decorated each motif with a border of diamonds, causing each strip of paper to zig-zag erratically back and forth. The three coloring of the pattern exemplifies the inherent rotational symmetry in this tiling. An interesting fact about this tiling is that there is only one type of strip in the underlying tiling (modulo rotations and translations). If the tiling was extended infinitely, any two paper strips would be indistinguishable. The assembly of this piece from the constituent paper strips took 6 hours.