Rashmi Sunder-Raj

Mathematical Artist
Waterloo, Ontario, Canada

I seek patterns to make sense of my world. Some of these I choose to interpret as visual images.

Sometimes this involves tessellations, sometimes crochet...and sometimes other things.

Patterned Penrose Pentagon
Digital Art

This year, Sir Roger Penrose won a Nobel Prize in physics for his work involving black holes. This piece is intended to be a general celebration of his work.

It consists of an impossible shape referred to as the Penrose Pentagon, which appears to be patterned with an Penrose rhombus tiling. In actuality, the tiling has been done over a large area, but is only visible through the strategically-aligned impossible shape, with shading providing the illusion of depth.

Last year the “shadow” of black hole at the center of galaxy M87 was “photographed” using the Event Horizon Telescope. Strangely enough, one can almost see a pentagon there. I have used a similar colour palette to tint this pentagon.

Bead Crochet Piece
Seed beads, thread

I often explore patterns involving regular polygons whose edges touch, and have found various ways to represent them using physical materials.

Edge-touching regular polygons can be approximated by round beads attached in such a way that their holes are perpendicular to the plane of the pattern. I have developed techniques for doing this with seed beads and thread using a fine crochet hook (.6mm or less).

This time, I have chosen to use 18-gons which can allow for rings of 3, 6, 9, or 18 polygons as well as other groupings. Here the crocheted piece is shown as part of a larger design.