<< Designers Corner is the place where ShapeDiver designers talk about their work. There is a story behind every model, and who better to tell the story than the designer herself? Introducing the series is Elissa Ross, a mathematician fascinated by the tight relationship between science and art.>>
I’m a geometer working as a consultant in the digital design industry. MESH Consultants is a small team of mathematicians, who work on all kinds of projects that involve both challenging geometry and computation.
We love to work on architecture projects, but we also do a lot of software development for everything from scientific simulation to apps related to 3D printing.
Sometimes we write code to help artists realize a particularly unusual geometric creation.
Physically we are situated in the Fields Institute for Research in the Mathematical Sciences,which is a world class mathematical research centre in Toronto. MESH itself has an active research mandate, and we both conduct mathematical research and also absorb and incorporate new findings in mathematics into our work.
More personally I completed a PhD in discrete geometry focusing on the rigidity of periodic frameworks (you can think of this as a mechanism based on a periodic tiling).
My recent research is focused in the field of architectural geometry, and the surprisingly related topic of simulating crystal growth.
The non periodic zeolites model is really exciting for me because it is the first time I’ve really had a good representation of an idea that I’ve been thinking about for a couple of years.
A non periodic tiling is a tiling that does not have a repeating unit of symmetry. The Penrose tilings are probably the most well known example. These non periodic tilings have a very immediate visual fascination — even though they do not have a periodically symmetric structure, they do exhibit a high degree of self-similarity.
I think this tension between order and disorder is part of what makes these patterns so compelling, and indeed non periodic tilings have been used decoratively in architecture (see for instance the so-called “fractal facade” of the buildings in Federation Square, Melbourne).
Zeolites on the other hand are actually a type of aluminosilicate mineral that have a curious structure at the atomic level. Looking at the pattern of silicon, aluminum and oxygen bonds, the molecular structure resembles a system of corner-sharing tetrahedra, with two tetrahedra at each corner.
This opens up a host of interesting questions about the generation of these minerals: what are the range of structures we can create by simply linking together tetrahedra in this way? Are they rigid or flexible? Can we predict the properties of these theoretical zeolites, before synthesizing them chemically in the lab? Because of their underlying structure, real zeolites tend to be very ordered and regular. The question that I had was whether we could find a non periodic example of a zeolite. In two dimensions the problem is about corner-sharing triangles. The non periodic zeolite model in the GH definition is the first example of this type of arrangement that I am aware of.
I actually answered this question several years ago (with a pencil and paper!), but it was a few more years until I learned enough about grasshopper to be able to implement the solution. It is satisfying to see it visualized at last, and being able to change the parameters is great. An open question is whether there exists a non periodic two dimensional zeolite consisting only of equilateral triangles of one size.
If anyone solves this, please let me know. Better yet, create a grasshopper model! I believe this is a great tool for mathematical exploration and research.