Archive for the 'symmetry' Category

Tilings and Friends: Celebrating Roli

Sunday, May 18th, 2014


A few weeks ago, I received an invitation to participate in a math conference called Kaleidoscope. The purpose of this conference was to celebrate the 60th birthday of an important Mexican mathematician called Roli by gathering the people he has influenced to talk about stuff he likes.

Roli happens to be a very good friend of mine, as well as one of my all-time mentors. Together with Luis Montejano and Jorge Arocha, he introduced me to contemporary geometry, and helped me find new directions in digital art and computational design. It was a big deal for me when I was tasked to deliver the closing keynote to the event. A great honor, and a big challenge: I was expected to hold myself together for an hour in front of an audience of world-class mathematicians, and I haven’t practiced any mathematics since my days at MIT. But I have never stopped making math-inspired art, and luckily, most of the conference attendants were my friends, and there was a deep pool of shared memories I could use to weave a thread through my personal experience of mathematics, art, and Roli.

My talk, entitled Tilings and Friends, narrated the story of a thirty year old friendship centered in a passion for the intersection of art, history, and combinatorial geometry in the form of tilings and low dimensional polytopes. Here is an excerpt from my notes:

If you read the abstract of my presentation you might have realized it didn’t make a lot of sense. At best I hope it made you laugh. It was inspired by a legitimate desire to challenge traditional representations of social engagement as mere connections in a network where individuals are reduced to labeled points.

I’d like to imagine—if not propose—alternative models, that will hopefully reflect upon things like friendship in a more truthful manner. Perhaps I am naive to be saying this, but we all know there is more to friendship than a simple connection. This is why most of our friends in Facebook are not really our friends.

Friendship is a process.

The reason I’m here is the friendship relationship I have with Roli, and with a group of mathematicians that were my teachers and classmates around twenty years ago.

To honor this relationship, and especially the projection of it that finds Roli at it’s epicenter, I want to suggest a model of friendship that goes beyond combinatorics, and takes into consideration the geometry of personality.

In this model, friends are tiles that share matching edges and fill portions of the plane. A friendship starts when a set of tiles match or fit-in together, and evolves as more tiles are added to the plane.

This friendship will be compromised once the tiles reach a configuration where they fail to tile.

A number of years ago, Roli told me a story about a construction worker or “maestro mosaiquero” as one would call him in traditional Alupyecan lingo. This worker’s job was to take piles of tiles and paste them over the surface of bathroom walls. He got used to work with squares and hexagons the most, a lot of times printed with patterns that limited the ways in which the tiles could be arranged. Through years of practice, he developed a good intuition of the seventeen crystallographic groups without ever knowing of their existence.

“What will he do if we give him a box full of pentagons?” —asked Roli. Years later I proposed this same question as the basis for my final project in the Symbolic Programming class at MIT, and the professor almost offered me a PHD based on it… just a good example of the depth in Roli’s insight.

For the next half hour I am going to touch upon ideas that are connected to an aspect of Roli that is not easy to find: His everlasting desire to establish a functional creative conversation about mathematical ideas with non-mathematicians.

One of them being me.

I met Roli a little over thirty years ago because he is the cool brother of my best friend from junior high and he once took us to a soccer game in the Azteca. We were roughly twelve or thirteen years old, and I didn’t see him again until college. But I remember that day well. A gentle and quiet man, he took us back to the apartment where he lived with Irene and Felipe in Villa Olimpica, and offered us limonadas. Felipe was probably seven eights of a year old, and was wearing a home-made helmet to keep him from bumping into furniture corners. There was a big tome of the lord of the rings on a table, and a blackboard with a drawing of something I had never seen before: a mathematical graph.

If you’re still with me after all this text, you probably got the picture. My keynote went really well and the conference was a great experience, hanging out with old friends and meeting some of my heroes from back in the day, like the legendary Egon Schulte (master of the polytopes), Asia Ivic Weiss (H.S.M. Coxeter‘s last student), and the not less amazing Chaim Goodman-Strauss, who’s had his own fantastic incursions in the realm of math-art.

Squares versus Triangles

Thursday, March 7th, 2013

Marvin Minsky once told me Triangles are smarter than Squares (and they are). It made total sense to me. Do you need an explanation?



Today is my father’s birthday. Feliz cumpleaños! (Dedicado a mi papá).

Tilings and Cars

Monday, September 26th, 2011

Some of my prints and laser-cuts have just been featured in a group show called Urban Nothingness, curated by Gene Wyrick for the Jefchak/Wyrick Gallery.

The work I have on this show is part of two ongoing series that I have been doing for a while:

Black and White City is a series of ongoing drawings, prints, animations and public interventions that I started in 2004 for my artistic residence in ISCP-NYC. My intention with this series is to extract a graphic language from the experience of big cities that separates urban technological elements from their human counterparts, to combine them later in sequences and configurations that explore ideas closely related to the life in the city, like routine, waiting, isolation, fear and pressure.

Reflections on Symmetry is a line of aesthetic research that I pursue to understand symmetry as concept, system and form. It started as a script for a short film on the work on Escher and Coxeter that I wrote in 2002 and 2003 with Javier Bracho. Over the years, this work has taken the form of writing, 3D models, animations, paper cuts, computer software, drawings and laser-cuts.

The show will open from August 22nd to October 24th at 8670 Wilshire Blvd. Beverly Hills CA 90211 Suite 114.

Geometry is back

Monday, July 25th, 2011

This weekend, I have been swimming inside a projection of the 120-cell courtesy of Jenn3D. The tetrahedrons stand for vertices. Jenn3D looks great. I downloaded the source code but I couldn’t understand most of it. At least I got it to compile.