This page is deprecated. The new page is blog-style and has an entry for each tesselation. It’s here.
Tesselations after #19 are not featured here; they are only on the new page.
At some point during my childhood, I was introduced to a simple pattern which can be generated with an easy sequence of steps and which produces startlingly beautiful patterns. I used to doodle it on my notebooks during classes in high school and college.
During the pandemic, I heard about Hagoromo chalk, which is (supposedly) raved about by mathematicians for being the ultimate tool of their trade. Hagoromo is to chalk as Stradivarius is to the violin. Luckily Hagoromo is reasonably affordable by the common man, so I bought some of it and a chalkboard to try it out. It was indeed remarkable stuff.
This was the pandemic, so I had tons of free time; I began to draw the geomoetric pattern on the chalkboard using the Hagoromo. My earliest efforts are shown at the bottom of this page. The addition of color, which I had not previously seen (I used single colors in my notebook doodles), put a very compelling new dimension into the artwork.
I only have one chalkboard, so the creation of a new piece requires the destruction of the old. The older designs exist only in photographs. Every time I erase the chalkboard and start over, my understanding of the pattern and the chalk increases, generating designs that are increasingly coherent and “real”, featuring larger shapes that seem to be connected. As you scroll down this page, you can see that evolution happening in reverse.
Tesselations 1-18 were done in my house on Harvard Street. I stopped creating them after my struggles with mental health. Tesselation 19 is the first one created after that period; it was begun a year and a half later in June 2022. I thought I was done with these, having explored them to their fullest extent, but Tesselation 19 is so compelling that I am inspired to create more.
I call these Tesselations because, while hidden, the base skeleton of these is a series of interlocking polygons. They could also be called Mandalas; they’re made of sand, are a meditative aid, and are destroyed soon after they’re created. I chose “Tesselation” to emphasize the mathematical viewpoint over the spiritual one.
See also: String Art
Tesselation 19: “Heat”. This is my first effort after a year-long hiatus.
Tesselation 16: “Snowfall over the Cathedral”
Rotated and cropped version of Tesselation 8. This one remained my favorite even after several additional iterations. It’s so lively.
Tesselation 8: By this point I had a much steadier hand, and got better at ‘healing’ areas that were redone or damaged, so the whole work is much more consistent. I also got better at planning ahead to link several spirals together into larger themes.
Tesselation 5: This was the first experiment with lines intentionally not straight, and also with 6-sided swirls. My favorite part of this one is the large, parallel vertical twists that come out of the hexagonal swirl in the bottom right. It was meant to be a very abstract landscape but I don’t think that really came through.
Tesselation 19: “Heat” on the wall in my apartment at The Wyeth.
Tesselation 17. Inspired by snowfall and the transition to springtime.
Tesselation 16, “Snowfall over the Cathedral” just after completion. Usually these get erased after a day or two because we use the whiteboard for other things. This one is inspired by the view from my front window during a very windy snowstorm. The snow allowed me to see the roller-coaster twists of the wind in the eddies caused by the large catholic church across the street, and I found that very beautiful.
Tesselation 14. Exploring warmth at one end and coolness at the other.
Tesselation 14 on the wall. My technical skill had improved by this point, but this one came out very cold.
Tesselation 3: By this point, I understood most of the rules, but my technique was still sloppy. I also explored tracing back over the edges of the curves in this one, but I ultimately dropped this technique. This image was rotated and retouched by Robert.