📄️ Ammann-Beenker Tiling
Most tilings we see around us are periodic tesselations. They are tesselations because there are no gaps, and periodic because they repeat like wallpaper. In fact, until the 1960s, people thought that any finite set of tile shapes that could tesselate could be used to tesselate periodically. Then researchers discovered tiles that only tesselate non-periodically. Such tiles are called aperiodic.
📄️ Archimedes' puzzling dissection
In 1906, Danish historian Johan Heiberg was in Constantinople (today called Istanbul), studying an ancient document, written on parchment about 1000 years earlier. Over the centuries, monks scraped off the markings on the document,
📄️ Celtic Knots
To artists and mathematicians, knots can be beautiful, interesting structures. Until recently, I hadn't explored them much from either perspective. Then my mother-in-law gave me a copy of George Bain's
📄️ Cipra City
We've been captivated by the Cipra Loops tiles, so we added another Barry Cipra invention to our lineup. Cipra again found inspiration in the work of Sol Lewitt, who often explored the possible combinations of a graphic idea. For these tiles, that graphic idea is vertical, horizontal, and diagonal lines on a square, and Cipra created a tile for each unique combination. The tiles are oriented. In the image below, the orientation is indicated by the blue arrow. All blue arrows will point in the same direction when composing the 16 tiles. Can you convince yourself that all possible combinations of lines are represented?
📄️ Corona Tiles
A tiling of the plane with shapes that completely fills the plane is a tessellation. We could allow a variety of tile shapes, but we will limit ourselves here to tiling with a single tile shape.
📄️ Ferns
The Barnsley fern looks like a real fern, but its form is actually generated from a sequence of random numbers fed into an algorithm. You can see an example of this generation process here.
📄️ Nessie
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📄️ Lexen's Tricurve
itle: Lexen’s Tricurve