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.
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,
This was an early exercise with p5. It stops drawing after 1000 frames. Refresh the browser to see it redraw.
I didn't formally studied computer graphics, so like many other areas of computer science, I get introduced to well-known ideas only when they appear in my line-of-sight. Years ago, when my son mentioned a college CS assignment using Bresenham's line algorithm, I'd never heard of it. I was attracted to the simplicity of the algorithm, and the fact that it addresses one of the earliest ad simplest computer graphics problems.
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
This was something we played around with at Cherry Arbor Design, and used it to create wall art, earrings, and when they were still a thing, fidget spinners.
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.
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.
Inspired by Izzy tiles.
itle: Lexen’s Tricurve
clock arithmetic
Most things that we observe vary. We don't pay attention to things that don't change. When we measure those variables, we often use statistics like average or median to summarize. But those statistics don't describe the variability of the distribution. Standard deviation works well if the distribution is a bell curve, aka normally distributed. But many things we observe are not normally distributed. Yet we want a concise summary. One way to summarize is using quantiles, which involves dividing our observations into more-or-less equal size buckets of non-overlapping ranges of values. Common examples of quantiles are quartiles, with four buckets, and deciles, with ten buckets.
rotating links
itle: spectres
Many of the things we play around involve geometric symmetry. There are several types. This post is about an unusual symmetry. But first, a quick recap of some more well-known symmetries…