math
On beauty bare
Wang tiles
Trees and graphs
A tree is a kind of graph, but a graph can be considerably more complex than a tree.
I have reason to believe, which for brevity’s sake I will treat elsewhere, that the most complex class of processes and structures we humans can consciously prescribe, reduces mathematically to a tree. A tree has a top, bottom, left and right. Its branches fan out from the trunk and they don’t intersect with one another. They are discrete, contiguous, identifiable objects which persist across time. Trees are Things.
Software and websites, however, reduce to arbitrarily more complex structures: they are graphs. A graph has no meaningful orientation whatsoever. No sequence, no obvious start or end—at least none that we can intuit. It is better considered not as one Thing, but as a federation of Things, like the brain or a fungus network, or perhaps a composite artifact left behind from an ongoing process, like an ant colony or human city.
Trees and semilattices
The tree of my title is not a green tree with leaves. It is the name of an abstract structure. I shall contrast it with another, more complex abstract structure called a semilattice.
Both the tree and semilattice are ways of thinking about how a large collection of many small systems goes to make up a large and complex system.
A collection of sets forms a semilattice if, and only if, when two overlapping sets belong to the collection, the set of elements common to both also belongs to the collection. That is, if [234] and [345] belong to the collection, then [34] belongs to the collection.
A collection of sets forms a tree if, and only if, for any two sets that belong to the collection either one is wholly contained in the other, or they are wholly disjoint. Every tree is trivially a simple semilattice.
We are concerned with the difference between structures in which no overlap occurs, and those structures in which overlap does occur.
The semilattice is potentially a much more complex and subtle structure than a tree. It is this lack of structural complexity, characteristic of trees, which is crippling our conceptions of the city.
A City Is Not a Tree
An Essay by Christopher Alexander- Strands of life
- Impending destruction
- The right overlap
- The difficulty of designing complexity
- Political chains of influence
Notes on the Synthesis of Form
A Book by Christopher AlexanderVisualizing Data
A Book by William S. ClevelandExploratory Data Analysis
A Book by John TukeyPlus Equals #4
An Article by Rob WeychertOne of the seeds for Plus Equals was planted a few years ago with Incomplete Open Cubes Revisited, my extension of a Sol LeWitt work. I learned a lot about isometric projection from that project, but my affection for the concept didn’t begin there. Whether I’m looking at a Chris Ware illustration or an exploded-view technical drawing of a complex machine, an isometric rendering always stirs something in me.
A brief foray into vectorial semantics
An Article by James SomersOne of the best (and easiest) ways to start making sense of a document is to highlight its “important” words, or the words that appear within that document more often than chance would predict. That’s the idea behind Amazon.com’s “Statistically Improbable Phrases”:
Amazon.com’s Statistically Improbable Phrases, or “SIPs”, are the most distinctive phrases in the text of books in the Search Inside!™ program. To identify SIPs, our computers scan the text of all books in the Search Inside! program. If they find a phrase that occurs a large number of times in a particular book relative to all Search Inside! books, that phrase is a SIP in that book.
tixy.land
A Websitesin(t * x) * cos(t * y)
Creative code golfing.
Rafael Araujo's Golden Ratio
A GalleryBlue Morpho Double Helix & Icosahedron
The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy
A Research Paper by Cyril Stanley SmithA pattern of tiles illustrated by Douat in 1722.
A translation is given of Truchet's 1704 paper showing that an infinity of patterns can be generated by the assembly of a single half—colored tile in various orientations.
Everything and More
A Book by David Foster WallaceInfoCrystal
A Research PaperThis paper introduces a novel representation, called the InfoCrystal, that can be used as a visualization tool as well as a visual query language to help users search for information. The InfoCrystal visualizes all the possible relationships among N concepts.
99% Invisible
The Worst Video Game Ever
A Podcast by Howard Scott WarshawSome Other Sign that People Do Not Totally Regret Life
An EpisodeThe Help-Yourself City
Astoria Scum River Bridge. Photo by Jason Eppink.
There are lots of actions that skirt the boundary between “formal” and “informal” urbanism. In the last decade, there’s been a rise in tactical urbanism and guerrilla urbanism, where regular people make interventions in their communities. This ranges from hastily painted bike lanes, to do-it-yourself park benches in under-served communities.
Lawn Order
In communities across America, lawns that are brown or overgrown are considered especially heinous. Elite squads of dedicated individuals have been deputized by their local governments or homeowners’ associations to take action against those whose lawns fail to meet community standards.
Call them—lawn enforcement agents.
Names vs. The Nothing
This is the first site along the tour. In here we have a void. I remember the building that used to stand here, it was painted blue. Passing through it, you can imagine how us, as ghosts – should the building be standing here – would have to actually be invisible to pass through these walls and now it’s the reverse. The building is the ghost and we’re passing through these walls.
Rain Chains & Musical Drains
A rain chain in winter; Dresden Kunsthof Passage; Drainage planters near Pike Place Market in Seattle.
If there is a larger takeaway here perhaps it is about paths of least resistance, with regards to both the actual flow of water and design decisions. On the one hand, it is easy to blindly follow regional precedents and traditions with long histories (or grab whatever is handy at the hardware store). On the other hand, sometimes it makes sense to take a step back and decide consciously how to reveal (or conceal) a natural process.
Thermal Delight
DIY Space Suits
Cameron Smith is building a space suit in his apartment.
Tracing Power Lines with the Pylon Appreciation Society
According to Emma Ailes of BBC News, the first pylons in the UK were designed by architect Sir Reginald Blomfield in 1928, with a “lattice” approach that “sought to be more delicate than the brutalist structures used in Europe and the United States.” Reportedly, he was “inspired by the root of the word pylon – meaning an Egyptian gateway to the sun.”
Take a Walk
Now that many of us are working from home, we’re walking in order to fill up space … to clear our minds … to cry … to talk on the phone … to entertain our kids … to do nothing … but walk.
Here Be Dragons
Dragon hole in Hong Kong by Tim Hill.
Such “dragon gates” are designed to let these mythical flying beasts pass from their hilltop homes down to the water each day and then return again each night. Considering the flow of dragons, air and energy is just one part of a much larger phenomenon: feng shui.
The Right to Roam
This walk across private land was not unusual. Thousands of distance walkers in Britain, regularly do the same thing , which is different from what people typically do in the United States. If you wanted to walk across America, you’d have to do it on a combination of public trails and roads and you certainly couldn’t cut across Madonna’s property.
In the United Kingdom, the freedom to walk through private land is known as “the right to roam.” The movement to win this right was started in the 1930s by a rebellious group of young people who called themselves “ramblers” and spent their days working in the factories of Manchester, England.