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.
Phenomenal: Exhibited Works
Untitled (Light Canvas)
A key transitional work for Wheeler is his untitled "light canvas" from 1965. The canvas was primed white, then over-sprayed..., but with no emblems or polished elements. The contrast in the light canvas is provided not by any imagery within the painting but by back-lighting; the canvas is backlit with neon light, which is embedded in a reverse bevel Plexiglass frame that projects the piece about five inches from the wall. The effect suggests an eclipse, or some other spectral occlusion of a bright light source.
Eindhoven
Stuck Red
Zero Mass
On an autumn night in 2009, I experienced a version of this piece installed in a stone barn in rural France. The evening was moonless and cold; I stood with two friends inside the piece for the better part of an hour, as our eyes adjusted to almost total darkness, before any of us could begin to see one another. It was the definition of a liminal, or barely perceptible, experience. Eric Orr, who died in 1998, was involved with Zen Buddhism and considered these pieces to be spaces for meditation. Experiencing them as intended requires the visitor to focus quietly on the mechanics of their own perception.
Little Blank Riding Hood
As a student at Chouinard, Larry Bell also started as a painter. His early canvases features simple shapes rendered in gestural strokes...From there he started eliminating the texture of the strokes, applying opaque color (thin Liquitex paint) to unprimed canvas, masking off shapes to create straight-edged parallelograms. An example of these works is Little Blank Riding Hood, whose top left and bottom right corners are clipped, suggesting an isometric projection of a three-dimensional form.
Afrum
Untitled (White Light Grid Series-H)
The entire box is suspended from the ceiling by only four evenly spaced monofilaments, so that it seems to float with no physical connection to the wall or to a power source. Behind the wall (which must be purpose-built and is quite thin) is a cabinet containing four Tesla coils. The coils emit a high-frequency energy that passes through the wall and lights the tubes. The energy pulses a bit, making the tubes flicker at times both vertically and horizontally. The Tesla coils make a crackling static sound that is mostly muffled by the barrier wall, while the neon tubes emit a low hum that is audible close to the work. The work is elegant and slightly menacing, evoking something of a mad scientist's experiment.
Five Paintings IV
One of the most extraordinary examples of McCracken's illusory surfaces occurs with Five Paintings IV, 1974. This wall-mounted work has a black polyester resin finish. From some angles the surface is opaque, from others highly reflective, and from still others it seems to reveal great depth. A happy accident in the creation of the work sealed many tiny air bubbles or particulates in the piece. When these catch the light, they suggest a galaxy of stars on a moonless night.
The Iceberg and Its Shadow