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.
Painting With the Web
So much about [Gerhard Richter's painting process] reminds me of designing and building for the Web: The unpredictability, the peculiarities of the material, the improvisation, the bugs, the happy accidents. There is one crucial difference, though. By using static wireframes and static layouts, by separating design and development, we are often limiting our ability to have that creative dialogue with the Web and its materials. We are limiting our potential for playful exploration and for creating surprising and novel solutions. And, most importantly, we are limiting our ability to make conscious, well-informed decisions going forward. By adding more and more layers of abstraction, we are breaking the feedback loop of the creative process.
A constant dialogue
Have you ever seen Gerhard Richter painting?
It is phenomenal to watch. He might start one of his large, abstract paintings by carefully applying oil paint to the canvas with a thick brush. Then, he begins to scrape, smear, or add new layers of paint with a large, home-made squeegee. After each change, Richter pauses, takes a step back, and looks at the result: What did just happen with the picture? What composition has come about? Where have interesting parts emerged? What is the next move that might bring the piece one step closer to completion? And which action would be a mistake? There is a lot of intention and carefulness in this process, yet Richter equally respects the results of accident and chance. He lets go of a certain kind of control to let things happen that are surprising and exciting. But at the same time, Richter always exerts enough control to influence the result. He decides what to keep and what to destroy. It is the ultimate creative process: a constant dialogue.
Constant reflection and refinement
Ask any artist, musician, or writer and they might tell you that this conversation at the heart of the creative process is what makes their work special and so fulfilling. No piece of art exists in its final form in the head of the artist before the first brush stroke is put on the canvas. No musician has a full piece of music in her head without a conversation with instruments or the score. And no novel is done before the first word is put on paper or a computer screen. Constant reflection and refinement are key to creating any piece of work. This is what lets creators of any profession learn and grow, and, ultimately, achieve mastery. And the same is true for any user interface, design pattern, piece of code, or content on the Web.