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.
Pair Design: Better Together
Pair design is the counterintuitive practice of getting more and better UX design done by putting two designers together as thought partners to solve design problems. It’s counterintuitive because you might expect that you could split them up to work in parallel to get double the design done, but for many situations, you’d be wrong. This document will help explain what pair design is, how it works, and tour through the practicalities of implementing it in your practice.
It involves two brains
It involves two brains on a project at the same time. This doesn’t mean part time, checking in with each other on work that’s been accomplished separately.
Pair design really means being in the same room, working on the same problem, with both brains focused on the problem simultaneously for the duration of the project.
A distinct and complementary stance
Each person in the pair takes a distinct and complementary stance toward the design problem as they work together. One generates solutions. That is, one individual materializes solutions to the problem at hand for discussion and iteration. The other synthesizes the proposed solutions.
Gens and synths
Gens are generally comfortable drawing and drawing in front of their partner. Additionally, the generator needs to have “fearless generativity,” to be able to come up with a dozen pretty good solutions to a problem even with incomplete information.
Designers in the synthesizer role need to be skilled at describing designs and explaining rationale in writing. The role requires the designer to be detail oriented and have a strong memory, to keep the big picture of the system, stakeholders, and users in mind as a reference for designs on the table.
We come as a team
There is a legend at Cooper of one team who found pairing with each other so powerful and fruitful that when they left that company, they sought out opportunities and even interviewed at other organizations as a pair.
Starting off with pair design
It’s better to start small. Find the “genniest” designer you can and pair her with the “synthiest,” have them work through a few projects as a pair to see how it goes, evolve a process that works for your organization, smooth out the wrinkles, and become resident experts. Then, split them up, assign them with new pairs, and begin to spread.
What are the benefits of pair design?
It Makes for Better Design
- Pairing forces constant iteration: idea testing and course-correction.
- It brings to bear two brains and two stances.
It Makes for Better Designers and Better Design Organizations
- They are happier.
- Pair design makes it easier to focus on core aptitudes.
- They cross-pollinate: a mechanism for a learning organization.
Pair Design Makes for a More Effective Process
- Pairing avoids the problem of dueling whiteboards.
- It encourages designers to materialize ideas early.
- It encourages designers to vocalize their rationale.
- It encourages constant course-correction.