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.
The vanishing designer
Visionary designers have lost their conceptual integrity to an industrial complex optimized for consensus, predictability, and short-term business gain. The rise of customer-obsession mantra and data-driven culture cultivated a generation of designers who only take risk-free and success-guaranteed steps towards the inevitable local maxima of design monotony.
The same, the same, the same
Look around us. Every business is an app and every app feels the same, because every designer has the same resume, follows the same process, graduates from the same program, uses the same tool, scrolls the same Dribbble feed, reads the same Medium articles, expects the same career outcome, lives in the same ideology bubble.
Design as an engineering problem
The Silicon Valley giants, testifying with their runaway success, claimed to have “solved” design as an engineering problem. The solution substituted the human essence of design — intuition, ingenuity, and taste— with the tangibles, measurables, and deliverables.
Companies say they are “design-driven”, but designers are actually driven by dashboards filled with metrics like CSAT, NPS, CES, DAU, MAU. We rigorously run tests, studies, experiments as if innovative ideas are hidden in spreadsheets, waiting to be extracted by data scientists.
The heat death of design
Losing the design diversity means falling into a singular narrative of how design must be done, which grants unfair and self-reinforcing advantage to the mainstream while discouraging, stifling, or even punishing the idiosyncratic designers who bring unorthodox but remarkably innovative processes to the table. The true opportunity cost is the diverse future that humanity can no longer access.
A future without diversity is fundamentally stagnant: imagine designs so standardized that you can’t tell them apart. While every design is guaranteed to be good, none will be great. New designs are marginally better than previous ones with the rate of improvement eventually approaching zero. We have reached the heat death of design.
Design with courage
- Make a bold decision (that is controversial).
- Make a mistake (as a result of a bold decision).
- Challenge “conventional wisdom”.
- Challenge authority (that preaches conventional wisdom).
- Challenge hierarchy (that perpetuates conventional wisdom).
- Ignore the committee (and the need to converge).
- Decide who your clients are (and aren’t).
- Ignore clients that aren’t (especially those who pay the most).
- Cultivate clients if none exists (instead of compromising your design).
- Be a generalist (and ignore your job title).
- Be a specialist (who specializes in being a generalist).
- Design things from scratch (and build them yourself from scratch).
- Design things that no one wants (yet).
- Design freely (and think freely).