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.
A Q&A with Figma's VP of Product
Since we launched FigJam back in April, teams having been using it to grow all kinds of ideas into great designs. We recently caught up with Figma's VP of Product, Yuhki Yamashita, to hear what it was like to build FigJam and how things have changed since then. Here, he reflects on the evolving role of design and product management, what it means to welcome “non-designers” into the process, and the future of FigJam.
Stretching the product
When we’re thinking about where to take our product next, we actually take a lot of inspiration from our customers and the Figma Community, to see how they’re stretching our product in interesting or unexpected ways. We saw this happening in the early days of the pandemic. Our users were starting to use Figma for everything from brainstorming ideas to running team warm-up activities, to even putting on social events for people to get to know each other. We saw a lot of use cases that got us thinking.
Engineering, design, and product management
The boundary between engineering, design, and product management is blurring. Some of us used to have a mental model in which roles and responsibilities dictated how things work—that designers do one thing and engineers do another, for example. Increasingly, more people are crossing team lines to problem solve together...Now, it’s not about who “owns” what—it’s more of a collective endeavor. And the roles have become more interlocked, and I think that’s fundamentally a good thing.
Embracing the mess
Design is non-linear. At Figma, we often talk about “embracing the mess,” and that really means leaning into the chaos and complexity that makes the design process what it is. Even once you have the seedling of an idea, you need to explore and iterate, then pull back and evaluate to see what’s working and what’s not. Sometimes you’ll scrap an idea after a brainstorm session, and other times you’ll get pretty far with a concept, but still need different perspectives and input to move forward.