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.
Man in the Middle: The Designer
The old unity
The most fundamental splits in contemporary life occur because of the break-up of the old unity of design, production and enjoyment.
Defining craftsmanship
By craftsmanship I refer to a style of work and a way of life having the following characteristics:
- In craftsmanship there is no ulterior motive for work other than the product being made and the processes of its creation.
- In craftsmanship, plan and performance are unified, and in both, the craftsman is master of the activity and of himself in the process. The craftsman is free to begin his working according to his own plan, and during the work he is free to modify its shape and the manner of its shaping.
- Since he works freely, the craftsman is able to learn from his work, to develop as well as use his capacities.
- The craftsman’s way of livelihood determines and infuses his entire mode of living. For him there is no split of work and play, of work and culture. His work is the mainspring of his life; he does not flee from work into a separate sphere of leisure; he brings to his non-working hours the values and qualities developed and employed in his working time.
The central value for which they stand
What I am suggesting to you is that designers ought to take the value of craftsmanship as the central value for which they stand; that in accordance with it they ought to do their work; and that they ought to use its norms in their social and economic and political visions of what society ought to become.
The star system
The distributor is ascendant over many producers who become the rank-and-file workmen of the commercially established cultural apparatus.
The star system of American culture – along with the commercial hacks – tend to kill off the chance of the cultural workman to be a worthy craftsman.
As if it were an advertisement
He designs the product itself as if it were an advertisement, for his aim and his task – acknowledged by the more forthright – is less to make better products than to make products sell better.
The Big Lie
“We only give them what they want.”
This is The Big Lie of mass culture and of debased art, and also it is the weak excuse for the cultural default of many designers.
The Fetish of human life
To understand the case of America today, one must understand the economic trends and the selling mechanics of a capitalist world in which the mass production and the mass sale of goods has become The Fetish of human life, the pivot both of work and of leisure.
Existing commodities must be worn out more quickly for as the market is saturated, the economy becomes increasingly dependent upon what is called replacement. It is then that obsolescence comes to be planned and the economic cycle deliberately shortened.
The big split
The big split among designers and their frequent guilt; the enriched muddle of ideals they variously profess and the insecurity they often feel about the practice of their craft; their often great disgust and their crippling frustration.