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 Elements of Style
- Choose a suitable design and hold to it
- Make the paragraph the unit of composition
- Use the active voice
- Put statements in positive form
- Specific, definite, concrete
Choose a suitable design and hold to it
A basic structural design underlies every kind of writing.
Writing, to be effective, must follow closely the thoughts of the writer, but not necessarily the order in which those thoughts occur. This calls for a scheme of procedure. In some cases, the best design is no design, as with a love letter, which is simply an outpouring, or with a casual essay, which is a ramble. But in most cases, planning must be a deliberate prelude to writing.
The more clearly the writer perceives the shape, the better are the chances of success.
Make the paragraph the unit of composition
As a rule, begin each paragraph either with a sentence that suggests the topic or with a sentence that helps the transition.
More commonly, the opening sentence simply indicates by its subject the direction the paragraph is to take.
Use the active voice
"I shall always remember my first visit to Boston” is better than "My first visit to Boston will always be remembered by me."
Put statements in positive form
Make definite assertions. Use the word not as a means of denial or in antithesis, never as a means of evasion.
"He was not very often on time” becomes “He usually came late.”
“She did not think that studying Latin was much use” becomes “She thought the study of Latin useless."
Consciously or unconsciously, the reader is dissatisfied with being told only what is not; the reader wishes to be told what is.
If your every sentence admits a doubt, your writing will lack authority.
Specific, definite, concrete
Prefer the specific to the general, the definite to the vague, the concrete to the abstract.
Omit needless words
When a sentence is made stronger, it usually becomes shorter.
Vigorous writing is concise. A sentence should contain no unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all sentence short, or avoid all detail and treat subjects only in outline, but that every word tell.
The principle of parallel construction
This principle, that of parallel construction, requires that expressions similar in content and function be outwardly similar.
Blessed are the poor in spirit; for theirs in the kingdom of Heaven.
Blessed are they that mourn; for they shall be comforted.
Blessed are the meek; for they shall inherit the earth.Steering by stars that are disturbingly in motion
Here we leave solid ground. Who can confidently say what ignites a certain combination of words, causing them to explode in the mind? Who knows why certain notes in music are capable of stirring the listener deeply, though the same notes slightly rearranged are impotent? These are high mysteries, and this chapter is a mystery story, thinly disguised. There is no satisfactory explanation of style, no infallible guide to good writing, no assurance that a person who thinks clearly will be able to write clearly, no key that unlocks the door, no inflexible rule by which writers may shape their course. Writers will often find themselves steering by stars that are disturbingly in motion.
Design informs even the simplest structure
Design informs even the simplest structure, whether of brick and steel or of prose.
Even the kind of writing that is essentially adventurous and impetuous will on examination be found to have a secret plan: Columbus didn’t just sail, he sailed west, and the New World took shape from this simple and, we now think, sensible design.
Do not overstate
When you overstate, readers will be instantly on guard, and everything that has preceded your overstatement as well as everything that follows it will be suspect in their minds because they have lost confidence in your judgment or your poise.
A single overstatement, wherever or however it occurs, diminishes the whole.
Do not explain too much
It is seldom advisable to tell all.
Place the emphatic words of a sentence at the end
The proper place in the sentence for the word or a group of words that the writer desires to make most prominent is usually the end.
The principle that the proper place for what is to be made most prominent is the end applies equally to the words of a sentence, to the sentences of a paragraph, and to the paragraphs of a composition.
Writing is one way to go about thinking
And the practice and habit of writing not only drains the mind but supplies it, too.
Style is not separate from substance
Young writers often suppose that style is a garnish for the meat of prose, a sauce by which a dull dish is made palatable. Style has no such separate entity; it is nondetachable, unfilterable. The beginner should approach style warily, realizing that it is an expression of self, and should turn resolutely away from all devices that are popularly believed to indicate style - all mannerisms, tricks, adornments. The approach to style is by way of plainness, simplicity, orderliness, sincerity.
The young writer should learn to spot them - words that at first glance seem freighted with delicious meaning but that soon burst in air, leaving nothing but a memory of bright sound.