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 Typographic Style
Leave the road when you wish
The subject of this book is not typographic solitude, but the old, well-traveled roads at the core of the tradition: paths that each of us is free to follow or not, and to enter and leave when we choose – if only we know the paths are there and have a sense of where they lead. That freedom is denied us if the tradition is concealed or left for dead. Originality is everywhere, but much originality is blocked if the way back to earlier discoveries is cut or overgrown.
If you use this book as a guide, by all means leave the road when you wish. That is precisely the use of a road: to reach individually chosen points of departure. By all means break the rules, and break them beautifully, deliberately and well. That is one of the ends for which they exist.
Typography exists to honor content
In a world rife with unsolicited messages, typography must often draw attention to itself before it will be read. Yet in order to be read, it must relinquish the attention it has drawn. Typography with anything to say therefore aspired to a kind of statuesque transparency. Its other traditional goal is durability: not immunity to change, but a clear superiority to fashion. Typography at its best is a visual form of language linking timelessness and time.
Typographic style
Literary style, says Walter Benjamin, “is the power to move freely in the length and breadth of linguistic thinking without slipping into banality.” Typographic style, in this large and intelligence sense of the word, does not mean any particular style – my style or your style, or Neoclassical or Baroque style – but the power to move freely through the whole domain of typography, and to function at every step in a way that is graceful and vital instead of banal.
A state of energetic repose
Read the text before designing it.
Discover the outer logic of the typography in the inner logic of the text.
Make the visible relationship between the text and other elements (photographs, captions, tables, diagrams, notes) a reflection of their real relationship.
Give full typographic attention even to incidental details.
Invite the reader into the text.
Reveal the tenor and meaning of the text.
Clarify the structure and the order of the text.
Link the text with other existing elements.Induce a state of energetic repose, which is the ideal condition for reading.
Evenness of color
The density of texture in a written or typeset page is called its color.
Once the demands of legibility and logical order are satisfied, evenness of color is the typographer’s normal aim. And color in the typographic sense depends upon four things: the design of the type, the spacing between the letters, the spacing between the words, and the spacing between the lines. None is independent of the others.
A single note
The simplest scale is a single note, and sticking with a single note draws more attention to the other parameters, such as rhythm and inflection. The early Renaissance typographers set each book in a single font – that is, one face in one size. Their pages show what sensuous evenness of texture and variety of rhythm can be attained with a single font of type.
The higher courts
Refer typographic disputes to the higher courts of speech and thinking.
Type is idealized writing, and its normal function is to record idealized speech. Acronyms such as CD and TV or USA and UFO are set in caps because that is the way we pronounce them. Acronyms such as UNESCO, ASCII, and FORTRAN, which are pronounced not as letters but as words, are in the process of becoming precisely that. When a writer accepts them fully into her speech and urges readers to do likewise, it is time for the typographer to accept them into the common speech of typography by setting them in lower case. Other acronymic words, such as laser and radar, have long since traveled the same road.
An antiphonal geometry
A book is a flexible mirror of the mind and body. Its overall size and proportions, the color and texture of the paper, the sound it makes as the pages turn, and the smell of the paper, adhesive and ink, all blend with the size and form and placement of the type to reveal a little about the world in which it was made. If the book appears to be only a paper machine, produced at their own convenience by other machines, only machines will want to read it.
Sizing and spacing type, like composing and performing music or applying paint to canvas, is largely concerned with intervals and differences.
The page is a piece of paper. It is also a visible and tangible proportion, silently sounding the thoroughbass of the book. On it lies the textblock, which much answer to the page. The two together – page and textblock – produce an antiphonal geometry. That geometry alone can bond the reader to the book. Or conversely, it can put the reader to sleep, or put the reader’s nerves on edge, or drive the reader away.
Pure but silent
Architects build perfectly proportioned kitchens, living rooms and bedrooms in which their clients will make, among other things, a mess. Typographers likewise build perfectly proportioned pages, then distort them on demand. The text takes precedence over the purity of the design, and the typographic texture of the text takes precedence over the absolute proportions of the pure but silent page.
A sterile sameness
Another kind of random variation involves the interaction of the craftsman’s skill and the texture of materials. The letterforms of Griffo and Colines were cut with immense care. But the letters they cut were struck by hand in copper or brass, then cast and dressed and set by hand, inked by hand with handmade ink and printed by hand in a handmade wooden press on handmade paper. Every step along with way introduced small variations planned by no one. In the world of the finely honed machine, those human-scale textures are erased. A sterile sameness supervenes.
The computer is, on the face of it, an ideal device for reviving the old luxury of random variations at the threshold of perception (quite a different thing from chaos). But conventional typesetting software and hardware focuses instead on the unsustainable ideal of absolute control – and has been hamstrung in the past by the idea of a single glyph per character. There have been several recent attempts to introduce a layer of random variation, but all have had to work against the grain of technological development.
Waiting to repay the gift of vision
Like a forest or a garden or a field, an honest page of letters can absorb – and will repay – all the attention it is given. Much type now, however, is delivered to computer screens. It is a good deal harder to make text truly legible on screen than to render streaming video. Both fine technology and great restraint are required to make the screen as restful to the eyes as ordinary paper.
The underlying problem is that the screen mimics the sky instead of the earth. It bombards the eye with light instead of waiting to repay the gift of vision – like the petals of a flower, or the face of a thinking animal, or a well-made typographic page. And we read the screen the way we read the sky: in quick sweeps, guessing at the weather from the changing shapes of clouds, or in magnified small bits, like astronomers studying details. We look to it for clues and revelations more than wisdom. This makes it an attractive place for the open storage of pulverized information – names, dates, or library call numbers, for instance – but not so good a place for thoughtful text.
Respect
Respect the text first of all, the letterforms second, the type designer third, the foundry fourth.
The needs of the text should take precedence over the layout of the font, the integrity of the letterforms over the ego of the designer, the artistic sensibility of the designer over the foundry’s desire for profit, and the founder’s craft over a good deal else.
Little by little
Check every text you set to see where improvements can be made. Then return to the font and make them. Little by little, you and the instrument – the font, that is – will fuse, and the type you set will start to sing. Remember, though, this process never ends. There is no such thing as the perfect font.
An end in itself
Typography, like language, is more important to me for what it allows to happen than for anything it accomplishes on its own. I hope that in writing a book on the subject I have not given the impression that either typography or design is an end in itself.
Not as a star
But I’m warning you,
this is my last existence.
Not as a swallow, not as a maple,
not as a cat-tail and not as a star.