Geometry
Isometry
A Website by Nick TrombleyLittle Blank Riding Hood
As a student at Chouinard, Larry Bell also started as a painter. His early canvases features simple shapes rendered in gestural strokes...From there he started eliminating the texture of the strokes, applying opaque color (thin Liquitex paint) to unprimed canvas, masking off shapes to create straight-edged parallelograms. An example of these works is Little Blank Riding Hood, whose top left and bottom right corners are clipped, suggesting an isometric projection of a three-dimensional form.
A rhombic geometry
The logo consists of a rhombic geometry which was inspired by Morioka’s drawing which he brought to the first meeting with Takram. During the process of design development, the team explored many different shapes and motifs other than the rhombic, but in the end came back to the very origin. In fact, the rhombic shape embraces two meanings, “an open single book” and “a single small room”. The first message was the vision team shared through the design process, and the second message was later proposed by Takram in order to make the geometry more connected to the character of the space, which Morioka often emphasised unconsciously.
1/3 House
Rever & Drage Architects.
Pylons
Not all the towers along a transmission line are identical. Look closely at a tower where the line makes a sharp turn and you will likely find it is wider and beefier than other towers along the route. The added strength and weight are needed to resist the unbalanced pull of the conductors, which might overturn an ordinary tower. These special towers are called deviation or angle towers.
The transmission-line tower everybody knows is an Erector Set latticework of steel girders and diagonal braces. The techniques for designing and building these towers are the same ones used in constructing steel bridge trusses or crane booms. The individual pieces can be made cheaply from rolled steel and then bolted together on the site. This last point is more important than it might seem: transporting a fully assembled tower 100 feet tall is an awkward and expensive business.
Authentic architectural experiences
Authentic architectural experiences consist of approaching or confronting a building, rather than the formal apprehension of a facade; of the act of entering, and not simply the visual design of the door; of looking in or out through a window, rather than the window itself as a material object; or of occupying the sphere of warmth, rather than the fireplace as an object of visual design.
Architectural space is lived space rather than physical space, and lived space always transcends geometry and measurability.
A World Where Things Only Almost Meet
Recall that great line from Umberto Eco’s novel The Name of the Rose
How beautiful the world would be if there were a procedure for moving through labyrinths.
Only, here, it’s some lonely postal worker—or a geography Ph.D. driven mad by student debt—out mapping the frayed edges of the world, wearily noting every new dead-end and cul-de-sac in a gridded notebook, diagramming loops, sketching labyrinths and mazes, driving empty streets all day on a quest for something undefinable, some answer to why the world’s patterns have gone so wrong. A self-diverging world, where things only almost meet.
Rearranged
Put together with odd bits of the useless Clarice, a survivors’ Clarice was taking shape, all huts and hovels, festering sewers, rabbit cages. And yet, almost nothing was lost of Clarice’s former splendor; it was all there, merely arranged in a different order, no less appropriate to the inhabitants’ needs than it had been before.
Simple variations of the parts
Symmetry, indeed, has been grossly overemphasized in both art and science: its main value is in giving meaning to its absence, dissymmetry, without which there could be no hierarchy.
The eye is repulsed by complexity if no order is detected, but it can be delighted by repetition, translation, rotation, reflection, magnification, and other simple variations of the parts.
The Topography of Tears
A Book by Rose-Lynn FisherThe Topography of Tears is a visual investigation of tears photographed through an optical, standard light microscope, a vintage Zeiss from the late 1970's, mounted with a digital microscopy camera.
Tears are the medium of our most primal language in moments as unrelenting as death, as basic as hunger, and as complex as a rite of passage. They are the evidence of our inner life overflowing its boundaries, spilling over into consciousness. Wordless and spontaneous, they release us to the possibility of realignment, reunion, catharsis, intractable resistance short-circuited. Shedding tears, shedding old skin. It’s as though each one of our tears carries a microcosm of the collective human experience, like one drop of an ocean.
Plus 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.
The joy of the humble brick
An Article by Tim HarfordThe brick is one of those old technologies, like the wheel or paper, that seem to be basically unimprovable. ‘The shapes and sizes of bricks do not differ greatly wherever they are made,’ writes Edward Dobson in the fourteenth edition of his Rudimentary Treatise on the Manufacture of Bricks and Tiles. There’s a simple reason for the size: it has to fit in a human hand. As for the shape, building is much more straightforward if the width is half the length.
Subtilitas
A BlogSUBTĪLITĀS (latin; noun f., 3rd):
fineness of texture, logic, detail; slenderness, exactness, acuteness; sharpness : precisionnarrowdesign.com
A Website by Nick JonesDesign
Prototype
CodeRafael Araujo's Golden Ratio
A GalleryBlue Morpho Double Helix & Icosahedron
Cityspace series
A Gallery by Emily GarfieldPrimary series for imaginary map drawings, spanning 2008-present and using various materials and techniques.
bees & bombs
A Blog
A City Is Not a Tree
- Strands of life
- Impending destruction
- The right overlap
- The difficulty of designing complexity
- Political chains of influence
Strands of life
For the human mind, the tree is the easiest vehicle for complex thoughts. But the city is not, cannot, and must not be a tree. The city is a receptacle for life. If the receptacle severs the overlap of the strands of life within it, because it is a tree, it will be like a bowl full of razor blades on edge, ready to cut up whatever is entrusted to it. In such a receptacle life will be cut to pieces. If we make cities which are trees, they will cut our life within to pieces.
Impending destruction
In any organized object, extreme compartmentalization and the dissociation of internal elements are the first signs of coming destruction.
The right overlap
Overlap alone does not give structure. It can also give chaos. A garbage can is full of overlap. To have structure, you must have the right overlap.
The difficulty of designing complexity
Designers, limited as they must be by the capacity of the mind to form intuitively accessible structures, cannot achieve the complexity of the semilattice in a single mental act. The mind has an overwhelming predisposition to see trees wherever it looks and cannot escape the tree conception.
Experiments suggest strongly that people have an underlying tendency, when faced by a complex organization, to reorganize it mentally in terms of non-overlapping units. The complexity of the semilattice is replaced by the simpler and more easily grasped tree form.
Political chains of influence
In Chicago, formal chains of influence and authority are entirely overshadowed by the ad hoc lines of control which arise naturally as each new city problem presents itself. These ad hoc lines depend on who is interested in the matter, who has what at stake, who has what favors to trade to whom.
This structure, which is informal, working within the framework of the first, is what really controls public action. It varies from week to week, even from hour to hour, as one problem replaces another. Nobody’s sphere of influence is entirely under the control of any one superior; each person is under different influences as the problems change. Although the organization chart in the Mayor’s office is a tree, the actual control and exercise of authority is semilattice-like.
Same name in the same basket
Does a concert hall ask to be next to an opera house? Can the two feed on one another? Will anybody ever visit them both, gluttonously, in a single evening, or even buy tickets from one after going to a performance in the other?
In Vienna, London, Paris, each of the performing arts has found its own place, because all are not mixed randomly. The only reason that these functions have all been brought together in Lincoln Center is that the concept of performing art links them to one another. The organization is born of the mania every simple-minded person has for putting things with the same name into the same basket.
Separation of concerns
Another favorite concept of the CIAM theorists and others is the separation of recreation from everything else. This has crystallized in our real cities in the form of playgrounds. The playground, asphalted and fenced in, is nothing but a pictorial acknowledgment of the fact that ‘play’ exists as an isolated concept in our minds. It has nothing to do with the life of play itself. Few self-respecting children will even play in a playground.
Play itself, the play that children practice, goes on somewhere different every day. In a natural city this is what happens.
Structural complexity
The idea of overlap, ambiguity, multiplicity of aspect, and the semilattice are not less orderly than the right tree, but more so. They represent a thicker, tougher, more subtle and more complex view of structure.
Neighborhoods
We cannot get an adequate picture of what Middlesborough is, or of what it ought to be, in terms of neighborhoods. When we describe the city in terms of neighborhoods, we implicitly assume that the smaller elements within any one of these neighborhoods belong together so tightly that they only interact with elements in other neighborhoods through the medium of the neighborhoods to which they themselves belong. Ruth Glass herself shows clearly that this is not the case.
Cities which are trees
Columbia, Maryland
Greenbelt, Maryland
Greater London Plan
Mesa City, Paolo Soleri
Tokyo Plan, Kenzo Tange
Chandigarh (Le Corbusier)
Brasilia, Lucia Costa
Communitas (Percival and Paul Goodman)
Roman town evolved from military campsIn the worst cases, the units of which these cities are composed fail to correspond to any living reality; and the real systems, whose existence actually makes the city live, have been provided with no physical receptacle.
In a tree structure, it means that within this structure no piece of any unit is ever connected to other units, except through the medium of that unit as a whole.
Sets and systems
When the elements of a set belong together because they cooperate or work together somehow, we call the set of elements a system.
From a designer’s point of view, the physically unchanging part of this system is of special interest. I define this fixed part as a unit of the city.
Whatever picture of the city someone has is defined precisely by the subsets he sees as units.
Natural and artificial cities
I want to call those cities which have arisen more or less spontaneously over many, many years natural cities. And I shall call those cities and parts of cities which have been spontaneously created by designers and planners artificial cities. Siena, Liverpool, Kyoto, and Manhattan are examples of natural cities. Levittown, Chandigarh, and the British New Towns are examples of artificial cities.
It is more and more widely recognized today that there is some essential ingredient missing from artificial cities.
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.