Architecture Thesis

VECTOR ARCHITECTURE

My research began by experimenting with different fluids studying their properties and how its interactions act as a trigger for a dynamic responsive tool.

Advancing my research on fluids into digital to study the complex interactions that occur within a city, such as different types of infrastructural flows, crowds as fluids masses and program navigation, I started reading fluids as vector fields to choreograph this complex systems into the urban scale.

The city’s recent evolution, particularly in the second half of the past century,

has brought about a gradual isolation of the area, that together with the popu-

Working with the intensity parameter in the vector field allowed us to translate 2d vector field into a 3d vector field that allowed me to control speed and directionality into a series of topological organizations.

lation’s settlement outside the historic center, has strongly contributed to its architectural and functional decay. Nowadays, abandoned buildings, empty lots, and inadequate uses are common. At the same time, the population’s

Our team’s exploration of vector to vector relations goes through a wide range of scales and levels of spatial, structural, material and programmatic differentiation, investigating flamenco as a catalyst for urban intensification by working with urban connectivity.

socioeconomic level is one of city’s lowest, sometimes living in overcrowded and uninhabitable places.

The studies on fluids interactions allowed me a first under-

This area has turned into a marginal pocket in the very heart of the historic

standing of dynamic systems, and how by studying not one

district. Through a Special Plan it has been possible to undertake a detailed

system but a combination of this generates a relation be-

analysis of every element, so unveiling the two aspects of this site: its historic

This competition arises from the opportunity and interestin internationally

value (very disfigured today), and the measures necesssary to invert its evolu-

tween properties, forces and qualities of each system.

promoting the art of flamenco from its birthplace, through the creation of an

tion, or rather, to turn it into a center of attraction because of the quality of its

Experimenting with fluids in a systemized way allowed a

emblematicand representative space able to accommodate, in the heart of

buildings and spaces. The urban void of the Plaza de Belén as it is today,

translation or interpretation of certain logics or principles to

the city of Jerez de la Frontera, the various institutions devoted to this end.

develop in a digital and analogue media.

“Recover the public space for the enjoyment of everyone, to promote the harmonious and sustainable development of the territory and to recover the heart of the city.”

Situated between the foothills of the mountain rangeand the sea, Jerez de la

The project,an artistic and cultural manifestation, will also be a key part of the revitalization process of the historic center of Jerez.

The studies about fluid interaction with a given object, gave

Frontera - whose municipal area covers 1.187 square kilometers - enjoys a

privileged location on the fertile lands of Cádiz.Ten kilometers away from the

Atlantic Coast and with approximately 200.000 inhabitants, Jerez’s urban center is the most densely populated of the province ofCádiz.

me the opportunities and the understanding of how fluid inJacques Herzog and Pierre de Meuron have been chosen to develop a project

teract with each other and with its surroundings. By taking

which the city of Jerez has received with enthusiasm, and that will give Fla-

this to a given part of the city, a time-based experiments on

menco a leading position in the promotion of the arts in Spain.

fluid into jerez gave me the first peaks of organization and of possibilities withing the jerez quarter.

“Cuidad del Flamenco”

Horses, wine, bulls, and especially flamenco are the distinctive symbols of a

Over twenty years have passed since we freed the Alcázar of Jerez from that

The design strategy has focused its design research on Vector Fields and Fluid

city that stands today as one of the economic centers of western Andalusia,

concrete mass. Today, in its place, myrtle, orange and olive trees grow; and one

dynamics as the conceptual and technical basis in the choreography of complex

and that possesses, at the same time, a vast historic and cultural heritage.

Based on the simulation of crowd interaction with the differ-

can hear the murmur of water inviting to contemplate and walk around one of

dynamic urban interactions.

ent masses of the context, the vector field pretends to be a

Andalusia’s most beautiful spots. And, very soon, amidst labyrinths, paths and

direct translation from the feedback that fluid behaviour and

plazas, the strollers entering the medieval patterns of Jerez will find another

The exploration of Vector fields as an urban tool allowed an alternative mode of

garden: one designed by Herzog & de Meuron for that city – of Flamenco – that

addressing masterplanning strategies, not as one that is fixed but as one that is

shall rise in the city.

relational to possible futures.

logic is extracting from the urban context.

Developing different parametric systems (landscape/multiple ground condition, circulation, massing, program distribution and navigation) as a series of urban

fields that correlate with one another to organizeand integrate differentiated urban space.

This project addresses urban space by studying different programs relations

A fluid is defined as a substance that continually deforms (flows) under an applied shear

through sectional field navigation. The resolution of the vector as a design tool

stress regardless of how small the applied stress. All liquids and all gases are fluids. Fluids are

explores different scales and levels of spatial, structural, material and program-

a subset of the phases of matter and include liquids, gases, plasmas and, to some extent,

matic differentiation by developing vector to vector properties from a local to a

plastic solids. The term “fluid” is often used as being synonymous with “liquid”. This can be

global field space.

erroneous and sometimes clearly inappropriate - such as when referring to a liquid which

“The design strategy does not or should not involve the gaseous state. “Brake fluid” is hydraulic oil which will not its required function if gas is present. The medical profession relies on the term “fluhas focused itsperform deids” in dietary references (“take plenty of fluids”) where the presence of gases is irrelevant or sign research on Vector even possibly dangerous.

Fields and Fluid dynamLiquids form a free surface (that is, a surface not created by the container) while gases do ics as the conceptual not. The distinction between solids and fluid is not entirely obvious. The distinction is made by evaluating the and technical basis inviscosity of the substance. Silly Putty can be considered either a solid or a fluid, depending on the time period over which it is observed. the choreography of complex dynamic urban interactions.”

Advancing our research on fluids into digital to study the complex interactions that

The The wing wing of of aa dragonfly dragonfly can can be be broken broken into into aa variety variety of of basic basic strucstruc-

occur within a city, such as different types of infrastructural flows, crowds as fluids

tures. tures. The The overall overall two two types types of of structure structure present present are are the the veins veins and and the the

masses and program navigation, we started reading fluids as vector fields to choreo-

membrane. membrane. Both Both consist consist of of cuticle cuticle which which is is composed composed of of the the matemate-

graph this complex systems into the urban scale.

rial rial chitin1. chitin1. The The veins veins provide provide the the primary primary structural structural support support for for the the

Working with the intensity parameter in the vector field allowed us to generate a 3d

wings. wings.

point cloud to then translate it into a 3d vector field that allowed us to control speed and directionality into a series of topological One interesting characteristic to note about a dragonfly wing is that there are several different kinds of patterns

VECTOR VECTOR ARCHITECARCHITECTURE TURE

organizations.

which which serves serves to to prevent prevent the the cuticle cuticle of of the the wing wing from from becoming becoming brittle1. brittle1.

present in the wing vein framework.

The The membrane membrane is is the the primary primary aerodynamic aerodynamic structure structure of of the the wings. wings. ItIt

The leading edge consists primarily of rectangular frames whereas the trailing surface is largel formed of hexagons

is is aa very very thin thin structure, structure, with with aa thickness thickness of of only only 22 to to 33 m2. m2. Because Because itit

and some other polygons with more than 4 sides.

Viewing anaglyphs through appropriately colored glasses results in each eye seeing a slightly different picAnother notable characteristic of wing structure is the three-dimensional structure present in the wing. Although ture. In a red-blue anaglyph, for instance, the eye covered by the red filter sees the red parts of the image as Elias Canetti (Rousse, Bulgaria, 25 July 1905–14 August 1994, Zurich) was “white”, and the blue parts as “black” (with the brain providing adaption for color); the they eye covered by to lay on a flat plane, in actuality the wings are full of three from some most photographs of wings, may appear a Bulgaria-born novelist of Sephardi Jewish ancestry who wrote in German the blue filter perceives the opposite effect. True white or true black areas are perceived the same by each dimensionalasrelief.

One eye. The brain blends together the image it receives from each eye, and interprets the differences being theexample of this, as mentioned before is in the leading edge. and won the Nobel Prize in Literature in 1981. result of different distances. This creates a normal stereograph image without requiring the viewer to cross his or her eyes.

is is such such aa thin thin structure, structure, the the membrane membrane is is thought thought to to carry carry only only tensile tensile

loading loading in in the the wings, wings, while while buckling buckling under under the the slightest slightest compressive compressive

“Movement “Movement governs governs the the events” events”

stress. stress.

The The primary primary overall overall structural structural property property of of wings wings is is span span wise wise stiffnesstiffnes-

sand sand chord chord wise wise flexibility. flexibility. The The leading leading edge edge of of the the wing wing is is comprised comprised

Crowd psychology, or social facilitation theory, is a branch of social psychol-

of of aa very very stiff stiff structure structure with with three three dimensionalrelief dimensionalrelief in in order order to to provide provide

ogy. Ordinary people can typically gain direct power by acting collectively.

Paul PaulVirilio Virilio

high high rigidity rigidity to to the the span span of of the the wing. wing. This This causes causes the the flexural flexural stiffness stiffness

Historically, because large groups of people have been able to affect dramatic

along along the the span span to to be be 1-2 1-2 orders orders of of magnitude magnitude greater greater than than along along the the

and sudden social change in a manner that bypasses established due pro-

chord5.It chord5.It is is obvious obvious that that this this quality quality contributes contributes greatly greatly to to the the wing’s wing’s

cess, they have also provoked controversy. Social scientists have developed

aerodynamic aerodynamic properties. properties. There There are are aa number number of of key key structures structures in in the the

several different theories for explaining crowd psychology, and the ways in

wing, wing, ,, which which contribute contribute to to the the manner manner in in which which the the wing wing bends bends in in flight flight

which the psychology of the crowd differs significantly from the psychology of

and and therefore therefore help help to to facilitate facilitate the the wing’s wing’s aerodynamic aerodynamic properties1. properties1.

those individuals within it. Carl Jung coined the notion of the Collective unconscious. Other major thinkers of crowd psychology include Gustave Le Bon,

“...recognizeWilfred thatTrotter, geographic localization Gabriel Tarde, Sigmund Freud and Elias Canetti.seem to have definitively lost its strategic value and, inversely, that is same The nonlinear interaction of the optical patterns of lines creates a real and value Advancing our research on fluids into digital to study the complex interactions that occur within a city, suchis attributed to delocalization of the vector, of a vector visible pattern of roughly horizontal dark and light bands, the moiré pattern, as different types of infrastructural flows, crowds as fluids masses and program navigation, we started reading fluids as vector fields to choreograph this complex in systems permanent movement - no matter if this movement aer-an effective method of representing the way in which Vector fields allows usis to develop superimposed on the lines.[1] More complex line moiré patterns are created into theial, urban spatial, scale. underwater or underground. All that counts forces are able to affectis eachthe other.

Working with the intensity parameter in the vector field allowed us to generate a 3d point cloud to then translate it into a 3d vector field that allowed us to control speed

if the lines are curved or not exactly parallel. Moiré patterns revealing com-

speed of the moving body and undetectability of its path.“

plex shapes, or sequences of symbols embedded in one of the layers (in form and directionality into a series of topological organizations. of periodically repeated compressed shapes) are created with shape moiré, otherwise called band moiré patterns. One of the most important properties of shape moiré is its ability to magnify tiny shapes along either one or both axes, that is, stretching. A common 2D example of moiré magnification occurs when viewing a chain-link fence through a second chain-link fence of identical design. The fine structure of the design is visible even at great distances.

By moving from a metrical conception in which these forces interact, to the vectorial

Paul Virilio

description where the actors become ephemeral in a continues variation of their values in free action (nomads, Deleuze and Guattari ). As information was the only evidence left in the amorphous result of our previous experiments, the vector description showed it’s richness in the event and the capacity to be more accurate in terms of performance with a intensive variable as the city.

The next series of experiments are based on a fluid dynamic simulation interacting with itself converted to a geometrical reference of a 3D vector field where we The next strategy towards the vector materialization was the

see its potential to address issues as intensity and directionality in an evolutionary way

loop scheme. By linking the different interactions of the vecto-

as the time line and the script are modify.

rial lines I managed to develop a variable organizationwithin a gradient logic. The continue relation from loop to loop appear as an interesting way to link space and navigation strategies.

I try to develop this continuity from the overall to the detail and tectonic organization in a series of parametric models.

In terms of material system, the vector field has been a tool that has allowed us to make many translations into the folding argument.

Worked along different software and material situations, the folding has

As As their their name name suggests, suggests, the the veins veins are are hollow hollow and and carr carr hemolymph hemolymph

I tried to close the gap between fluid dynamic behavior and material organization demonstrating the power of fluid to de-

given us various conclusions across the different possibilities of materiality for the project.

scribe interactions beyond matter into spatial and program-

We can see in the diagram the evolution of the different translations of what has become a principle for us.

matic distribution. The vectorial coordination is spread along

Anaglyph images are used to provide a stereoscopic 3D effect, when

the different orientation issues like views, slops, air control,

viewed with 2 color glasses (each lens a different color). Images are made

temperature, etc… allowing us to spread this logic across the

up of two color layers, superimposed, but offset with respect to each other

site as an organization urban statement.

to produce a depth effect. Usually the main subject is in the center, while

JEREZ DE LA FRONTERA

the foreground and background are shifted laterally in opposite directions.

The picture contains two differently filtered colored images, one for each eye. When viewed through the “color coded” “anaglyph glasses”, they reveal an integrated stereoscopic image. The visual cortex of the brain fuses this into perception of a three dimensional scene or composition.

Advancing my site analysis with fluids and vec-

During the late-eighteenth to mid-nineteenth centuries, flamenco took on a number of unique

tor fields not only to address infrastructural flow

characteristics which separated it from local folk music and prepared the way to a higher profes-

but to develop more the use and application of

sionalization and technical excellence of flamenco performers, to the diversification of flamenco

the system to generate relations with different

styles (by gradually incorporating songs derived from folklore or even other sources), and to the

program and therefore a navigational logic that

popularization of the genre outside Andalusia.

interacts with the urban space.

To make an anaglyph containing color information using color images, replace the red channel

The first time flamenco is mentioned in literature is in 1774 in the book Cartas Marruecas by

of the right-eye image with the red channel of the left-eye image. To do this, select the entire The aim of this studies will be to test site rela-

José Cadalso. During this period, according to some authors, there is little news about flamenco

right eye image (if the original is a crossed eye stereogram this will be on the left) and make tions with different ways of distributing program

except for a few scattered references from travellers. This led traditional flamencologists, like

a new document. Paste the right eye image in. Move the selection to the left eye image (with through the site, and most importantly the way

Molina and Mairena, to call the period of 1780 to 1850 as "The Hermetic Period" or the "private

consideration as above for crossed eye stereograms) and using the channels dialog select program could generate at the same time gradi-

stage of flamenco". According to these flamencologists, flamenco, at this time was something

the red channel. Copy the red channel from this source image. Return to the new document ent fields of activity through variations of inten-

like a private ritual, secretly kept in the Gypsy homes of some towns in the Seville and Cádiz

and select the red channel. Paste the left eye image into the red channel. Depending upon the sity; mix of program through gradient fields of

area. This theory started to fall out of favour in the 1990s. José Blas Vega has denied the abThe exploration of Vector fields as an urban tool allowed an alternative mode

colors this might look rather good as a color image (but not exactly true to the original color). relations.

Eye sensitivity balance can be improved by selecting the green channel and reducing it using

of addressing masterplanning strategies, not as one that is fixed but as one

a linear curve selection (e.g. reduce by 12.5%). Select the blue channel and reduce somewhat

that is relational to possible futures.

less (e.g. reduce by 5%). This action compensates for the eye’s lower sensitivity to red and The resolution of the vector as a design medium explores different scales and

side or to each side of an object). Without the anaglyph glasses the picture will appear reddish

levels of spatial, structural, material and programmatic differentiation by devel-

and somewhat dimmer, but the overall effect is improved when the glasses are used. The dim-

oping vector to vector properties from a local to a global field space.

ness can be corrected by increasing the overall brightness 15 to 20% and the contrast 10 to 15%. All of these adjustments will depend upon color balance, brightness, and contrast of the original image and the nature of the subject material.

Using color information, it is possible to obtain reasonable (but not accurate) blue sky, green

SORRY NO IMAGE HERE

these contain colors that are close to red or cyan.

Anaglyphic processes are not really able to reconstruct full-color 3D images. Colors which are combinations of red-green (yellow);and red-blue (magenta) would reproduce. However, to get full-color photos or movies, a polarizing filter system (or an adapted Russian LCD shutter system) must be used. Polarizing filters steer the vibrations of light analogous to a Window blind.

Two synchronized projectors are used, overlapping the images into an aluminum screen. The shutter system, on the other hand, switches back and forth rapidly for left- and right-eye images, synchronized to the image input, and alternating so fast that the eye cannot detect the changes. This is similar to how LCD shutter glasses work.

images which surround the

cess involving social, economic, architectural, etc., forces, and the city as a temporary,

rhythm, the poetic stanzas, and the ambience. (Quoted by Ríos Ruiz 1997)

viewer with an environment

diagrammatic manifestation of the urban. The French urbanist Henri Lefèbrve wrote

normal photographs, or captured with specialized panoram-

in 1970 that the urban as such is not yet a completed reality, but it is a potentiality,

to its late 1780 mentions, it is because flamenco simply did not exist. The whole theory about

does not necessarily lead to a transglobal urban zone. Rather, the urban is a complex,

a hermetic stage would then be a fantasy, caused by the aura of mystery surrounding Gypsy

multi-directional process of connection and separation, of layering, enmeshing and cutting, which leads to ever different formations.

If the urban is something that one can work with, intervene into, or become a part of,

3D-modeled scenes. There are

then it is important to understand its forces and layers and also to understand how it

two type of VR Panorama:

Álvarez Caballero (1998) goes further, stating that if there are no news about flamenco previous

an ‘enlightening virtuality’. The path of urbanisation, however, is not undirectional and

ic cameras, or rendered from

interlaces the global with the local.

“It’s important to use your hands, this is what distinguishes your from a cow or a computer operator.”

Single row panoramas, with a

Given a vector space V, a nonempty subset W of V that is closed under addition and scalar multiplication is called a subspace of V. Subspaces of V are vector spaces (over the same

single horizontal row of photo-

field) in their own right. The intersection of all subspaces containing a given set of vectors is called its span; if no vector can be removed without changing the span, the set is said to

graphs. multi-row panoramas,

be linearly independent. A linearly independent set whose span is V is called a basis for V.

with several rows of photographs taken at different tilt angles.

According to entertainment trade papers, 3D movies are now more popular than ever. The A pair of eyeglasses with two filters of the same colors, once used on the cameras (or now simulated by image processmodern processes allow maximum comfort and minimum eyestrain. 3D provides an entertain- ing software manipulations) is worn by the viewer. In the case above, the red lens over the left eye allows only the red part

Using Zorn’s Lemma (which is equivalent to the axiom of choice), it can be proven that every vector space has a basis. It follows from the ultrafilter lemma, which is weaker than the

axiom of choice, that all bases of a given vector space have the same cardinality. Thus vector spaces over a given field are fixed up to isomorphism by a single cardinal number (called the dimension of the vector space) representing the size of the basis. For instance, the real finite-dimensional vector spaces are just R0, R1, R2, R3, …. The dimension of the real vector space R3 is three.

ment experience still not possible with television (though certain experimental processes, the of the anaglyph image through to that eye, while the cyan (blue/green) lens over the right eye allows only the blue and quasi-holographic “volumetric displays”, have been used, for example, to show real images of green parts of the image through to that eye.

It was F. Hausdorff who first proved that every vector space has a basis. Andreas Blass[1] showed this theorem leads to the axiom of choice.

cars in a display setting, with no viewing glasses required).

distribution and navigation through the site. The research on massing as

of dances and toques, the musical scores, the newspapers, the graphic documents in paintings and engravings; and all of this with no interruptions, in continuous evolution together with the

“stitched” together from several

brightly colored and high contrast objects such as signage, toys, and patterned clothing when

sheets, the narrations and descriptions from travellers describing customs, the technical studies

We must distinguish between the urban as a discontinuous flow, a transformation pro-

sense of place. They can be

vegetation, and appropriate skin tones. Color information appears disruptive when used for

theatre movement of sainetes (one-act plays) and tonadillas, the popular songbooks and song

VR Panoramas are panoramic

(inside, looking out), yielding a

Different type of crowd movement triggered differences of programs

Nowadays, we know that there are hundreds and hundreds of data which allow us to know in detail what flamenco was from 1760 until 1860, and there we have the document sources: the

its high sensitivity to green, but may induce bleed through (you may see ghost images on one

VECVECTOR TOR ARARCHICHITECT TECT

sence of evidences for this period:

Portions of the image that are red will appear dark through the cyan filter, while portions of colors composed only of

A basis makes it possible to express every vector of the space as a unique tuple of the field elements, although caution must be exercised when a vector space does not have a finite

green and blue will appear dark through the red filter. Each eye therefore sees only the perspective it is supposed to see.

basis. Vector spaces are sometimes introduced from this coordinatised viewpoint.

one of the parametric urban tools allows us to negotiate the context and

musical genre with strong, rhythmic undertones and is often accompanied with a similarly impas-

thefuture conditions, rather than fixed, but gives the input to the site and

sioned style of dance characterized by its powerful yet graceful execution, as well as its intricate

One often considers vector spaces which also carry a compatible topology. Compatible here means that addition and scalar multiplication should be continuous operations. This re-

also be affected by the densification of the site. By setting up the urban

hand and footwork. Flamenco embodies a complex musical and cultural tradition. Although con-

quirement actually ensures that the topology gives rise to a uniform structure. When the dimension is infinite, there is generally more than one inequivalent topology, which makes the

inputs we are able to control two or three different type of programs and

sidered part of the culture of Spain in general, flamenco actually originates from one region: An-

tectonic system specifically, from either smooth, singular program to the

dalusia. However, other areas, mainly Extremadura and Murcia, have contributed to the develop-

more extreme conditions, which could have the extreme density and

ment of several flamenco musical forms, and a great number of renowned flamenco artists have

height

been born in other territories of the state. The roots of flamenco are not precisely known, but it is

study of topological vector spaces richer than that of general vector spaces.

Only in such topological vector spaces can one consider infinite sums of vectors, i.e. series, through the notion of convergence. This is of importance in both pure- and applied math-

generally acknowledged that flamenco grew out of the unique interplay of native Andalucian, Islamic, Sephardic, and Gypsy cultures that existed in Andalucia prior to and after the Reconquest.

For a complete picture of the possible influences that gave rise to flamenco, attention must be paid to the cultural and musical background of the Iberian Peninsula since Ancient times. Long be-

Latin American and especially Cuban influences have also been important in shaping several

fore the Moorish invasion in 711, Visigothic Spain had adopted its own liturgic musical forms, the Visigothic or Mozarabic rite, strongly influenced by Byzantium. The Mozarabic rite survived the

flamenco musical forms.

Gregorian reform and the Moorish invasion, and remained alive at least until the 10th or 11th century. Some theories, started by Spanish classical musician Manuel de Falla, link the melismatic forms and the presence of Greek Dorian mode (in modern times called “Phrygian mode”) in flamenco to the long existence of this separate Catholic rite. Unfortunately, owing to the type of musical

Once the seeds of flamenco were planted in Andalucia, it grew as a separate subculture, first

notation in which these Mozarabic chants were written, it is not possible to determine what this music really sounded like, so the theory remains unproven.

centered in the provinces of Seville, Cádiz and part of Málaga—the area known as Baja Andalucía (Lower Andalusia)—but soon spreading to the rest of Andalucia, incorporating and transforming

Moor is not the same as Muslim. Moor comes from the Latin Mauroi, meaning an inhabitant of North Africa. The Carthaginians, for instance, came from North Africa. Moorish influence in the penin-

local folk music forms. As the popularity of flamenco extended to other areas, other local Spanish

sula goes back thousands of years, but it was the Islamic invasion, by largely Berber armies in 711, that determined the main musical influences from North Africa. They called the Iberian Peninsula