Environment and Planning B: Planning and Design 2014, volume 41, pages 690 – 716

doi:10.1068/b38121

The dynamic façade pattern grammar

Sotirios D Kotsopoulos ¶ Department of Architecture, Design Laboratory, Mobile Experience Laboratory, Massachusetts Institute of Technology, Cambridge MA 02139-4307, USA; e-mail: [email protected] Guglielmo Carra Department of Building Environment Science and Technology, Politecnico di Milano, Milan 20133, Italy; e-mail: [email protected] Wesley Graybill Department of Computer Science, Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge MA 02139-4307, USA; e-mail: [email protected] Federico Casalegno ¶ Department of Architecture, Design Laboratory, Mobile Experience Laboratory, Massachusetts Institute of Technology, Cambridge MA 02139-4307, USA; e-mail: [email protected] Received 13 July 2011; in revised form 9 April 2013; published online 10 April 2014 Abstract. This paper presents a generative grammar producing a language of patterns for the south façade of a prototype sustainable house. The patterns are produced through the activation of the electrochromic material that is applied on the windowpanes of the façade. The class of the performatively effective configurations of the façade is approached as a visual language and the productive (generation), combinatorial (enumeration) and performative (verification) attributes of this language are examined. Random, performance driven, patterns could supply sufficient interior daylight without acknowledging the visual potential of façade pattern generation. The uniqueness of the chosen approach is that the shape grammar encodes the performative constraints pertaining to the generation of façade patterns in a visual manner by associating principles of two-dimensional pattern generation to levels of illuminance. Keywords: shape grammars, electrochromic windows, autonomous control, daylight performance, aesthetics

1 Introduction Light is an essential aesthetic and performative aspect of architecture. The lighting of interior spaces typically involves natural and artificial light sources. Given that artificial lighting contributes considerably to energy consumption, natural lighting is favored during daytime. This paper presents an example of how shape grammars, artificial intelligence (AI) methods for building control, and electrochromic technology can be combined to regulate natural lighting in the interior of residential buildings. The association between a specific architectural element of a prototype house—a façade involving 100 electrochromic windows—and the adjustment of the natural lighting conditions in the house interior is treated algorithmically. The façade operates as a dynamic filter between interior and exterior permitting the ¶ Current address: School of Humanities, Arts and Social Sciences, Comparative Media Studies, Mobile Experience Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA.

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modification of the incoming solar radiation and heat through the adjustment of the chromatism and the light transmittance of each individual windowpane. Changing the number and the distribution of the active electrochromic windows on the façade affects the intensity of the incoming sunlight, thus permitting more effective management of the high-thermal-mass house envelope, but also transforms how the house is perceived from the public street. A shape grammar drives the activation of the electrochromic windows on the basis equally of performative and visual criteria. The increasing cost and scarcity of nonrenewable energy sources promote the use of sustainable principles in the design and operation of buildings. However, the principles of orientation and plan organization for breeze, and sectional organization for crossventilation and cooling can turn into a design tyranny. New optimization and automation techniques promise to secure economical management and compliancy of performance, but they usually disregard building aesthetics. Motivation for this research was to provide an environmentally conscious mode of building with an original design vocabulary that is in alignment with technological innovation so as to supply architecture with new tectonic means. An architectural solution was proposed which satisfies the environmental requirements of its function and makes elegant architecture out of the provisions needed for their satisfaction. Traditional buildings combine conservative, selective, and regenerative modes of envi­ ronmental management to conserve heat, to admit selectively elements from the exterior environment, and to restore favorable conditions by artificial means (Banham, 1969). Thick walls conserve heat and return it to the interior environment after the heat source is no longer active in the winter, and delay the effects of solar heat in the summer. Glazed windows admit light but exclude the direct sun, and louvered grilles admit air but exclude visual intrusions. Heating ventilating and air conditioning systems and artificial lighting restore desired temperature and light settings at the expense of using energy. Recent building paradigms use productive systems to harvest the power of the sun, the wind, or biomass, and responsive systems to provide adjustability of performance ‘in response to’ real conditions (Klein and Kaefer, 2008). In the presented prototype the form and the fabric of the building envelope are used as a filter of the external environment, in combination with dynamic control and energy production capabilities, to provide an energy-saving, environmentally sound, and architecturally rich living environment. The prototype consists of an open-plan interior measuring 7.75 m × 20.00 m with a programmable solar wall facing south. The house envelope secures high thermal resistance and low conductivity, conserving heat during the winter and preventing excessive heat during the summer. A single pitched roof stands 2.95 m high on the north and pitches up to 3.65 m on the south, thus exposing a wide façade area to the sun. The south façade is a solar wall of individually addressable windows whose configurations enable the precise adjustment of light, heat, air, and view. A solar cogeneration plant produces electricity, hot water, and heated/cooled air, while a central, autonomous control system offers parallel, integrated adjustment of all house systems in response to a broad spectrum of natural conditions and user needs. Hence, on a hot summer day the control sets the electrochromic material of a number of windows to its minimum solar transmittance to protect the house interior from direct sun exposure, while on a cold winter day it sets it to maximum solar transmittance in order to expose the interior to the winter sun. The adjustment of the number and distribution of the active electrochromic windows on the façade causes the formation of visual patterns. Since there is no standard class of patterns satisfying all weather conditions the adjustment of the façade remains dynamic. Randomly generated performance-driven patterns could supply adequate interior daylight without acknowledging the visual attributes of the patterns.

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The presented grammar is applied dynamically by the control system of the house to generate façade patterns complying both on performative constraints of daylight adjustment and on visual principles of pattern generation on the plane. After an exposition of the research background, this presentation is organized into three sections: generation, enumeration, and verification. Generation presents the productive scope of the façade pattern language, including the grammatical rules producing the patterns. Enumeration presents the combinatorial scope of the pattern language including the count of patterns and their classification based on symmetry and illuminance. Verification presents the performative scope of the language by determining how variation in the number and distribution of active windows affects the levels of interior illuminance. The sequencing generation–enumeration–verification is retrospective. The generation of façade patterns and the verification of their performance were advanced in parallel, whereas enumeration was conducted last. 2 Background The connected sustainable home concept (figure 1) aims to provide a living environment that is constantly well tuned to the comfort levels of the inhabitants. A key aspect to this is the fine management of the house system dynamics. Natural conditions vary and so do the activities of the inhabitants, but an intelligent control can always supply the desirable comfort levels at minimal energy cost. A full-scale prototype with these capabilities is in the final stage of construction in Trento, northern Italy.

Figure 1. Rendition of the prototype connected sustainable home in Trento, northern Italy.

The dynamic façade covering the patio and the kitchen on the south elevation of the house is a matrix of 5 × 20 windows 700 mm × 700 mm in size (figure 2). The lower 3 × 20 rows of vertical window panes include operable windows, which can be opened and closed at precise angles using electronic actuators, so that the permeability pattern to air flow is automatically and precisely adjusted. The upper 2 × 18 rows of tilted window panes include inoperable windows tilted by 75° to form the patio roof, while the upper right two corner windows are inoperable and not tilted. Each triple-glazed window involves an overlay of two electronically switched materials and has an overall thickness of 43 mm. The glazings are separated by two Argon-filled gaps of 12 mm and 6 mm. The electrochromic coating applied on the external glazing enables the adjustability of solar radiation and permits precise light and thermal management. The polymer dispersed liquid crystal film applied on the internal glazing supplies adjustability of visibility and secures privacy. The control system of the house applies grammatical rules to dynamically adjust the levels of the admitted daylight by generating façade patterns that conform to performance and visual principles. The role of the control system is to compile feedback from sensors, statistical climatic data, and ambient data, to provide real-time building performance

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Figure 2. The south elevation of the prototype, incorporating the dynamic façade.

evaluation. The residents specify ranges of room temperature and their schedules and the control minimizes the energy consumption while guaranteeing that the desired comfort levels are always maintained. To minimize the risk of constraint violation the control allows operating an uncertain system within acceptable risk bounds that are specified by the residents (Graybill, 2012; Ono, 2012). 2.1  Generative apparatus

The presented generative grammar determines the states of the dynamic façade on the basis equally of performance and aesthetics. In the past Stiny and Mitchell (1978a; 1978b; 1978c) described a shape grammar encoding stylistic principles of generation, enumeration and verification of Palladian villa plans. An insightful discussion of the dual character, generative/expressive of spatial rule systems exists in Knight (2005). Two noteworthy articles on optimization and performance-driven generative design are those by Luebkeman and Shea (2005), and Shea et al (2005). Luebkeman and Shea (2005) show how navigating the performance space of a design solution promotes design thinking and exhibits the association between variations and performance. Shea et al (2005) use performance-driven generative methods in producing designs based on modeling of conditions and performance. This paper extends the previous contributions in two ways. First, similar to Stiny and Mitchell (1978a; 1978b) and Stiny and Gips (1978) it presents the generation, enumeration, and verification of a design language. However, instead of simply encoding stylistic conventions of form generation, the grammar captures conventions of daylight adjustment and encodes them visually. Second, the rules of the grammar determine the states of the dynamic façade that is made out of a specific variable transmittance material. Hence, the grammar exploits the visual potential of the performance conventions underpinning the operation of the specific façade throughout the four seasons. A shape grammar consists of a calculating part and a syntactic–interpretive part. The calculating part engages an algebraic framework in which elements of 0, 1, 2, and 3 dimensions (points, lines, planes, solids, or combinations of these) are used in calculations that may happen in a space of 0, 1, 2, or 3 dimensions. The syntactic–interpretive part consists of production rules confining the syntactic (structure) and semantic (meaning) attributes of sets of products, which are conventionally called languages. An algebra Xij formalizes the interaction of i-dimensional elements on a j-dimensional space (Stiny, 1991). For example, the algebra U12 formalizes the graphic computations that designers execute with lines on the graphic plane: it captures the interaction of one-dimensional elements, lines (i = 1), on the twodimensional plane ( j = 2). This treatment can be expanded to include algebras with labeled points (Vij), which serve the naming of elements, and algebras with colors and properties like weights (Wij) which serve their visual distinction in desired ways (Stiny, 1992). Product algebras can be formed as combinations of any of the above algebras to allow the execution of calculations with labeled and colored forms. Within this framework, the elements are composed with the aid of production rules. A product algebra GU12 × U22 H including black

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lines and planes is used in the next example of a rule that is similar to the rules used in the dynamic façade pattern grammar: Within the semantic context of façade pattern generation a rule ri checks a number of neighboring cells depicted on the left-hand side, and ‘activates’ a number of cells by modifying their state from off to on as depicted on the right-hand side. The rule is of the general form: x " prt C (x) + b-1 6 prt (x) @ .

If x is the shape appearing on the left-hand side of the rule, then some part of x is ‘activated’ by applying a uniform tone to its area, b−1[prt(x)], while its complement prtC(x) remains intact (Stiny 2011). The rule of the example applies on a shape C capturing two neighbouring window cells: to produce shape Cl: in two steps. First, a transformation t is used to recognize through matching, some part of C, which is geometrically similar to x—the shape that appears on the left-hand side of the rule—and, second, the same transformation t is used to modify C. It substitutes t(x) with t {prt C (x) + b-1 [prt (x)]} to produce Cl. Concisely, Cl = 6C - t (x) @ + t " prt C (x) + b-1 6 prt (x) @, .

Rule ri can be applied to C to produce Cl under a transformation t in two ways: identity or under mirror reflection (or 180º rotation). These correspond to the ways the shape on the left‑side of the rule can be ‘matched’ on C:

2.2  Performative premises

The number and distribution of the active electrochromic windowpanes on the façade can be determined to always supply levels of interior daylight illuminance above a preset value. Two performative premises assure the generation of effective façade patterns. The premises were extracted via simulation with Relux Professional and Relux Vision by Relux Informatik AG, assuming that there were no neighboring buildings casting shadows. Climatic data for the location of the prototype and the lighting standards determined by Italian law were provided by the database of the software. The specifications of the electrochromic material were provided by Sage Electrochromics. In the simulations transmittance τ was set to 62% for glass at state off and to 3.5% for glass at state on. Several recent papers describe state-of-the-art research in electrochromic technology. Lee et al (2006) present a study in which the effects of electrochromic technology are monitored in a cube 3.0 m × 3.0 m × 3.0 m. Hausler et al (2003) present a technical comparison of electrochromic glass. Gugliermetti and Bisegna (2003) examine the visual and energy management of electochromic windows in Mediterranean climates. Mardaljevic et al (2009) review the history of building compliance methods determining energy efficiency and comfort and propose a new basis of more efficient metrics. Two models established by the Commission Internationale de l’Eclairage were used in the simulations. The Standard Overcast Sky model provides an account of the natural light

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emitted through cloudy sky. The Standard Clear Sky model computes natural light assuming that the sun is the single lighting source without calculating the diffused and reflected light by the sky. After compiling the meteorological records of the last decade for the Province of Trento, the percentage of rainy days was determined to be 36% and the percentage of sunny days 64%. These numbers determined the days per year in which the Overcast Sky and Clear Sky models were used. However, both models provide incomplete understanding of the phenomenon of illuminance as they exclude the assessment of transitory conditions, such as the passage of clouds across the sun (Wienold, 2007). For this reason, simulation data for each day of the year were evaluated and classified for the integration of an optimization algorithm in the control system. Combined with real-time input from sensors made the efficient management of the façade possible even in conditions that cannot be captured by the static models. Typical outputs of the simulations included the minimum, maximum, and average values of illuminance, the uniformity values and average daylight factor, the Isolux maps for assigned planes, and the tridimensional illuminance diagrams. The interior daylight conditions are determined by the average illumination Eave, the uniformity G1, and the daylight factor Dave. Italian law adopts both a national law Circ. Min n° 3151 22/5/67 and the UNI EN 12464, which is a norm defining the lighting of workplaces. Although the minimum daytime value of illuminance Emin for residential buildings is 300 lux, this threshold was raised in the prototype to 500 lux to reach higher levels of visual comfort. Uniformity G1 captures the smoothness of daylight distribution defined by the ratio Emin/Eave. A satisfactory value is G1 = 0,5. Lastly, the daylight factor represents a physical feature of windows, which is constant and set to Dave = 3. The simulation tests indicated that in order to achieve Emin H 500 lux with smooth interior daylight distribution Emin/Eave H 0.5 the façade must satisfy two provisions, namely: Provision I: In an average luminous day, out of 100 electrochromic window cells, 50–75 cells need to be active (on) to secure luminosity levels above the threshold value. Provision II: No four consecutive window cells can be concurrently active on the same row. Dense accumulation of consecutive active cells horizontally produces linear shadows that disrupt smooth light distribution. Hence, if n is the number of consecutive active cells in any row then n G 3, to secure fine distribution of active cells. 3 Generation Each electrochromic glass cell of the façade can be set on (active) or remain off (inactive). Three general use modes were determined for the façade based on illuminance performance: (a) 0% active, a single rule is required, do nothing; (b) 50%–75% active, twelve rules organized into a grammar generate façade patterns; (c) 100% active, a single rule is required, activate all. Hence, the façade can remain clear, be activated in a 2/4–3/4 ratio of its area, or be fully active. The grammar generates patterns for (b) by activating a number of electrochromic cells within the range 50–75. Starting from an initial state a new state is produced after a rule is applied. A rule may apply while taking into account the state of a single cell and the state of at most four more cells arranged in the same row. A neighbourhood of cells involves at most m cells arranged in the same row, with m G 5. 3.1  Modes of rule application

Modes of rule application enforcing the generation of visually distinct patterns are explained next. The 5 × 20 matrix of inactive electrochromic cells is depicted below in the algebra U12:

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Auxiliary markings are introduced: namely, boundaries and axes depicted in dashed grey line, in the algebra W12. The axes organize the matrix into four partitions of 2½ × 10 glass cells each. A pair of labels (V, V) in the algebra V02 allows the distinction between vertical and horizontal direction. Neighboring partitions are bilaterally symmetrical along the vertical or horizontal central axes. This augmented description is formed in the product GU12 × W12 × V02 H:

Rule modes determine general ways by which the rules ri can be applied on the matrix. Seven modes of rule application are outlined based on the above partitioning. Rule modes (i)–(vii) involve the application of a rule ri and oftentimes parallel application of copies of ri under transformations t*. This allows for multiple similar parts of the matrix to be ‘activated’ in parallel, and for various symmetries to be used in the generation of façade patterns. Based on the schema of subsection 2.1 the rule modes have the general form: x"

/ t* " prt (x) + b C

-1

6 prt (x) @, .

The rule modes are divided into two classes based on the position of the cells they affect. To generate a façade pattern it is mandatory to use at least one mode from each of the two classes. The first class includes modes affecting only cells positioned along the horizontal axis:

In the first class a rule ri can be applied along the horizontal axis in two ways: ri

r i ri (ii) The second class includes modes affecting cells in the remaining four partitions of the matrix: These five ways correspond to the symmetry group of the matrix and its partitions, and more specifically, the number of symmetry subgroups of the dihedral group of order 2 (March, 1972). (i)

In the second class a rule ri can be applied on the four 2 × 10 partitions of the matrix in five ways: ri ri ri ri r i (iii) (iv) (v)

(vi)

ri

ri (vii)

ri ri

ri ri

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Modes (i) and (iii) involve application of a single rule ri , respectively. Modes (ii) and (iv) involve parallel application of a rule ri and of a copy of ri under a transformation tl that is a mirror reflection along the vertical axis. Mode (v) involves parallel application of a rule ri and of a copy of ri under a different transformation tll that is a mirror reflection along the horizontal axis. Mode (vi) involves parallel application of a rule ri and of a copy of ri under a transformation t n that is 180° rotation around the center point of the matrix. Transformation t n is a transformation tl + tll involving mirror reflections, along the vertical and the horizontal axes. Mode (vii) involves parallel application of ri and of three copies of ri under transformations tl, tm , t n: that is, mirror reflection along the vertical and the horizontal axes and 180° rotation, respectively. Table 1 presents the rule schemata expressing the modes (i)–(vii) based on the general rule schema of subsection 2.1. Table 1. Rule schemata capturing the general form of the rule modes (i)—(vii). Modes

Rule schemata

(i), (iii) (ii), (iv) (v) (vi) (vii)

x → {prtC(x) + b−1 [prt(x)]} x + tl(x) → {prtC(x) + b−1 [prt(x)]} + tl{prtC(x) + b−1 [prt(x)]} x + tll(x) → {prtC(x) + b−1 [prt(x)]} + tll{prtC(x) + b−1 [prt(x)]} x + tlll(x) → {prtC(x) + b−1 [prt(x)]} + tlll{prtC(x) + b−1 [prt(x)]} x + tl(x) + tll(x) + tlll(x) → {prtC(x) + b−1 [prt(x)]} + tl{prtC(x) + b−1 [prt(x)]}  +  tll {prtC(x) + b−1 [prt(x)]} + tlll{prtC(x) + b−1 [prt(x)]}

All seven modes of the rule application may be used to generate patterns with no overall symmetry. Combination of the mode (ii) with the mode (vi) or (vii) generates patterns with rotational symmetry. To generate a pattern with reflectional symmetry along the vertical central axis, the modes (ii) and (iv) can be used. To generate a pattern with reflectional symmetry along the horizontal central axis the modes (i) or (ii) can be combined with (v) or (vii). To generate a pattern with reflectional and rotational symmetry only the modes (ii) and (vii) can be combined. 3.2  Algebras and descriptions

The necessary graphic elements for deriving a pattern are finalized and presented based on their corresponding algebras Uij, Wij, and Vij. Initial shape is the augmented description of the 5 × 20 matrix, including grey line axes and labels. The pair of labels (A, A) along the horizontal axis indicates the ongoing stage of the derivation:

Three possible graphic illustrations of window cells are determined, on (active), off (inactive), and the auxiliary state, excluded. Cells are marked excluded to become inaccessible. In this way they are distinguished from remaining inactive cells, which can still become active. At the terminating stage of a derivation all excluded cells turn into inactive cells. The graphic illustrations of the three possible window states are depicted below, on (active-left), off (inactive-center), and excluded (right): In the calculations to follow all graphic elements are manipulated on the plane (j = 2). Active cells are depicted as black squares in the algebra U22. Inactive cells are depicted with black lines in the algebra U12. Excluded cells are depicted as grey squares in the algebra W22.

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Auxiliary axes are depicted with grey lines in the algebra W12. Letters A, B, and C are used as labels in the algebra V02. The overall algebraic component is a product: GU12 × W12 × U22 × W22 × V02H. A typical step C & Cl in a derivation is formed in the product: GU12 × W12 × U22 × W22 × V02H & GU12 × W12 × U22 × W22 × V02H . Components W12, W22, or V02 in this product algebra can be substituted with the empty shape. For example, when the excluded window cells turn into inactive their grey tone is erased (W22 & Q) and their linear boundaries are redrawn in the U12 component of the product. Hence, the terminating step, where all the auxiliary graphic elements are erased, is expressed: GU12 × W12 × U22 × W22 × V02H & GU12 × Q × U22 × Q × QH . 3.3  Derivation stages

Façade pattern generation involves twelve rules satisfying provisions I and II. Derivation is organized in three stages A, B, and C the productive objectives of which are explained next. All three stages include a number of productive rules and a terminating rule, applying at the end to introduce the consecutive stage or to terminate the derivation. Stage A—the initiating stage—includes four rules in total. These apply on the outmost four columns of the matrix. Stage A is terminated when all the outmost cells are active or excluded. The cells that can be affected in stage A are depicted below:

Stage B—the main productive stage—includes five rules in total. Generation at this stage proceeds until all available cells are either active or excluded. The cells that can be affected in stage B are depicted below:

Stage C—the terminating stage—includes three rules in total. Generation at this stage proceeds until all available excluded cells are turned inactive and all axes are erased. The shapes that can be affected in stage C include the entire matrix:

3.4  Generative rules

Rules are named with the letter ri (i = 1, 2,…, 12). Each productive rule scans a neighborhood of cells, as depicted on the left-hand side and modifies the state of a number of cells as depicted on the right-hand side. Productive rules always apply until they exhaust the available window cells. The number of the activated cells can be 0, 1, or 2. Rules apply in three stages.

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Stage A initiates the derivation. Stage B is the main productive stage. Stage C terminates the derivation. The positioning of grey axes and labels in the rule expressions is parametric. 3.4.1  Stage A Productive rules 1–3 initiate the process. They are parametric and apply on the outmost left or right window cells lying next to the vertical boundary axes. Rule 1 scans one cell and excludes it by applying a grey tone to its area. Rules 2 and 3 scan and activate one or two cells, respectively. The performance of each rule is 100%. Rules 1–3 apply until all the outmost left and right cells are activated or excluded. Rule 4 terminates stage A and introduces stage B as shown below: r1

r2

r3

r4

3.4.2  Stage B Productive rules 5–8 are parametric. They affect the entire matrix except from the outmost left and right cell columns. Rules 5 and 6 scan two cells and activate or exclude one. The percentage of contribution of each of these rules is 0 G x G 50. Rule 7 scans three cells, activates one cell, and excludes one cell. Rule 8 scans five cells, activates one cell and excludes one cell. The percentage of contribution of these two rules is 0 G x G 33.3. Rules 5–8 apply until all available cells are either active or excluded. Rule 9 terminates stage B and introduces stage C: r5

r6

r7

r9

r8

3.4.3  Stage C Productive rules 10 and 11 are also parametric. Rule 10 erases the grey markers from the excluded cells anywhere on the matrix and turns them into inactive cells. Rule 11 eliminates the auxiliary grey axes. Rules 10 and 11 apply until all excluded cells are made inactive, and all axes are erased. Rule 12 applies last to erase the labels and terminate the process: r10 3.5  Derivation

r11

r12

The generation and illuminance performance a the façade pattern are calculated in the online appendices A and E, respectively (http://dx.doi.org/10.1068/b38121). The pattern includes seventy-four active windows; it involves rotation around the center of the vertical axis; and it is produced after modes (ii) and (vi) of the grammar:

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4 Enumeration The enumeration computes the number of the patterns and it places them into subclasses based on illuminance and symmetry. The enumeration is computed assuming provisions I and II. First, a calculation is performed of the total number of patterns with density between fifty and seventy-five active windows. Then, the consideration of their symmetry further refines the enumeration. If n denotes the number of active windows, the interest is on 50 G n G 75, due to provision I. The façade is decomposed into rows numbered i = 1, 2,..., 5, with ri denoting the number of active windows in row i. The n active windows are distributed across the rows with the requirements ri = n , and 0 G ri G 20. Given a fixed number of active windows ri the number of ways in which these can be arranged across any row i is calculated. The function P(r, k) is defined to compute the number of arrangements of r active windows across a row of length k, subject to provision II. The goal is to calculate P(ri, 20). Two cases are distinguished. Case 1: The leftmost window is inactive. Then, there are P(r, k−1) ways to distribute the r active windows across the remaining k−1 windows, noted as: k

/

1

k−1

Case 2: The leftmost window is active. Then, three subcases are distinguished. Subcase 2.1: If the consecutive window is inactive the leftmost portion of the row will not violate provision I. The state of the third window may be chosen from the left without restriction. This leaves r−1 windows to activate across a total of k−2 remaining windows in the row. Hence, there are P(r −1, k−2) possibilities, noted as: k 1

2

k−2

Subcase 2.2: If the consecutive window is active the two leftmost windows are active and the third window from the left is inactive. This leaves r−2 windows to activate across a total of k−3 remaining windows in the row. Hence, there are P(r−2, k−3) possibilities, noted as: k 1

2

3

k−3

Subscase 2.3: If the consecutive window is active, the three leftmost windows are active. Then, the fourth window from the left is necessarily inactive. This leaves r−3 windows to activate across a total of k−4 remaining windows in the row. Hence, there are P(r−3, k−4) possibilities, noted as: k 1

2

3

4

k−4

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In total, a recursive equation can be formed: P(r, k) = P(r, k−1) + P(r −1, k−2) + P(r −2, k−3) + P(r −3, k−4) . The base cases of the recursion are P(1, 1) = 1 and P(1, 2) = 2. The argument establishes an expression for the productive possibilities on a single row. For a given assignment to r1,…, r5 this number is denoted by the product of these expressions: 5

% P^r , 20h . i

i =1

To calculate the total number of arrangements for a given n, sum over all values r1,…, r5 to yield an equation for the number of arrangements E, as a function of the number of active windows n: E (n) =

5

/ % P^r , 20h .

r1, f, r5 i = 1 / ri = n 0 G ri G 20

i

Restricting the production to any n in the range 50–75 yields 1.285 × 1024 configurations. The results of the computation for E are provided in table 2. Table 2. Enumeration of distinct façade patterns, within the range of 50%–75% activation. n

E(n)

n

E(n)

n

E(n)

50 51 52 53 54 55 56 57 58 59

1.751 × 1027 1.191 × 1027 7.566 × 1026 4.484 × 1026 2.470 × 1026 1.265 × 1026 5.986 × 1025 2.610 × 1025 1.048 × 1025 3.844 × 1024

60 61 62 63 64 65 66 67 68 69

1.285 × 1024 3.891 × 1023 1.061 × 1023 2.590 × 1022 5.611 × 1021 1.069 × 1021 1.774 × 1020 2.529 × 1019 1.285 × 1018 1.285 × 1017

70 71 72 73 74 75

1.285 × 1016 1.285 × 1015 1.285 × 1013 1.285 × 1012 1.285 × 1010 5.507 × 108

Five subclasses account for the symmetry of the patterns in the language: (1) no symmetry, (2) rotational symmetry, (3) reflectional symmetry about the vertical axis, (4) reflectional symmetry about the horizontal axis, and (5) rotational and reflectional symmetry. Class (1) includes patterns that can be generated through translation on the plane. Class (2) includes patterns that remain identical upon 180° rotation. Classes (3) and (4) include patterns that remain identical when reflected about the central axis of the façade, either vertical or horizontal. Class (5) includes patterns for which the distinction between horizontal and vertical axis is unnecessary. The five classes are denoted S0, Srot, Sref v, Sref h, and Sref, rot. Let n denote the number of tinted windows and let ki denote the number of windows tinted in row i of the 5 × 20 matrix. The function P(k, m) is defined to be the number of possible ways to tint k cells in a row of length m cells, according to the rules of the grammar. Let S(k) denote the number of arrangements with k tinted cells in a row of length 20 that are bilaterally symmetric about the center. Two cases can be distinguished in calculating S(k).

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Case 1: The two-centermost cells are tinted. Then, the cells to either side of the two centermost cells must remain clear. Thus, there are P(k/2−2, 8) possible arrangements: k k/2–2

k/2–2

Case 2: The two-centermost cells are clear. Then, there are P(k/2, 9) possible arrangements: k k/2

k/2

Therefore: S (k) = )

P (k/2, 9) + P (k/2 - 2, 8), if k is even. 0 if k is odd.

First, the subclass S0 of patterns that do not involve overall symmetry is enumerated. All modes of rule application may be used to generate a pattern in S0 and all possible configurations are included in the class. The total number of configurations in S0 is the product of P(ki, 20) over each row i summed over all possible partitions of n tinted cells across the five rows: E s0 (n) =

/ % P (k , 20) . i

i

k1, f, k5 / ki = n 0 G ki G 20

For the subclass Srot of patterns involving rotational symmetry the analysis proceeds separately for the window cells of the horizontal axis and those of the remaining two 2 × 20 partitions (see subsection 3.1). Only mode (ii) can be used on the horizontal axis, since the center row must be bilaterally symmetric. The number of arrangements is S(k3). Modes (vi) and (vii) can be used on the remaining two 2 × 20 partitions. This implies that the configuration of the bottom two rows is determined by that of the top two rows (or vice versa). Hence, it is sufficient to count the arrangements of one section. Let E2(n) denote the number of arrangements of n tinted cells across two rows. This value can be calculated similarly to E S : 0

E 2 (n) =

/ % P (k , 20) .

k1, k2 k1 +k2 = n 0 G ki G 20

i

i

The enumeration of configurations in the subclass Srot is calculated as follows: E srot (n) =

/ S (k ) E (k 3

2

12

k12, k3 2k12 +k3 = n 0 G k3 G 20 0 G k12 G 40

),

where k12 denotes the total number of tinted windows between rows 1 and 2. For the Sref v subclass of patterns involving reflectional symmetry about the vertical axis, the calculation is similar to S0 except that only modes (ii) and (iv) can be used, since each row is bilaterally symmetric. For even n, the enumeration in the Sref v subclass is calculated as: E sref v (n) =

/ % S (k ) . i

k1, f, k5 / ki = n 0 G ki G 20

i

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To generate a pattern in the subclass Sref h of patterns involving reflectional symmetry about the horizontal axis, modes (i), (ii), (v), and (vii) can be used (see subsection 3.1). Modes (i) and (ii) can be used on the center row and the number of arrangements is P(k3, 20). For the remaining four partitions it is sufficient to count the number of arrangements for one section of top or bottom rows. As in the Srot subclass this number is E2(n). Summing over all partitions of n tinted cells across the rows calculates the enumeration: ESref h (n) =

/ P (k , 20) E (k 3

2

k12, k3 2k12 +k3 = n 0 G k3 G 20 0 G k12 G 40

12

).

For the Sref, rot subclass of patterns involving rotational and reflectional symmetry, only modes (ii) and (vii) can be used (see subsection 3.1). Mode (ii) implies that there are S(k3, 20) arrangements for the center row. To calculate the arrangements for the remaining four 2 × 10 sections, define E2S(n) to be the number of arrangements of n tinted cells across two rows such that each row is symmetric. E2S is calculated similarly to E S : 0

E 2S (n) =

/ % S (k ) . i

k1, k2 k1 + k2 = n 0 G ki G 20

i

Summing over the partitions of n across the rows, the enumeration is calculated as: ESref, rot (n) =

/S (k ) E 3

k12, k3 2k12 + k3 = n 0 G k3 G 20 0 G k12 G 40

2S

(k12) .

Complete numeric results of the enumeration of façade patterns in each symmetry subclass are provided in appendix B. 5 Verification This section demonstrates the validity of the adopted performance constraints that are encoded in the grammar. The constraints are pertinent to the adjustment of daylight illuminance at the examined location in Trento, northern Italy, throughout the four seasons. The demonstration exposes the simulation steps and the analysis that had led to provisions I and II of the grammar. Simple façade patterns were tested first, including the patterns with all the windows clear, or tinted, or with consecutive active windows arranged in rows, or in columns, or in a ‘chessboard’ formation. Composite façade patterns were tested afterward, including combinations of the simple façade patterns. A link was determined between pattern configuration and interior illuminance, and general principles applicable to any façade pattern were extracted. The notion of an equivalence class was introduced to designate classes of façade patterns having the same number of active windows and reaching proximate values of interior illuminance independently of pattern configuration. Equivalence classes allow switching from one pattern to another while maintaining a desired level of illuminance in order to satisfy other factors of performance such as thermal comfort or aesthetic preference. Lastly, a predictive model was specified associating coverage ratio and illuminance, and having the capacity to project the performance of any façade pattern during any day of the year. 5.1  Daylight performance with the façade in clear state

The distribution of interior daylight was simulated at the simplest possible condition, with all the windows inactive and the façade in a clear state. The detailed results of this simulation, including the minimum, maximum, and average illuminance values calculated at hourly intervals during four days of the year (winter/summer solstice and spring/fall equinox) in

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Eave(lux)

3000 2000 1000

December

March

June

20:00

19:00

18:00

Eave

17:00

16:00

15:00

14:00

13:00

12:00

11:00

10:00

08:00

09:00

0

September

Figure 3. Average illuminance Eave for the interval 8:00 to 20:00 in Overcast Sky.

Overcast Sky are presented in appendix C. Figure 3 summarizes in a comparative diagram the average illuminance values from this simulation. Based on the results of the simulation, the highest values of illuminance were recorded during the summer and the values decreased during the winter. On 21 December the illuminance value was zero after 17:00 as the sun drops below the horizon. Zero illuminance values also occurred on 21 March after 18:00 and on 21 September after 19:00. The obtained uniformity G1 remained constantly three times lower than the threshold value G1 = 0.5. The uniformity G1 defined by the ratio Emin/Eave captures the smoothness of daylight distribution. The obtained G1 values capture the high density of windows towards the south. Since the east and west elevations are blind and the north elevation has only a limited number of windows, the north windows cannot balance the light intensity of the south windows, which are always exposed to direct sunlight. In the tridimensional diagram of figure 4, the illuminance values in lux that correspond to the south façade are higher and they are decreasing towards the north façade. Exceptions apply locally at values corresponding to the north windows, where the illuminance distribution is slightly higher.

ce

ista n

D

E(lux)

North

to

South ) (m

(m)

m

....

roo

.....

ng

of r

oom

Le

Wid th

th

of

e to

)

tanc

(m

E(lux)

....

.... .

Dis

(m)

(lux)

Figure 4. [In color online.] Tridimensional diagram of illuminance distribution for the interior of the prototype.

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5.2  Daylight with the façade in various active configurations

Proper management of the façade permits the adjustment of the incoming daylight reaching an interior work plane. The activation of a horizontal zone of windows causes a corresponding “shaded zone” in the house interior. But what would be the effect of a more complex façade pattern composed of dispersed windows on and off, and how could we always ascertain the appropriate number and distribution of active windows to obtain illuminance values that are above the threshold? To examine these questions a limited number of façade patterns were tested during specific days. These tests helped to establish a link between coverage ratio a and illuminance Eave, where coverage ratio a corresponds to the ratio of the number n of active windows versus the total number of windows (a = n/100). The patterns included linear arrangements (rows or columns) of active windows. The most critical lighting condition occurred in 21 June at 13:00 when illuminance reached its highest, during the summer equinox. 5.2.1  Rows The tested façade patterns include ten patterns obtained by switching on or off various configurations of window rows and examining how they affect the distribution of interior daylight. During the tests the north widows remained at state off and their transmittance was set to 62%. The transmittance values are included in table 3, and diagrams of the simulations appear in Figure 5. Windows at state off appear as white squares and windows at state on as grey squares. The simulations model the conditions of 21 June at 13:00 in Trento, Italy. The illuminance values (minimum, maximum, average), the uniformity value (G1) and the average daylight factor (Dave) are simulated next for the same ten façade patterns. The values are calculated for a plane placed 0.75 m above the floor and in parallel to it. Table 4 summarizes the results obtained. Figure 6 offers a comparative presentation of the obtained illuminance levels. Table 3. Transmittance values for various rows of the windows south façade. Line

Pattern 1

2

3

4

5

6

7

8

9

10

Skylight transmittance 1 (%) 2

62

3.5

3.5

3.5

3.5

3.5

3.5

3.5

3.5

62

Windows transmittance (%)

62

3.5

62

3.5

3.5

3.5

62

62

62

3.5

2

62

3.5

62

3.5

62

3.5

3

62

62

3.5

3.5

3.5

62

0.6

0.8

0.8

0.8

0.6

0.6

1

0

Coverage ratio (a)

1

0.6

0.4

Table 4. Illuminance values (minimum, maximum, average), uniformity value (G1), and average daylight factor (Dave) for a plane placed 0.75 m above the floor, for the ten patterns on 21 June at 13:00. Pattern Emax (lux) Emin (lux) Eave (lux) G1 Dave

1

2

3

4

5

6

7

8

9

10

4880 204 1400 0.15 7.2

1440 12 159 0.075 0.82

4340 180 1080 0.17 5.6

2740 102 572 0.18 3

1470 44 228 0.19 1.18

2520 65 496 0.13 2.6

2120 86 679 0.13 3.5

4160 153 1020 0.15 5.3

2400 128 768 0.17 4

1510 41 593 0.07 3.06

Pattern 7

Pattern 8

Pattern 9

Pattern 10

Pattern 2

Pattern 3

Pattern 4

Pattern 5

Figure 5. [In color online.] Comparative presentation of the isolux diagrams for ten distinct façade patterns involving active windows arranged in rows.

Pattern 6

Pattern 1

South

North

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5000

Maximum

E(lux)

4000

Minimum Average

3000 2000 1000 0 1

2

3

4

5

6

7

Pattern

8

9

10

Figure 6. Comparative diagram of illuminance E for the specified interior work plane.

Table 4 and figure 6 demonstrate that the highest illuminance value is achieved in the first configuration, where all the windows are at state off. The lowest value is achieved in the second configuration, where all the windows are at state on. Variation in the number and distribution of active windows causes variation in daylight distribution. This is captured by the fluctuation in the uniformity G1 and average illuminance Eave values. Alteration in the combinations of active window rows affects interior daylight drastically. Long rows of tinted windows cast long linear shadows disrupting smooth daylight distribution. This result was encoded by provision II. 5.2.2  Columns This class of simulations shows how various vertical configurations of active windows (columns) affect the distribution of interior daylight. Figure 7 offers a comparative presentation of the levels of illuminance and the uniformity G1 for the simulations of figure 8. Figure 8 includes diagrams for eight façade patterns. A ‘chessboard’ pattern was simulated last in order to be compared with the simpler patterns The simulations model the conditions of 21 June at 13:00 in Trento, Italy. The diagrams of figure 8 reveal that the variance in illuminance, average daylight factor, and uniformity G1 depends on the number of active windows. Configurations with the same number of active windows yield proximate values despite pattern dissimilarities. For example, patterns 1 and 8 yield proximate values of illuminance, average daylight factor, and uniformity G1, despite pattern dissimilarity. The same is true for patterns 6 and 7. 6000

(a)

4000 2000

Emin

0

00:14 G1

Illuminance (lux)

00:21 Emax

1

Eave 2

3

4 5 Pattern

6

7

00:07 00:00

8

(b)

1

2

3

4

5 6 Pattern

7

8

Figure 7. Minimum, maximum, and average illuminance (a) and uniformity G1 (b) for the same eight patterns.

5.2.3  Composite patterns Additional simulations modeling different hours and days of the year demonstrate whether the illuminance, the average daylight factor, and the uniformity G1 values remain relevant under a broader spectrum of conditions. The comparison of results for patterns 1 and 8 configuration offered a basis for generalizing the conclusions on illuminance and on whether two distinct

pattern 6

pattern 7

pattern 8

pattern 2

pattern 3

pattern 4

Figure 8. [In color online.] Comparative presentation of the isolux diagrams and tridimensional diagrams for eight façade patterns, involving active windows arranged in columns.

pattern 5

pattern 1

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Table 5. Interior daylight conditions. 10:00

16:00

pattern 1

pattern 8

pattern 1

pattern 8

21 December Emax (lux) Emin (lux) Eave (lux) G1 Dave

650 27 199 0.13 4.4

679 28 197 0.14 4.3

273 83 10 0.12 4.3

285 83 11 0.13 4.3

21 March Emax (lux) Emin (lux) Eave (lux) G1 Dave

1590 67 486 0.14 4.3

1670 68 482 0.14 4.3

1300 54 398 0.14 4.3

1360 54 395 0.14 4.3

21 June Emax (lux) Emin (lux) Eave (lux) G1 Dave

2060 83 623 0.13 4.3

2120 86 617 0.14 4.3

2400 99 730 0.14 4.3

2500 101 724 0.14 4.3

21 September Emax (lux) Emin (lux) Eave (lux) G1 Dave

1340 56 408 0.14 4.3

1400 57 404 0.14 4.3

1630 68 495 0.14 4.3

1690 68 490 0.14 4.3

patterns can yield the same level of illuminance performance. The interior daylight conditions were monitored in two daytime moments, at 10:00 and 16:00 on 21 December, 21 March, 21 June, and 21 September (table 5). The specific daytimes were selected because of their dissimilarity in solar radiation. The results of table 5 establish that the performance of two distinct façade patterns can be invariable throughout the year. Hence, a façade pattern can be modified from one configuration to another while maintaining constant levels of interior illuminance. Next it was determined whether any two distinct patterns with the same coverage ratio a could yield invariable illuminance values. If performance and coverage ratio were analogous, then the visual configurations could vary while retaining a constant coverage ratio a. This result would establish that façade pattern generation could follow a range of generative rules while satisfying any preset value of illuminance, average daylight factor, and uniformity G1. Figure 9 presents three combinations of patterns 1 and 8. These composite patterns are formed by substituting a number of active windows arranged in columns with an equal number of active windows arranged in chessboard formation. Testing a limited number of composite patterns was sufficient to generalize the results. The tables and diagrams of figure 9 present the results for 21 June at 13:00. Variation in daytime or season does not affect illuminance, average daylight factor, or uniformity G1 under constant coverage ratio conditions.

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Pattern 1

Pattern 8

Composite pattern 1

Composite pattern 2

Composite pattern 3

Figure 9. [In color online.] Patterns 1 and 8 appear in the top row. Three composite patterns appear in the left column. A comparison of results, including tridimensional diagrams, appears on the right.

5.2.4  Equivalence classes In Overcast Sky the patterns 1 and 8 and their three composites with constant coverage ratio a, reach proximate values of illuminance (minimum, maximum, average), average daylight factor, and uniformity G1. These results are presented in figure 10 and table 6. 3500 Pattern 1

3300 Illuminance (lux)

2500

8

2000 1500

Composite 1

1000

Composite 2

500 0

Composite 3

Emax (lux)

Emin (lux)

Eave (lux)

Figure 10. Graph of minimum, maximum, and average illuminance, uniformity G1, and daylight factor values for patterns 1, 8, and their three composites, in Overcast Sky.

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Table 6. Minimum, maximum, and average illuminance, uniformity G1, and daylight factor values for patterns 1, 8, and their three composites, in Overcast Sky. Pattern Emax (lux) Emin (lux) Eave (lux) G1 Dave

1

8

composite 1

composite 2

composite 3

2780 113 840 0.14 4.3

2850 115 833 0.14 4.3

2850 110 811 0.14 4.2

2870 113 802 0.14 4.1

3090 112 785 0.14 4.1

Patterns with the same total number of windows at state on yielding a specific value of illuminance belong to the same equivalence class. This provides an option of switching from one configuration to another while maintaining a desired coverage ratio a, in order to satisfy other factors related to aesthetics or performance. 5.3  Determining the desired coverage ratio

The option of modifying a façade pattern within an equivalence class based on coverage ratio requires determining what the desired coverage ratio is, for every daylight condition of the year. A predictive model of this kind is obtainable. The model associates coverage ratio a and daylight illuminance Eave during various time intervals for each day of the year in Overcast Sky. A model for Clear Sky is specified in appendix D. Eleven base configurations were tested, including the two marginal conditions with the façade clear and tinted. Table 7 shows the number n of active windows for each configuration and the corresponding value in lux. Figure 11 depicts the association between Eave and coverage ratio a. The simulations model the conditions of winter solstice on 21 December at 13:00. Table 7. Association of Eave and cover­ age ratio a for 21 December at 13:00 in Overcast Sky.

a 

n

a

extreme a mixed 7th vertical 3rd vertical 8th vertical 1st verrtical 6th vertical 5th vertical 2nd vertical 4th vertical extreme a

0 40 45 50 50 50 55 60 70 75 100

0.00 0.40 0.45 0.50 0.50 0.50 0.55 0.60 0.70 0.75 1.00

Eave (lux)

Extreme configurations are: clear (first) and fully tinted (last).

497 335 308 305 303 293 286 241 221 188 82

600 500 400 Eave (lux)

0 1 2 3 4 5 6 7 8 9 10

Base configuration

300 200 100 0 0.0

0.2

0.4

0.6 a

0.8

1.0

1.2

Figure 11. Association of Eave and coverage ratio a for 21 December at 13:00 in Overcast Sky.

The interpolation of values from the table in the graph determines an equation that calculates the illuminance value in lux corresponding to a coverage ratio a associated with it. This expression determines the number of active windows yielding a specific illuminance level. It is a linear equation of the form y = an + b, where y represents the lux value

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corresponding to the number n of active windows, with n = 100a (100 is the total number of façade windows). Four expressions calculate the values at 13:00 for solstice and equinox: 21 December: y =- 411.86n + 500.69, 21 March: y =- 839.84n + 1020.4 . 21 June: y =- 1113.1n + 1365.4, 21 September: y =- 848.63n + 1033.1. Table 8. Association of Eave and cover­ age ratio a for 21 March, 21 June, and 21 September at 13:00 in Overcast Sky. Eave (lux)

0 40 45 50 50 50 55 60 70 75 100

0.00 1010 0.40 682 0.45 625 0.50 621 0.50 617 0.50 597 0.55 583 0.60 491 0.70 452 0.75 382 1.00 167

21 June 0 extreme a 1 mixed 2 7th vertical 3 3rd vertical 4 8th vertical 5 1st vertical 6 6th vertical 7 5th vertical 8 2nd vertical 9 4th vertical 10 extreme a

0 40 45 50 50 50 55 60 70 75 100

0.00 1340 0.40 923 0.45 846 0.50 840 0.50 833 0.50 808 0.55 788 0.60 655 0.70 611 0.75 516 1.00 226

21 September 0 extreme a 1 mixed 2 7th vertical 3 3rd vertical 4 8th vertical 5 1st vertical 6 6th vertical 7 5th vertical 8 2nd vertical 9 4th vertical 10 extreme a

0 40 45 50 50 50 55 60 70 75 100

0.00 1020 0.40 693 0.45 635 0.50 631 0.50 624 0.50 607 0.55 591 0.60 499 0.70 459 0.75 387 1.00 169

a

 Extreme configurations are: clear (first) and fully tinted (last).

1200 1000 800 Eave (lux)

21 March 0 extreme a 1 mixed 2 7th vertical 3 3rd vertical 4 8th vertical 5 1st vertical 6 6th vertical 7 5th vertical 8 2nd vertical 9 4th vertical 10 extreme a

600 400 200

(a)

0 1600 1400 1200 1000

Eave (lux)

a

800 600 400 200

(b)

0 1200 1000 800

Eave (lux)

Base n configuration

600 400 200

(c)

0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

a

Figure 12. Association of Eave and coverage ratio a for (a) 21 March, (b) 21 June, and (c) 21 September at 13:00 in Overcast Sky.

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Expressions yielding the y value for every hour of the year can be formed and the required number of active windows can be specified for any condition. Hence, it is possible to determine the required number of active windows for reaching the illuminance threshold and confine the patterns to this threshold. Table 8 and figure 12 capture the association between Eave and coverage ratio a for the remaining days of solstice and equinox at 13:00. The presented predictive model calculates the required number of active windows to reach the value of 500 lux. The error between prediction and simulation is 3–4%, but the error rises to 5–6% for patterns with coverage ratio beyond 50–75%. It is still possible to activate a lower number of windows, thus achieving an Eave higher than 500 lux. Using the inverse process, if the desired illuminance Eave is 500 lux and Eave = y, then reaching 500 lux in Overcast Sky in December requires all windows to be off. This is necessary due to the low levels of sky radiation during December in Trento. In all, the values n ensuring illuminance value of 500 lux during December, March, June, and September, are: 21 December: 21 March: 21 June: 21 September:

y =- 411.86n + 500.69 " n = y/411.86 - 500.69/411.86 " n . 0. y =- 839.84n + 1020.4 " n = y/839.84 - 1020.4/839.84 " n . 62. y =- 1113.1n + 1365.4 " n = y/1113.1 - 1365.4/1113.1 " n . 78. y =- 848.63n + 1033.1 " n = y/848.63 - 1033.1/848.63 " n . 63.

If the number of active windows ensuring the threshold of 500 lux is known, then it is possible to vary the façade configurations without affecting the levels of illuminance. The calculation can be extended—for hourly intervals—over the entire year, and a general database can be obtained determining the required number of active windows to reach the threshold value. The generation of façade patterns halts when the number of active windows reaches the value of 75. This condition was encoded by provision I of the grammar. Table 9 and figure 13 summarize the numbers of active windows n ensuring 500 lux on the 21st day of each month, at 13:00 in Trento, Italy. Table 9. The maximum num­ ber of active windows, n, on the 21st day of each month at 13:00 in Overcast Sky. Month

n

a

80

December January February March April May June July August September October November December

0 18 45 62 72 75 75 75 72 62 45 16 0

0.0 0.18 0.45 0.62 0.72 0.75 0.75 0.75 0.72 0.63 0.45 0.16 0.00

70 60 n (100a)

1 2 3 4 5 6 7 8 9 10 11 12 13

90

50 40 30 20 10 0

0

2

4

6

Month

8

10

12

14

Figure 13. The maximum number of active windows, n, on the 21st day of each month at 13:00 in Overcast Sky. The dotted line is the 75% limit.

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6 Discussion A generative approach in the production of patterns for the principal façade of a prototype house in Trento, northern Italy was presented. The façade is a dynamically controlled solar wall including 100 individually addressable, electrochromic windows 700 mm × 700 mm in size, enabling the precise adjustment of daylight, heat, view, and ventilating air at the house interior, and affecting the way the house is perceived from the public street. After compiling feedback from sensors, statistical climatic data, and ambient data, the control system of the house provides real-time performance evaluation and generates electrochromic patterns on the façade in response to the conditions and the needs of the inhabitants for various combinations of privacy, visibility, and view. The uniqueness of the presented approach lies in the deployment of a shape grammar to configure the state of the dynamic façade equally based on performance and aesthetic criteria. The grammar treats the class of the effective façade patterns as a design language, where the full spectrum of visual and performance attributes of the configurations is taken into account. The increasing cost and scarcity of nonrenewable energy sources promote the use of sustainable principles in the design and operation of buildings. The accumulation of precise knowledge on the association between man and environment, and the availability of new optimization and automation techniques force a reassessment of the energy management methods. But to be adopted, the new techniques need to be integrated in engaging ways into building aesthetics and not just to be efficient. Unfortunately, the acquisition of precise knowledge and control capabilities is rarely accompanied by the required sensitivity to apply them in aesthetically pleasing ways into the built environment. Motivation for this research was to provide an environmentally conscious mode of building an original tectonic vocabulary that is in alignment with technological innovation. An architectural solution was proposed employing generative grammars, AI methods of building control and electroactive materials, which satisfies the environmental requirements of its function and makes elegant architecture out of the provisions needed for their satisfaction. Buildings can become the embodiment of specialized technological innovation in response to given problems. But a sophisticated approach to sustainable architecture should not simply rely on new machinery. It should be able to express unique features related to the environment, the culture, and the context in which it is situated. The prototype house in Trento is an example of environmentally responsible architecture that points to certain visionary technological possibilities without disregarding their impact on the habits of local people. In the context of Trento, the principal façade of a building has a predominantly expressive purpose as the primary interface between interior and exterior. The management by means of a generative grammar of the electrochromic technology that is deployed on the dynamic façade of the prototype acknowledges this purpose by equally addressing performance and aesthetic factors. Façade patterns produced randomly based only on performance would supply adequate daylight while disregarding the aesthetic potential of electrochromic technology. The chosen generative approach both takes full advantage of this potential and is computationally elegant. The grammar is applied dynamically by the intelligent control system of the house to produce façade patterns by linking principles of two-dimensional pattern generation to constraints of daylight adjustment. Three general conditions of operation were determined for the dynamic façade: façade fully inactive, façade active in a ratio equal to 2/4–3/4 of its area, and façade fully active. The presented generative grammar determines the configuration of the façade when 2/4–3/4 of its area is active. This is possible through the application of twelve rules that apply under seven different modes, while satisfying two performative premises. The first premise specifies that in an average luminous day between fifty and seventy-five of the hundred windows need

The dynamic façade pattern grammar

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to be active, in order to achieve interior luminosity levels above the threshold required by Italian law. The second premise specifies that to ensure smooth daylight distribution no four consecutive windows can be concurrently active on the same row. In clouded sky conditions the generative grammar exhibits great flexibility in producing patterns ensuring interior daylight comfort. The façade pattern language extends to 1.285 × 1024 patterns—more than the stars in the observable universe. In clear sky conditions full activation of select façade subareas, leaving others inactive, could allow for optimal daylight conditions to occur locally while heat flow through the inactive façade sections will be still possible. The absence of adequate real building data from experiments characterizing the performance of environmental management systems similar to the one that was presented in this paper dictates that the assessment of the proposed apparatus will be subject of future research, after quantifiable data from the prototype become available. And, yet, it is likely that in the future the use of programmable materials and AI methods of building control will attain a higher degree of influence in the architecture of buildings. In a similar way to how the supply of electricity had profoundly affected architecture at the close of the 19th century, real-time supply of computational power into built environments will gradually transform their aesthetic and physical attributes, giving rise to new conceptions of space. The absorption of this capacity provides an opportunity for producing buildings that are energy saving, environmentally sound, and architecturally rich. The design of the prototype house in Trento is a paradigm of an eloquent application of algorithmic design methods, AI methods of building control, and material engineering research, pointing to original tectonic possibilities without disregarding the consequences of the ongoing transformation in environmental management. Acknowledgments. This paper is dedicated to William J Mitchell (1944–2010), who pioneered multidisciplinary research in design. Thanks are due to Professors Terry W Knight, George N Stiny and Thanos Economou for technical remarks. The research was conducted within the Green Home Alliance between the Mobile Experience Lab at the Massachusetts Institute of Technology and the Fondazione Bruno Kessler in Trento, northern Italy. References Banham R, 1969 The Architecture of the Well-tempered Environment (Architectural Press, London) Graybill W, 2012, Robust, “Goal-directed planning and plan recognition for the sustainable control of homes”, master’s thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA Gugliermetti F, Bisegna F, 2003, “Visual and energy management of electrochromic windows in Mediterranean climates” Building and Environment 38 479–492 Hausler T, Fischer U, Rottmann M, Heckner K H, 2003, “Solar optical properties and daylight potential of electrochromic windows”, paper presented at International Lighting and Colour Conference, 2–5 November, Cape Town, pp 102–106, http://gesimat.de/data/PaperSolOptEC.pdf Klein C, Kaefer G, 2008, “From smart homes to smart cities: opportunities and challenges from an industrial perspective”, in Next Generation Teletraffic and Wired/Wireless Advanced Networking Eds S Balandin, D Moltchanov, Y Koucheryary (Springer, Berlin) page 260 Knight T, 2005, “Creativity • rules”, in Computational and Cognitive Models of Creative Design VI Eds J S Gero, M L Maher, Key Centre of Design Computing and Cognition, University of Sydney, pp 155–174 Lee E S, Di Bartolomeo D L, Klems J H, Yazdanian M, Selkowitz S E, 2006, “Monitored energy performance of electrochromic windows controlled for daylighting and visual comfort”, ASHRAE Transactions, June 24–28, Quebec City, LBNL-58912, http://escholarship.org/uc/item/76z069h7

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