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Hierarchial cooperation in architecture and the mathematical necessity for ornament

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Abstract

The case is made that architectural design needs to be organized hierarchically. A method and formula for doing so is derived based on biology and computer science. Fractal simplicity, in which there is self-similar scaling, replaces the outdated notion of rectangular simplicity. Architectural units on different scales are able to cooperate in an intrinsic manner to achieve an emergent property, which is not present in the individual components. The theory of hierarchical systems explains how to relate different scales to each other. In buildings, the correlation between architectural scales determines whether a structure is perceived as coherent or incoherent, independently of its actual design. This paper gives scientific proof of why ornament is essential to the overall cooperation of architectural forms, thus revising one of the basic tenets of modernist design.

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... High levels of complexity seem to be accepted beter by architects than by the general public, in special for modern architectural styles [25,[30][31][32]. Traditional architectural styles achieved a beter acceptation of complex paterns among the general public [33][34][35][36]. However, some researchers have found a threshold point in complexity above which the visual acceptance was impaired in all cases, irrespective of professions or architectural styles [24,37]; so, the controversy remains open. ...
... This is the most likely explanation for the low rating achieved by visual proposals presented in image set D, where the randomization of the boundaries of the stone baseboards did not follow either coherent or familiar design paterns. Such presentation disorganizes complexity and impairs human comprehension [36]. At the opposite extreme, small scales were removed from façades in image set A, which minimized the complexity of forms. ...
... It enables a lighter and cheaper construction, seting up wide interiors and large external openings, in special on upper loors [54]. Materials and structural subdivisions create architectural scales by themselves that can be intensiied through moderate intervention [36]. Seting these materials together is not, however, enough, but the achievement of a coherent whole via hierarchical and structural organization of the materials is required. ...
... For instance, Brolin (Brolin, 2000) suggests that the visual texture 'composed primarily of small scale details' is the most critical factor to consider when locating a new building within an existing built context. Methods used in architecture to determine scale within a building include massing, where the largest scale is usually defined by an outline of the building itself (Salingaros, 2000b). Elements within the façade such as openings, detail, trim and the material itself will then successively identify smaller scales. ...
... Symmetry is a condition of massing and is manifested through the recurrence of shapes in a regular way, and can help connect elements forming a single element at a greater scale (Salingaros, 2000b). Once formed, this arrangement can be thought of as modular, repeated through the 'economy of thought and action' (Salingaros, 2001) Bentley (Bentley, 1987) suggests that 'richness' can be created through details within the walls that incorporate patterns of material and colour. ...
... Scale is of important characteristics that affect the aesthetic construction properties where constructional elements vary in their sizes. The architect, then, should know how to utilize the construction width using a certain scale or comparing with other neighboring architectural elements [12]. Salingaros has viewed this relation through stating that forming scale in architecture and architectural constructions for any structure, even columns, is clear through graded relations of scales. ...
... These units could be a constructional unit, like constructional space or even the constructional unit (brick and concrete units) The architect Mees Vandro used constructional frame units in a mathematical relation through repeating regular unit that make the final shape more arranged and flexible in use [14] Pillared corridors, as he thinks, represent the pattern frame of the human scale where distance among columns is about 1-5m, close to human scale of movement. Charelson indicated that gathering the various constructional details in a graded from has varied the scale [12] while Ching stated that proportions and size of constructional elements related with constructional tasks could be visual indicators for size and scale of spaces through which space will have scale in element proportion and this is applied on walls and ceilings [1]. The impact of scale on construction is clear through formal properties like repetition, gradation, partitioning and flexibility which are the treatments adopted by the designer in dealing with parts and components of the constructional system. 1) Arabic Mohammedean Type: Prophet mosque is the important example of this type that represents the Arabic type from which most of the Arabic mosques are driven [15] and includes: A.Hypostyle Pillared Type where grid system is adopted using the constructional frame with repeated columns within equal distances (about 3-7m) that correspond the dimensions needed during prayer in order not to have gaps among the columns (according to Sunna). ...
... Hull et al ((Hull IV, 1993) finds that decorative style valued highly by residence, possibly because it creates a sense of identity by distinguishing one place from another. Methods used in architecture to determine scale within a building include massing, where the largest scale is usually defined by an outline of the building itself (Salingaros, 2000b).Elements within the façade such as openings, detail, trim and the material itself will then successively identify smaller scales. Symmetry is a condition of massing and is manifested through the recurrence of shapes in a regular way, and can help connect elements forming a single element at a greater scale (Salingaros, 2000b). ...
... Methods used in architecture to determine scale within a building include massing, where the largest scale is usually defined by an outline of the building itself (Salingaros, 2000b).Elements within the façade such as openings, detail, trim and the material itself will then successively identify smaller scales. Symmetry is a condition of massing and is manifested through the recurrence of shapes in a regular way, and can help connect elements forming a single element at a greater scale (Salingaros, 2000b). Once formed, this arrangement can be thought of as modular, repeated through the 'economy of thought and action' (Salingaros, 2001). ...
... Something similar occurs in the Stockholm Library, where there is little at the scale between the window, blocks, and the width of the building. These buildings show a lack of hierarchy of sizes, something that has been criticised as unnatural in architecture, notably by Salingaros (2000). ...
... So fundamental was this dynamic view of architecture to him that, in a survey of Ruskin's writings on architecture, Unrau (1978) found it convenient to divide the writer's opinions into chapters on ornament viewed at long distance, intermediate distances, and at close range. A modern version of this argument is to be found in Salingaros (2000), where the author reasons that buildings ought to possess features in a scaling hierarchy of sizes, justifying this by likening buildings to complex hierarchical systems found in nature and engineering. Other reasons why hierarchies of sizes are most naturally based on power law, such as equation (1) here, may be found in Salingaros and West (1999). ...
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Old buildings may be easier to read than modern buildings because they possess visual depth. This is the finding of an experiment that analysed building elevations and newspapers looking for a connection between their character and the size – frequency distribution of their component parts. It was found that drawings of older buildings sometimes displayed 1/ f scaling and thus resembled natural scenes, but that this was rarely the case for modern buildings. The same distribution was also found in newspaper pages. We hypothesise that this distribution allows buildings to appear interesting and changeful when approached from afar in the same way that it makes newspapers easy to read over a range of distances, on a newsstand, over a shoulder, and so forth.
... This is a straightforward result from fractal fluency, since a fractal will incorporate several levels of scale into itself. When working with buildings (say, up to six stories), the number of well-defined scales from the overall size down to the architectural detail is somewhere around seven if we use the most common traditional scaling factor of approximately 3 [131]. ...
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... Although more challenging, incorporating fractal patterns into the built environment will be more impactful. The call for fractal architecture is not new and today's advocates [18][19][20][21][22][23] are often inspired by Alexander's work. Yet the need for fractal designs-whether for the interior or exterior of individual buildings, or for the arrangement of multiple buildings-is escalating. ...
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Fractal objects are prevalent in natural scenery. Their repetition of patterns at increasingly fine magnifications creates a rich complexity. Fractals displaying mid-range complexity are the most common and include trees, clouds, and mountains. The “fractal fluency” model states that human vision has adapted to process these mid-range fractals with ease. I will first discuss fractal fluency and demonstrate how it enhances the observer’s visual capabilities by focusing on experiments that have important practical consequences for improving the built environment. These enhanced capabilities generate an aesthetic experience and physiological stress reduction. I will discuss strategies for integrating fractals into building designs to induce positive impacts on the observer. Examples include fractal solar panels, fractal window shades, and fractal floor patterns. These applications of fractal fluency represent a fundamental and potentially impactful form of salutogenesis.
... Ornaments can help to relate different-scale regions to each other. It can also embody a level of scale itself in order to allow people to relate to an object or building' (Salingaros, 2000). Defining transition zones: an ornament is often found in areas that attract attention, whether used to disguise particular parts or to amplify specific features. ...
... Each architectural construct includes several geometrical relationships, through which styles and affiliations can be distinguished. And this study deals with shape morphology, correlations and topological sequence [7], as follows: ...
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All buildings are characterized by possessing a set of architecturalelements and details that are most important in giving the characteristic ofthe architecture as a style, where these details and architectural elementshave configurations structurally different and this difference in structuralismdistinguishes the form of another where any architectural configuration ischaracterized whether to indicate functional aspects or aesthetic formalaspects that has privet and special style which is consistent with thegeographical or historical background to this style. This study will focus onone of the architectural configurations of the gates, by testing a sample ofthese architectural configurations from different time periods such asAssyrian style gate, Romanian style gate and Babylonian style gate ... Etc.as a sample for analyses. This study consist of three stages, the first one isthe theoretical framework for analysis and the formation of gates ingeneral, the second stage is a test of the sample of gates by analyzing anddismantling of components to the basic elements of form and then encodedin digital form and make it a matrix , finally the last stage .It is the processof restructuring elements (Re-forming elements) by using the probabilitiesof the matrix to produce new patterns which has structural propertiessimilar to the original elements.
... For repetition in architectural composition and its effects on the form's visual structure, it may be indicated in various appearances. That can appear through the building's structural elements, architectural elements such as opening system (doors and windows), or the ornamental decorations which repeated in geometrically arranged chains of shapes, and all that emphasizes a clear image of the whole composition's parts (Salingaros, 2000). ...
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This research is a study on the facade of shophouses in George Town, Penang and how they are affected by the installation of modern building services elements. The unplanned insertion of their equipment distorts of the visual characteristics of the shophouses facade. Thus, the research's primary objective is to explore the necessary means to achieve integration between these two architectural systems namely, the authenticity of the facade and the positive inclusion of the services elements. Visual analysis as a measurement tool is the key for linking the two sides of its equation, by adopting qualitative exploratory designed methodology, as it is adequate to fulfill the research objectives, lines with inquiries and fitting for the scope of research. Theoretical and purposeful sampling were utilized to select the six known styles of the shophouses facade in George Town, and also to choose from the six conservation areas in George Town World Heritage Site (GTWHS). Framework analysis, as well as content analysis techniques, was used to analyze the different types of the collected data. Various kinds of findings have resulted from the analysis: Visual characteristics of each style of the shophouses facade in George Town based on principles of design analysis. Also, the impact of the modern building services on the shophouses facade, as some types of building services installations have more visual impact on the shophouse facade than others. The highest impact is the outdoor air-conditioning units, commercial signboards, and shading parts, which affect more than 60% of the visual characteristics of the shophouse facade. The study identified the transformation of the relation type and visual integration level between building services and the facade in the original and the current state of the shophouse. Finally, the primary outcome of the study is concluding improvements of the guidelines for the building facade components that related to the building services installations. The refined recommendations included original colors paintings, traditional shapes mimicking, and precise positioning for any new installations. These recommendations can be adopted for the optimum visual integration for conserving heritage shophouses in future.
... This tool can enhance the interaction and shared understanding among team members and can assist in the efficient coordination of design activities [3]. The information contained in the patterns can provide critical guidance to urban designers on how to make appropriate decisions about the design task at different levels of scale and detail [23,24]. ...
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Urban design is a complex problem-solving activity that commonly requires the aid of a variety of methods to support the process and enhance the quality of the outcomes. How to help designers with suitable methods to deal with ill-defined urban problems constitutes a major challenge in the urban design domain. In this regard, the use of urban design patterns is considered as a method that can contribute to urban design problem-solving. However, this tool was never investigated to understand its role in the task-related activities that take place during the design process by designers working in a team, and its influence on the creativity of the final design outcome as perceived by urban designers and students. Therefore, an empirical research based on a controlled experiment was carried out to explore the aid provided by design patterns during the conceptual stages of the process. Sixty-three master students working in teams of three were assigned a set of patterns to solve an urban design task. They were requested to use this material to produce as many creative conceptual solutions as possible. At the end of the sessions, they evaluated the creativity of their outcomes, and they completed a questionnaire about the aid afforded by the patterns. The solutions were also assessed by two independent urban designers. The study contributed to gain a better insight into the main design activities derived from the use of patterns as problem-solving tools and to unveil their contribution to urban design. The aid provided by the urban patterns was mainly concerned with task-related activities, and thereafter with team interactions. Overall, the use of patterns was seen to enhance the functionality of the design. Implications for design practice and design education are discussed.
... Each architectural construct includes several geometrical relationships, through which styles and affiliations can be distinguished. And this study deals with shape morphology, correlations and topological sequence [7], as follows: ...
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All buildings are characterized by possessing a set of architectural elements and details that are most important in giving the characteristic of the architecture as a style, where these details and architectural elements have configurations structurally different and this difference in structuralism distinguishes the form of another where any architectural configuration is characterized whether to indicate functional aspects or aesthetic formal aspects that has privet and special style which is consistent with the geographical or historical background to this style. This study will focus on one of the architectural configurations of the gates, by testing a sample of these architectural configurations from different time periods such as Assyrian style gate, Romanian style gate and Babylonian style gate ... Etc. as a sample for analyses. This study consist of three stages, the first one is the theoretical framework for analysis and the formation of gates in general, the second stage is a test of the sample of gates by analyzing and dismantling of components to the basic elements of form and then encoded in digital form and make it a matrix , finally the last stage .It is the process of restructuring elements (Re-forming elements) by using the probabilities of the matrix to produce new patterns which has structural properties similar to the original elements.
... This tool can enhance the interaction and shared understanding among team members and can assist in the efficient coordination of design activities [3]. The information contained in the patterns can provide critical guidance to urban designers into how to make appropriate decisions about the design task at different levels of scale and detail [23,24]. ...
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Urban design is a complex problem-solving activity that commonly requires the aid of a variety of methods to support the process and enhance the quality of the outcomes. How to help designers with adequate methods to deal with ill-defined urban problems constitutes a major challenge in the urban design domain. In this regard, the use of urban design patterns is considered as a method that can contribute to urban design problem-solving. However, this tool was never investigated to understand its role in the task-related activities that take place during the design process by designers working in team, and its effect on the creativity of the final design outcome as perceived by urban designers and students. Therefore, an empirical research based on a controlled experiment was carried out to explore the aid provided by design patterns during the conceptual stages of the process. The study contributed to gain a better insight into the main design activities derived from the use of patterns as problem-solving tools, and to unveil their contribution to urban design. Implications for design practice and design education are discussed.
... Advocates of fractal architecture (Bovill, 1995;Joye, 2007;Salingaros, 1999;Salingaros, 2002;Salingaros, 2006;Salingaros & West, 1999) are often inspired by the work of the architect Christopher Alexander who was a critic of conventional architecture and its lack of reflection of human aspirations and needs (Alexander, 1975). Yet, although fractals appear in the patterns generated by the skylines (Stamps, 2002) and boundaries (Batty & Longley, 1994) of cities, fractal buildings remain conspicuously absent. ...
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... Pattern representations also provide explanations about how they relate to other patterns, and offer solution examples through photographs, diagrams, and text information. The principles represented by the patterns can advice designers how to take appropriate decisions at different levels of scale and detail (Salingaros 1999;2000a). ...
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... The largest scale establishes relations between distant elements in a manner that renders their arrangement ordered (rather than random). The relationship between these two scales contributes to the positive perception of a building's architecture (Mehrabian, 1976;Salingaros, 2000). Finally, the overall harmony links all the intermediate scales together through techniques that employ symmetries common in traditional design and architectures. ...
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... Consequently, the fractal geometry helps to create mixed, dynamic and personalized façades, Salingaros [11] In order to come up with a coherent façade, the hierarchical subdivision of the architectural scales must be clearly defined, and the small units should be coordinated with the large ones. Basing on empirical researches of Christopher Alexander, Salingaros [12] proposes a specific ratio for the consecutive scales in the hierarchy, given approximately by the constant e ≈ 2.7. This constant constitutes the base of natural logarithms and arises in the most successful and psychologically comfortable buildings. ...
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... This type of structure often occurs in natural landscape formations, such as mountains and valleys. Proponents of more organic, humanistic architecture have argued convincingly in favour of multi-scale architectural design (Alexander, 1979; Salingaros, 2000). ...
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... Research into complex systems has been stimulated in recent years by studies of chaos. One outcome of this research has been a greater interest in the study of complexity in its own right (Simon, 1996, p.181;Salingaros, 1997) including the study of complex systems that are ordered and not at all chaotic. It is proposed that CAD models, at least as we currently understand them, belong in the latter group, in both: a) design complexity, since order is normally an objective of design; and b) CAD complexity, since the CAD model is an embodiment of some form of order. ...
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... (1996, p. 183) Research into complex systems has been stimulated in recent years by studies of chaos. One outcome of this research has been a greater interest in the study of complexity in its own right (Simon 1996, p.181;Salingaros 2000), including the study of ordered complex systems. ...
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... An objectively measurable structural quality of nature is the selfsimilarity observed across different size scales. This special quality of scale invariance can be identified and quantified by a parameter called the fractal dimension, D. Fractal geometry has been used successfully to describe many common natural patterns (Gouyet 1996; Mandelbrot 1983) and also man-made patterns in art (Frame and Mandelbrot 2002; Mandelbrot 1983), architecture (Bovill 1995; Goldberger 1996; Salingaros 2000 ), landscape design (Van Tonder et al 2002), and archaeology (Brown et al 2005). The powerful Investigations of human EEG response to viewing fractal patterns Abstract. ...
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Abstract— The concept of Scaling has received attention in many different fields, including the fields (fractional geometry, biology, physics, shape, function, architecture). The Scaling is considered one of the shape characteristics of the forms in nature and has a fixed hierarchical scaling coefficient (2.7). The previous knowledge pointed to its importance because it is related to the degree of cohesion of the formations of these forms and the degree of human perception of them. But, there is a need to study the scaling of the shape aspect of the architectural facades in general and the facades of the Mosul architecture in particular.Thus, the research problem is defined as "there is a need to determine the scaling within the shapes in architecture in general and in the facades of mosul architecture in particular." The research have a basic hypothesis that states "The traditional architecture facades have number of scaling more than modern architecture facades"and secondary hypothesis stating "The scaling of traditional Mosul housing are more numerous and coherent and closer to nature than the scaling in modern housing." Thus, the research used the quantitative approach consisting of three stages, the first stage is creating a theoretical framework on the characteristic of the scaling within the shapes in architecture, and the second stage is determining the method of measurement and method of data analysis, where 9 samples were selected for facades of housing in Mosul city distributed within four Periods, each period include three samples.The third stage was to discuss the results and determine the conclusions. The research found that the houses facades of traditional period focused on small scales while the transitional period focused on the big scales. The modern and contemporary period was characterized by a balance between those scales, as well as the houses of the transitional and modern period were characterized by the small number of Scaling in its facades unlike the contemporary and traditional heritage period. Keywords— Scaling, Shape dimension, Hierarchical scaling coefficient, ideal number of scale, Mosulian housing
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Hierarchical Scaling is one of the Architectural Engineering principles. this principle is determined by the apparent scales within the basic elements of architectural design and the nature of the hierarchy in its dimensions. This principle was discussed in previous studies in terms of its relation to nature, its types in different levels of architecture and city.The property of the hierarchical scale was discussed in the previous knowledge in terms of its relation to nature, its types and its general bases at the level of architecture and city. Therefore, the need to study this principle appeared at the level of house layout through studying its space syntax in different time periods and its reflection on several aspects.Thus, the research problem was determined by "the need to explore the levels of the hierarchical scale within the space syntax of the houses especially Mosulian house, and its variation within different time periods." The research adopted the quantitative approach consisting of three steps, after introducing general knowledge base of the concept of the hierarchical scale and the studies that dealt with it in architecture, first: building a theoretical framework on the vocabulary associated with measuring the spatial hierarchical scale within the space syntax, second: conducting a practical study on an elected group of Mosulian houses within four periods, (20 houses distributed through, traditional, traditional-heritage, transitional and contemporary),third: analysis of results and identification of conclusions.The research found that the Mosulian houses within (the traditional -heritage period) was distinguished by its having a deep spatial hierarchical scale, unlike the Mosulian houses (with a transitional period) that entails many indicators at the level of the social dimension in achieving social isolation. Keywords— hierarchical scale, space syntax, Mosulian houses .
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Hierarchical Scaling is one of the Architectural Engineering principles. this principle isdetermined by the apparent scales within the basic elements of architectural design and the nature of thehierarchy in its dimensions. This principle was discussed in previous studies in terms of its relation tonature, its types in different levels of architecture and city.The property of the hierarchical scale wasdiscussed in the previous knowledge in terms of its relation to nature, its types and its general bases at thelevel of architecture and city. Therefore, the need to study this principle appeared at the level of house layoutthrough studying its space syntax in different time periods and its reflection on several aspects.Thus, theresearch problem was determined by "the need to explore the levels of the hierarchical scale within thespace syntax of the houses especially Mosulian house, and its variation within different time periods."The research adopted the quantitative approach consisting of three steps, after introducing generalknowledge base of the concept of the hierarchical scale and the studies that dealt with it in architecture, first:building a theoretical framework on the vocabulary associated with measuring the spatial hierarchical scalewithin the space syntax, second: conducting a practical study on an elected group of Mosulian houses withinfour periods, (20 houses distributed through, traditional, traditional-heritage, transitional andcontemporary),third: analysis of results and identification of conclusions.The research found that theMosulian houses within (the traditional -heritage period) was distinguished by its having a deep spatialhierarchical scale, unlike the Mosulian houses (with a transitional period) that entails many indicators at thelevel of the social dimension in achieving social isolation.
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This research presents an analytical tool to quantitatively assess and compare the aesthetic value of facades, by focusing on their formal order (O) and complexity (C). A total of fifteen facades of the colonial building heritage (19th–20th centuries) of Algiers old city center were aesthetically assessed and compared. The method uses Birkhoff’s aesthetic measure and calculates the aesthetic value for each facade. These values were ranked and compared using statistical analysis. The results lead to classify the evaluated facades into four sets according to the importance of their aesthetic values: very high, high, average and low. The results can serve to elaborate a guideline of design principles to help operating on this site. However, this research shows some limitations and suggests the need for further research into aesthetic preference. A valuation survey is necessary to improve this method and to test Birkhoff’s formula empirically.
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Aesthetics, in essence, is a mathematical phenomenon. The ancient Pythagoreans were not the only ones who explicitly held this opinion. Others described the enjoyment of art as the unconscious calculations of numerical proportions between time intervals or between spatial distances in the case of visual art or architecture. Philosophers and Art Critics have been widely debating about the nature of beauty and other aesthetic concepts for long times. Although the debates may offer important insights into the aesthetic questions and provide useful perspectives, they do not provide a tool for measuring Aesthetics. One often cannot confirm why an object is beautiful or not. Aesthetics is commonly approached as a qualitative issue. The architectural aesthetics assessment is suffering the diversity of different philosophical approaches concerning aesthetics and the vagueness of its related terminologies. Moreover, the subjective biases of the evaluator penetrate the credibility of architectural aesthetic assessment. The Quantitative Aesthetics is presented as a complementary realm for the existing qualitative aesthetic approaches for more refine architectural aesthetic assessment. The Across-Cultural aesthetics is the departure point in this research for an objectively based aesthetic assessment. The universal agreement on the beauty of some works of art and architecture emphasizes the existence of some universal laws that is innately manipulated in our cognitive machinery. Some theorists searched this objective beauty and formed different models to evaluate the objective aesthetics quantitatively. The research presents some of quantitative measures, applies, analyses, and criticizes their resultants. The researched quantitative measures are: Birkhoff's Edited Measure for Architectural Aesthetics, Salingaros Thermodynamic Measure, Levels of scale, and Scale Coherence Factor. The research hypothesizes the usefulness and the variability of these measures by applying them on different buildings covering diverse architectural aesthetic probabilities.
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