Artificial Buildings: Safety, Complexity and a Quantifiable Measure of Beauty
AA RTIFICIAL B UILDINGS : S
AFETY , C
OMPLEXITY AND A Q UANTIFIABLE M EASURE OF B EAUTY
Arash Mehrjou ∗ A BSTRACT
A place to live is one of the most crucial necessities for all living organisms since the advent of lifeon planet Earth. The nature of homes has changed considerably over time. At the very early stages,human begins lived in natural places such as caves. Later on, they started to use their intelligence tobuild places with special purposes. Nowadays, modern technologies such as robotics and artificialintelligence have made their ways into the construction process and opened up a whole new areaof opportunities and concerns that may be of interest to both technologists and philosophers. Inthis article, I review the evolution of buildings from fully natural to fully artificial and discussphilosophical thoughts that a fully automated construction technology may raise. I elaborate on thesafety concerns of a fully automated architectural process. Then, I’ll borrow Kolmogorov complexityfrom algorithmic information theory to define a complexity measure for buildings. The proposedmeasure is then used to provide a quantifiable measure of beauty. K eywords Architecture · Artificial Intelligence · Philosophy
The concept of living organisms often comes with a property that determines a place where an organism lives. In thisarticle, my focus will be on the organisms known as human beings since the very early years of their appearance onEarth. I use the general term “people” for all human beings over the history of their existence on Earth and the generalterm “building” for their living places. This article concerns one aspect of buildings which I call “Naturalness”. Eventhough this term may have intuitive meaning, the exact definition requires further elaboration. It is intuitively clearthat buildings were more natural initially and turned into more artificial products as a result of advances in civilization.In this article, first, the historical evolution of buildings is presented with a focus on the naturalness aspect of them.Then, the use of modern automated technologies in the construction process is introduced followed by philosophicalimplications that the combination of architecture and automation can bring up.
Looking for natural buildings, one can refer to caves as one of the first residential places which were found not built byhumans. One example of such caves is Lascaux cave in Montignac France. This cave can be seen as a natural buildingthat is supposedly a place of the congregation which is also decorated by ancient paintings. Regardless of the purposeof this place, it is important to notice that this place was found not made by men or their skills. Even though caves areobvious examples of natural buildings, it is difficult to define natural buildings in contemporary understanding of theconstruction technology. Hence, a deeper investigation into the concepts of natural and artificial buildings is required.It is useful to agree on the definition of nature in the first place. Ralph Waldo Emerson (May 25, 1803 – April 27,1882), an American philosopher published an essay on “Nature” in which he stated “Whatever is not me is consideredas nature” [Emerson and Cameron, 1940]. There is also a common understanding that “The nature is what is untouchedby men”. Emerson provided an example of a house and the role of “will” in its construction. The “will” can be seen asthe design intention of the architect which is in contrast with the unconscious intent of the nature that constructs placessuch as caves. ∗ Department of Computer Science, ETH Zürich & Max Planck Institute for Intelligent Systems: [email protected] a r X i v : . [ c s . OH ] J un a) Charles-Dominique-Joseph Eisen’s drawing for Marc-Antoine Laugier’s Essai sur l’architecture (b) The frontispiece of Marc-Antoine Laugier’s Essai surl’architecture Figure 1: Illustrations of early examples of natural buildingsA possible historical next step after caves is sod houses which were used in various places such as in Nebraska, theU.S. in 18’s. In sod houses, the grass and the soil beneath it which is held together by the grass’s roots are used toconstruct walls. Even though these houses are built by humans, given our current idea of buildings, these houses can beconsidered as natural constructs since they were built with natural untouched materials.The tension between the concepts of natural and artificial buildings can be traced back to artistic illustrations, forinstance, in the paintings by Charles-Dominique-Joseph Eisen (17 August 1720 – 4 January 1778) for Marc-AntoineLaugier (January 22, 1713 – April 5, 1769) who is considered as the first architectural philosopher – see Figure 1.Those paintings illustrate an architect as one who willfully changes trees and other natural objects to consciously buildsomething like a roof. Although those paintings show primitive man-made constructs, they are still inspired by naturethat shows a smooth transition from natural buildings to the modern concept of artificial buildings. Another interestingidea in line with the interaction between a building and nature was
Tree Shaping proposed by the German landscapearchitect Arthur Wiechula (January 20, 1867 – 1941) who guided the branches of a tree to form a target design such asa building or a dance stage.In the early th century, industrialization took off and started to impact architecture. The new doctrine followed thelogic of efficient satisfaction of a goal, for example, the rational way that a meal is prepared in a kitchen efficiently ascan be seen in a couple of Margarete Schütte-Lihotzky’s works (January 23, 1897, January 18, 2000) – see Figure 2.Some ideas of that period especially in Hugo Häring’s (11 May 1882 – 17 May 1958) works, were inspired by thehuman body and called Organic Architecture that saw elements of the house as human organs that are in coordinationwith each other.In line with the transition to industrialized fabrication, Konrad Wachsmann (May 16, 1901 – November 25, 1980)took the machines as expressions for automation with feedback all the way from products to materials and proposed auniversal building method that integrates the designer, the architect, and the construction engineers [Wachsmann, 1961].Considering the important role of humans as the residents of houses in the design of buildings, Cedric Price (11September 1934 – 10 August 2003) proposed interactive buildings that reconfigure in response to the behavior of theirusers. One futuristic idea was implemented by computer pioneer John Frazer in
The Generator Project where thebuilding was assumed as an electrical circuit whose elements relocate according to a written code and within a feedbackloop that integrates the behavior of the user and the environment – see Figure 3. In summary, John Frazer consideredarchitecture as a form of artificial life that evolved in coordination with its surrounding environment[Frazer, 1995]. Photo from Photo from a) Entrance view (b) Inside view Figure 2: Two view of the kitchen designed by Margarete Schütte-Lihotzky for architect Ernst May’s social housingproject “New Frankfurt” in Frankfurt The development of 3D animation software in the 90s and early 2000s decade allowed architects to visualize theirvisionary ideas. I can exemplify “Embryological House” by Greg Lynn (1964,) and complex design forms by MichaelHansmeyer (1973,) which were later 3D printed to become real objects. The fast progress in the development of 3Ddesign softwares gave architects the unique opportunity to come up with extremely complex designs. However, theimplementation of the designs as real-world objects was not straightforward.The serialized automation line started in 1913 by the Ford assembly line. It took almost thirty years that such serializedautomation paved its way to architecture in a project called “Hausbaumaschine” by a German architect Ernst Neufert(March 1900 – February 1986) who proposed the standardization of the construction process of buildings – see Figure 4.Such a process was highly needed to contribute to the speed and efficiency of rebuilding the German cities during andafter World War II.The robots were introduced to the serial industrial production in the 60s by Ford and General Motors. It took twentymore years when the first attempts were made to use robots for building houses in Japanese company Goyo andPenta-Ocean Construction in 1998 in Tokyo.Nowadays, robots are used in many stages of the construction process. In recent advances, robotic technology is used tobridge the gap between the abstract 3D computer designs and real-world buildings. In the next section, I’ll focus on acouple of technologies developed in one of the leading research groups in Europe that introduce state-of-the-art robotictechnology to different stages of the architectural design and construction. Most of the described projects in the nextsection are chosen from a talk given by Dr. Hannes Mayer in the seminar “Images of an Artificial” in Fall 2019 at ETHZürich.
To exemplify uses of robotics and artificial intelligence in architecture, I discuss some of the technologies developedin Gramazio Kohler Research group from ETH Zürich as one of the world’s leading groups in using robotic andcomputational methods in architecture.Gramazio Kohler Research group started a branch in digital fabrication in 2005 and chose industrial robots as a universaltool to externalize digital design into the real world. The initial projects done by this group, even though very simple,were good illustrations of the philosophy they follow. For example, “The Programmed Wall” is a robot-constructedwall by stacking the bricks with a programmed code that controls the location and angle of the bricks . Such a simple Photos from https://gramaziokohler.arch.ethz.ch/web/e/lehre/81.html Figure 4: Ernst Neufert’s Husbaumaschine Project program, when implemented by the robot on real material, gives rise to complicated-looking walls whose designs wereinformed by the computer programs provided by the designer.Another example of their illustrative work is a robot that pours sand on specified locations for a given period of time .Depending on a simple code that only controls how long the sand valve remains open at each location, various-shapedstructures are made. The important thing to notice is that the result is not merely caused by the robot or by the material.The combination of the robot’s programmed movement and the natural behavior of the material, such as granularity andsolidness causes the final outcome of the digital process.The next project from the same group is a digitally designed wooden pavilion in Rome where a natural hygroscopicproperty of wood, i.e., “the wood gets shrunk when dried and gets expanded when it is moistened”, was used to connectthe timbers all over the structure without any fastener. A similar idea called Holzdübel-Verbindungen has been practicedin German houses for joints in timber pillars since the th century. The same idea combined with computationaldesign methods allows scaling up the design from simple joints to the entire structure .Another example in the same line of projects is based on the behavior of stones as another natural material. The othermaterial used in this project is a sort of string as a man-made material. The string is used to jam stones in order to formstable structures. The idea is to use computational methods that are informed by the behavior of the involved materialsto cleverly combine them such that the final outcome takes the desired shape and remains stable under pressure. Arobotic arm is used to place the string in a circular shape layer by layer that acts as a belt holding stones together. Therobustness of the structure is tested by pressuring it from different angles. Surprisingly, such simple materials gaverise to a stable structure with reasonable resilience analogous to conventional walls where stones are glued togetherby cement or concrete. The other interesting feature of this structure is the convenience of destruction. Collecting thestring from the top releases stones gradually and the entire structure becomes a pile of stones when the string is fullycollected. Vertical and horizontal working robots allow complex shapes of structures formed by the same simple law.Even though the current instances of this design is mainly used in art galleries, it can be used in practice as pillarsfor actual buildings. To showcase its practical uses to the public, the group built several pillars using this method andput a roof on top of them in a public park in Zürich and showed that the pillars successfully held the burden for onemonth as good as steel pillars. One stark difference with traditional architecture is that the outcome of this design is notpredicted in advance despite the conventional design methods when the strength of materials in different configurationsare all calculated. Here, the synergic effect of all small stones gives rise to the stable pillar whose exact simulation ischallenging even using current powerful computers .The important takeaway message from these projects is that by the use of digital computational methods, it is not alwaysnecessary to work with fully artificial materials such as carbon fiber. It is possible to use a mixture of fabricated andnatural material when the behavior of the natural material is a key factor in the desired outcome.The combination of natural sciences, digital calculations, and robotics are shown in another project by the same groupwhere the purpose is to stack large stones to form a wall without using any glue or string [Furrer et al., 2017]. Eachstone is scanned and its center of gravity is estimated by the computer. Then, its target position is calculated in relationto other stones and an autonomous excavator places the stone accurately in its calculated target location . Photo from Photo from https://thefunambulist.net/architectural-projects https://gramaziokohler.arch.ethz.ch/web/e/projekte/321.html https://ethz.ch/en/news-and-events/eth-news/news/2018/08/programming-for-perfect-shade.html https://gramaziokohler.arch.ethz.ch/web/d/projekte/297.html
4n another project, using Augmented Reality (AR), a recently popularized technology, the group showed the applicationof AR in the construction process. The design is first calculated by the computer. The bricks are scanned by a cameraand their desired locations are calculated according to the target design. A frame of the brick in its target location willappear on the real scene via augmented reality eyeglasses. This allows the worker to know exactly where the brick mustbe placed .The question of whether the entire process of stacking bricks can become autonomous was one of the initial concerns ofthe pioneers of artificial intelligence such as Marvin Minsky (August 9, 1927 – January 24, 2016) as he mentioned inhis book “The Society of Mind”, where he emphasized that the construction process requires much more than simplecalculus. Due to the multitude of skills necessary to stack bricks to form a proper wall, he connected such capability togeneral intelligence.Minsky’s argument adds another dimension to the concept of artificial which is mind . Theoretical Philosopher NormanSieroka (1974,) listed three prominent opposites to nature as Mind (mind vs matter), Technology (man vs robot), andCulture (nature vs nurture).The last comment I would like to make on this line of projects is the role of learning in architectural processes. In theabove-mentioned works, the employed robots are fully programmed and are considered blind in this sense, i.e., therobots do not learn from their experiences. They merely do a simulation followed by execution.In another project, deep reinforcement learning is used to give learning capability to the robot to fit two elements ineach other. A reward function is designed that punishes the robot whenever it fails to complete the task. The algorithmis trained first in simulation and then transferred to reality when the robot is only equipped with a force/torque sensor.The employed algorithm is Deep Deterministic Policy Gradient developed in DeepMind [Lillicrap et al., 2015]. It has agenerative algorithm that runs the robot and a critique that measures how good the robot is at accomplishing the task.Reinforcement Learning algorithms are easy to think of in architecture since the goal is clear. However, they are hard toimplement due to the enormous number of trials they may need to arrive at a good policy to do the task .The combination of all the above-mentioned projects can be distilled into a term “Robot Builds a House”. This term,hypothesized a robot that takes a computer program as input and manipulate the provided materials to build a houseas the output product. This definition abstracts away the construction details and focuses on the role of the robot as afunction that maps a computer program into a physical object – a house in this case. In this section, I will extend the ideas mentioned in previous sections to areas at the intersection of architecture,intelligent robotics, and algorithmic information theory. First I will take a closer look at the concept of “Naturalness”that was introduced in Section 2. Then, using the concept of “Robot Builds a House” which implicitly exists in theprojects mentioned in Section 3, I will discuss the potential safety concerns that are probable if the technology is widelydeployed. Finally, in a more abstract discussion, I will combine the idea of “Robot Builds a House” with UniversalTuring Machine to provide a measure of complexity for physical objects such as buildings. As an application, thismeasure of complexity is used to define a quantifiable measure of beauty.
Regarding Section 2 that was about the evolution of the concept of artificial buildings in history, I can summarize thechanges as the evolution of the concept of natural . The more advanced our technology becomes, the more distant theconcept of natural will be from the true nature. For example, although caves were considered as natural residentialplaces in the early era, the buildings made of tree branches or even cages are considered as natural buildings in ourtoday’s concept of natural . I would like to provide a different view to the comparison of artificial vs natural thingsincluding buildings. I put more emphasis on the appearance of the object than on how it is constructed. To simplify theproblem, we can focus only on the photos taken from objects and identify the features of the image that categorize it asnatural or artificial. When we look at a scene, there are features that we can objectively see as artificial [Ruderman andBialek, 1994]. I summarize all these features as regularity . Notice that regularity in artificial scenes does not imply thatnatural scenes are random. Nature imposes its own regularity even though it is totally different from artificial scenes.For example, an extremely straight line in a scene that belongs to a steel product or a carefully smoothed wall made ofbricks is a unique character of artificial buildings which are in contrast with those made by nature that often comeswith rough and noisy surfaces. Similarly, highly symmetric structures such as circles or curves are other examples of https://gramaziokohler.arch.ethz.ch/web/e/projekte/371.html https://gramaziokohler.arch.ethz.ch/web/e/forschung/369.html In this section, I consider the question of whether it is possible to construct a building that satisfies the characteristicfeatures of natural buildings as measured by the features proposed in Section 4.1. To this end, we must first recognizethe unique features of a natural scene that rarely occurs in scenes consisting of artificial products. Fractals are one of thestereotypical features of nature that are seen very often in photos taken from natural products [Voss, 1988]. In abstractterms, a fractal structure refers to a pattern that consists of copies of the same pattern with different scales. Such apattern is seen in many natural objects such as leaves, roots, branches, snowflakes, broccoli or aerial photos of coastlines,mountains, and glaciers. Such self-similarity seems to be a characteristic feature of nature that is absent in goal-directedindustrial products. For example, if the goal of an industrial process is to build a wall with minimum energy and material,embedding a form of such self-similarity will not be advised by engineers. Hence, if one wants to construct a buildingthat looks natural, self-similarity is one of the key features that must be included in every scale. However, currentindustrial mechanisms are not designed to implement nature-inspired structures. One way to implement self-similarityis to copy the same pattern over and over in the construction process. However, I believe the correct way to buildan artificially natural building is to take one step back from the final product and imitate the construction processrather than only the final product. Self-similarity is the outcome of a hierarchical construction process consisting ofemploying the same process on multiple levels. Hence, the efficient implementation of a nature-inspired buildingrequires implementing the nature-construction process in the first place.
One of the projects mentioned in section 3 was about combining the pre-programmed robots and simple materials suchas stones and strings to construct structures that can be used as elements of more complex structures such as buildings.The researchers had tested the robustness of such structures against external disturbances by loading the structures withdifferent loads. Even though the structures built this way, for example, pillars, showed a fair amount of robustness, thetype of loads and disturbances were not rich enough to validate the stability of the structure in every condition. Here,I will introduce the concept of adversarial robustness and argue that such a notion of stability can be hazardous inrobot-built structures even more than human-built ones. When a team of humans builds a house, the algorithm they arefollowing is only approximately determined by the architect via a plan. However, construction workers can take minorinitiatives at every stage of the construction process which is seen as a source of randomness that makes every buildingunique in terms of details. This might not be important in a small apartment, but when it comes to large architecturalproducts such as a mall or an opera house, these small details accumulate and give rise to a unique character. However,when a pre-preprogrammed robot is employed to build a building, the used program contains every single movement ofthe robot. Meaning that, if an adversary has access to this program, it can simulate the final product in a test condition.This transparency gives the adversary all the tools to detect the weaknesses of the building and take advantage of them.For example, if there is a weakness in the construction process that is caused by a programming fault, the weaknessis replicated in every building constructed by the same program and the adversary can attack all buildings with thesame adversarial plan. However, in a human construction process, the randomness caused by human workers makes itdifficult for the adversary to come up with a single attack that applies to all buildings. Notice that this inherent risk iscaused by the fact that all the construction process comes from a few lines of deterministic codes that are executed bythe robot rather than the complex thinking and decision-making process of human workers.
In this section, I define the concept of complexity for buildings as physical objects and show how the conceptualtechnology “Robot Builds a House” can be used to measure this seemingly intractable quantity in practice. Inspiredby the algorithmic information theory, the notion of
Kolmogorov complexity [Kolmogorov, 1963] is proposed as ameasure of complexity for objects. In simple terms, the Kolmogorov complexity of object x is the minimal descriptionof that object. In algorithmic information theory, the description is defined as the computer program P ( x ) thatinstructs a general computing machine on how to produce x . The general computing machine is known as the TuringMachine [Turing, 1948]. A Turing Machine is capable to perform any computation in finite time. In our case, theTuring Machine T takes the description of the object P ( x ) as input and produces x in a finite time. There may bemany programs that all produce x when they are fed to the Turing Machine. Among all programs that produce x ,the complexity of x is defined as the length of the shortest program. More specifically, the complexity of the object x is defined as c ( x ) = min { l ( x ) : l ( x ) is the length of the computer program P ( x ) that produces the object x } . Aninteresting property of Kolmogorov complexity is its independence of the Turing Machine that is used to interpret P ( x ) .6o give an intuition on why this is the case, we can restrict ourselves to a class of computing devices called UniversalTuring Machines (UTM). UTMs are Turing Machines with the added property that they can reproduce any other TuringMachine. Therefore, a special choice of a Turing Machine appears as an overhead program that remains the samefor every input program and makes no difference in the relative complexity of objects since the overhead program iscanceled out.In the following, I establish the connection between the Universal Turing Machine and the “Robot Builds a House”technology. The employed robot is considered as a universal machine that is programmed to build something. In thisdefinition, we can see the program defined in the syntax of the programming language of the robot as input P ( x ) . Therobot takes the program and produces the house x as its output. Hence, among all programs { P i ( x ) : i = 1 , , . . . , M } that build an identical house, the length of the shortest program is an approximation to the complexity of the house.As mentioned above, this measure of complexity is independent of the robot being used. For convenience, we restrictourselves to the specific robot which is used to build the houses. Conditioned on a particular robot, we can compareconstructed houses in terms of their relative complexity since the complexity of the robot with respect to the universalrobot is canceled out in relative comparisons according to the argument I made for Universal Turing Machines. Havinga measure of complexity, we can think of several applications. In the following two applications are discussed. There have been several efforts throughout the history of art towards coming up with a precise definition of beauty.A fundamental question is whether there exists a quantifiable measure of beauty? Inspired by [Schmidhuber, 1997],I propose a quantifiable measure of beauty for the buildings as objects produced by computer programs using thetechnology “Robot Builds a House”. Our everyday experience suggests that beauty is a relative term and its perceptiondiffers across individuals. This means that the beauty of an object x must be defined as a function of how it is perceivedby a particular preceptor. Humans perceive external stimuli via their brains. Let B ( x ) be the function of the brainthat takes the object x and generates the feeling of the beauty of x . It is normally assumed that evolution favorsenergy-efficient systems. Hence, I reasonably assume that B ( x ) is inversely proportional to the energy consumed by thebrain to perceive x . Due to the personalized attitude to beauty, I further assume that it is more convenient for the brain B to perceive a set of N patterns Θ = { θ , θ , . . . , θ N } . These patterns can be seen as the characteristic parameters ofthe brain that is now denoted by B ( · ; Θ) . Hence, if the pattern x is close to one of θ i ∈ Θ , the brain can perceive it withless energy consumption that corresponds with a higher sense of beauty. Notice that Θ is individual-dependent, i.e.,every brain has its own set of easily-perceived patterns. In other words, every brain perceives a particular set of patternsas beautiful. Furthermore, the patterns in Θ are primitives. I assume the combination of these primitive patterns givesrise to a space spanned by Θ every member of which is sensed as beautiful by the brain B ( · ; Θ) .I argue that a universal measure of beauty can be defined as a sum of two factors: The complexity of the preceptor + theresidual complexity of the object that remains out of the space characterized by Θ . To give an intuitive sense of thisdefinition, assume an imaginary brain that perceives every possible pattern. This brain cannot discriminate betweenbeautiful and non-beautiful patterns. On the other end of the spectrum, imagine a brain that is fully blind to the stimuli.This brain can also not discriminate patterns in the input. Hence, we need a fairly simple brain that equally perceives afew patterns not too many patterns. This suggests that the complexity of the brain itself must be taken into accountwhen we talk about the beauty of an object such as a building. Hence, a simple definition of the beauty of x can be D ( x ; Θ) | Θ | + r ( x | Θ) , where r shows how much detail of x is left unexplained by the patters Θ embedded in the brain. D is the description length of x given the brain with patterns Θ and | Θ | is simply the number of patterns perceived bythe brain which is an indication of the complexity of the brain itself. In the next section, I discuss how this definitionand assumptions, can be used to construct personalized buildings. In this section, I discuss the potential idea of designing a house customized to the personalized taste of beauty. Iassumed in Section 4.4.1 that every brain has its own prior patterns based on which it gives beauty score to externalpatterns. Based on the hierarchical nature of the processing in the brain [Meunier et al., 2009], rather than consideringthe patterns as complete buildings, it is likely that a brain B has a set of primitives denoted by Θ B which are combinedtogether to make a complete building. In this sense, infinitely many buildings can be made by a continuous combinationof finitely many primitives. Assume the set of buildings made of these primitives is denoted by S (Θ B ) . The set S (Θ B ) consists of all buildings known as beautiful by the brain B . However, these primitives concern only the aestheticaspects of the buildings. Nevertheless, a building must be functional in the first place. Assume a set of constraints C (Θ B ) = { c (Θ B ) , c (Θ B ) , . . . , c M (Θ B ) } that must be satisfied by the building primitives to make a functionalbuilding. Therefore, the building x which is made by the robot T must be as close as possible to the set of beautifullyperceived buildings for the brain B and at the same time satisfy the engineering constraints C (Θ B ) . This gives us the7ollowing optimization criterion P ( x ) = argmin P d ( T ( P ( x ) , span(Θ B )) + i = M (cid:88) i =1 (cid:96) i ( c i (Θ B )) (1)where d ( · , · ) is the distance function that determines how far the resultant building T ( P ( x )) is from the space ofbuildings perceived as beautiful by the brain B . The function (cid:96) i is the cost incurred by violating the i th constraint.Solving 1 gives the program P that when realized by the robot T gives the house T ( P ( x )) that is close to the set ofbeautiful houses for brain B and also satisfies the engineering constraints C . The distance d between the constructedhouse and the set of houses constructed using primitives is measured in the sense of Kolmogorov Complexity. Roughlyspeaking, the distance is the minimal length of the program that constructs those parts of the building which cannot beconstructed using the primitives Θ B . Intuitively, the first term makes sure that the brain can perceive the appearance ofthe building with minimum energy consumption and hence saw it as a beautiful object. The second term makes surethat the building is designed such that the final product is still functional. I used the notion of universality in the concept of “Robot Builds a House”, that is a universal robot is seen as a genericbuilding machine, to make a connection with Universal Turing Machines as general computing devices. Borrowingconcepts from algorithmic information theory, I proposed a method to quantify the complexity of the buildings.Motivated by the hypothesis that human brains have evolved to favor the stimuli which are processed with less energy, Iproposed a quantifiable measure of beauty that can be possibly used to customize buildings according to individuals’taste of beauty.
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