See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/349645124 Back To The Fractal: Lessons Learned from Precolonial African Settlements Research · December 2019 DOI: 10.13140/RG.2.2.19114.54722 CITATIONS READS 0 6 1 author: Aikin Karr University of Westminster 1 PUBLICATION 0 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Back to the Fractal View project All content following this page was uploaded by Aikin Karr on 27 February 2021. The user has requested enhancement of the downloaded file. Table of Contents 33 Abstract…………………………………………………………………………………………………………………………………………………………………………………… 4 4 Introduction……………………………………………………………………………………………………………………………………………………………………………… 5 5 Methodology…………………………………………………………………………………………………………………………………………………………………………….. Findings: 6 6 What is Fractal Geometry……………………………………………………………………………………………………………………………………… Fractal Geometry In Vernacular African Architecture………………………………………………………………………………… 8 Fractal Nature of the Ba’Ila Settlement…………………………………………………………………………………………..9 Environmental and Economic Sustainability……………………………………………………………………………….. 10 12 Spacial and Anthropological Optimisation…………………………………………………………………………………………… Supplementary Case Studies……………………………………….…………………….…………………….……………………….14 16 Contemporary Evolution of a Synthetic Vernacular…………………………………………………………………………………………… Conclusions: 18 Optimisation through Fractal Geometry…………………………………………………………………………………………………………19 20 Informing Design………………………………………….………………………………………………………………………………………………………… 25 Bibliography……………………………………………………………………………………………………………………………………………………………………………… 2 Abstract Fractals in mathematics is the concept of a never ending pattern driven by recursion that are self similar at an infinite scale. This recursion of a simple process over and over creates an ongoing feedback loop that can be visualised through fractal geometry. The term fractal was coined by Benoit Mendelbrot in 1975 and has since laid the foundations for research and development in several industries from medical screening for lung diseases to better understanding the formations of leaf veins in botany. Fractals are everywhere, from the microstructure villi in our intestines to clouds to mountains and coastlines. With a ubiquitous presence of the self organising phenomena in nature, it is no wonder that spontaneous architecture of early settlements around the world developed a similar methods of self organisation that manifested in fractal geometries when observed at varying scales. However, the beauty in fractals is not only due to its natural occurrences, the concept also has a great impact and close relationship with human beings. As beings whose brains have evolved to detect patterns as a survival mechanism, humans are greatly influenced by the geometry of their environment. As Yannick Joye explains in his article of how ‘Fractal Architecture Could Be Good For You’, “Settings with a high fractal dimension could contain hidden dangers, such as ambushing predators, while those with a low fractional dimension do not contain enough elements in order to offer protection and sources of food. Hence, we will be more aesthetically attracted and more relaxed in environments with an intermediate fractal dimension.” This dissertation focuses on the fractal geometry that has developed over centuries of vernacular evolution in Sub Saharan Africa and aims to study and explain the formation of such emergence through the use of case studies specific to Cameroon, Burkino Faso, Mali and Nigeria among other references. This dissertation will also propose methods of reimplementing such geometry in favour of euclidian geometry for a more biophilic, sustainable and optimised approach to the built environment. 3 Introduction Since the dawn of man, humans have always sought out means of shelter and protection. This critical need for establishing a ‘home base’ for groups of humans has manifested into what we know today as vernacular architecture. It is decribed as architecture characterised by the use of local materials and knowledge, usually without the supervision of professional architects. This manifestation of optimisation, sustainability and social awareness gives way to the spontaneous emergence of self organised settlements typically constructed with great craftsmanship, a community effort and most importantly, without architects. A great example of such structures can be seen in Djenne, Mali (The Great Mosque of Djenne) pictured in Fig1. A type of Sudano Sahelian archetype typically built from adobe mud — which has a high thermal capacity that absorbs heat during the day and keeps the interior space warm during the night — in 13th century and was designated a world Heritage site in 1988. Quite astonishingly the building holds great “cultural significance as the entire community of Djenné takes an active role in the mosque's maintenance via a unique annual festival” ("Great Mosque Of Djenné" 2019). Another example of vernacular architecture could be seen in the Ba’ila settlement in north Zambia (pictured in Fig2) which exhibits a ring like self recurring organisational pattern known in mathematics as fractal geometry. These structures constructed of primarily mud and stone seem to self replicate as one cluster of domes looks identical to the whole when magnified. Such organisation spontaneously emerges from the negotiation between spacial arrangement and social functions. Although vernacular architecture is a broad term that encompasses all spontaneous settlements that have historically materialised as a direct response to environmental and social conditions, fractal geometry in the vernacular architectural discourse is a phenomena that is sparsely observed. This is not however due to a lack of such geometry existing but rather modern architectural journalism’s naivety in believing primitive civilisations had little or no knowledge of fractal geometry. Yet, as this dissertation will investigate, in most cases, this is far from true. Figure 1 Image of The Great Mosque of Djenne, Djenne, Mali Figure 2 Aerial image of The Ba’Ila settlement, Southern (Google Images: Ella Morton, 2014) Zambia (Google Images: Mary Meader, 1937) The first section of this dissertation will study the nature of fractal geometry in historical African settlements on the urban scale in terms of its materiality and how they are constructed, their spacial arrangement and social interconnectivity and environmental performance with regard to how they allowed their inhabitants to dwell comfortably and connect with the natural environment as well as each other. It will also explore the very definition of fractal geometry 4 and the different types of fractal architecture found around the world, their identifiable characteristics and their contextual presence in historical Subsaharan African settlements. The second section will go on to explore the benefits of using fractal geometry in architecture as a form of organisation (as opposed to euclidian geometry for example). It will also begin to develop a contextual methodology of how such geometry that emerged in Subsaharan Africa can be transposed to respond to contemporary regional, climatic and socialeconomic conditions. The final conclusion will be the starting point of a thesis project that aims to test whether such methodology towards constructing a self organised system through fractal geometry to unite, educate and stimulate the minds of the youth is plausible. Methodology The investigation of this dissertation aims to address the ways in which and to what extent fractal geometry created a sustainable, self sufficient and environmentally and socioeconomically responsive vernacular in Subsaharan Africa. The investigation also aims to question whether the methodology used in generating this self organised ecosystem is transposable to other contexts. A mixture of qualitative and quantitative analysis tools will be used in the approach for this dissertations findings. Both will have elements of primary and secondary research. The primary will be in the form of information collated from interviews to further understand the methods of construction and social cohesion from vernacular African architecture. Primary research will also be conducted to further analyse the social logic of space within fractal geometry in the context of vernacular architecture. Whereas most information collated in the form of case studies, references and observations will be derived from secondary research. All analyses undertaken in this dissertation will provide a detailed description of the technique and tools used to generate any findings for the sake of reproducing experiments. As per precedence, secondary research collated for this dissertation is heavily based on the research already conducted on vernacular architecture and fractal geometry by Ron Eglash (an American who works in cybernetics and is the professor in the School of Information at the University of Michigan), Nikos A. Salingaros (mathematician and polymath known for his work on urban theory), Yannick Joye (a senior researcher at ISM University of Management and Economics), Bernard Rudofsky (who was an Austrian American writer, architect, collector, teacher, designer, and social historian), Kaj Blegvad Andersen (author of African Traditional Architecture), as well as the remaining visuals of fractal African settlements and dwellings for which has no architect nor urban planner but can rather be attributed to the group(s) of people that they are associated with. The reliability of the results concluded from this dissertation is limited by three main factors. These are the reliability of the aforementioned sources of collated information, the generalisation or assumptions made in determining function or impact of the relationships between the spacial arrangement derived from fractal geometry and its social cohesive counterpart and finally the margin of error for the softwares and calculations used in the analyses of fractal geometry. Although all precautions are taken to maintain a level of certainty and validity some factors are unavoidable. This includes generalised derivations made about historical architectural systems and the specific meanings behind them. In these cases educated guesses and theories are developed rather than concrete statements. Although these factors are relatively important in attaining validity of results, the consistency of methodology behind them is far more important and can therefore offset the cost of error. 5 What is Fractal Geometry This idea of repeating an operation on a geometry in order to create an infinite number of iterations is known as recursion. Cantor used this simple line exercise to reintroduce the concept of infinity back to a scientific community that neglected its mathematical applications for decades. The phenomena was further developed in the early 1900s by Swedish mathematician Helge Von Koch in his eponymous Koch curves but instead of erasing lines in the recursive operation , added lines to create a complex form that propagated a lines perimeter towards infinity. However, the practical applications of fractal geometry was only introduced to the scientific community in 1924 by a French and American mathematician and polymath named Benoit Mandelbrot who was able to identify and more importantly rationalise the ubiquity of fractal patterns and geometry in nature. “As he began to apply computer graphics, he found that these shapes were not pathological at all, but rather very common throughout the natural world. Mountain ranges had peaks within peaks, trees had branches made of branches, clouds were puffs within puffs — even his own body was full of recursive scaling structures.” (Eglash 1999) According to Ron Eglash, there are five essential components of fractal geometry that determines whether or not such geometry can be described as being fractal. This includes fractional dimension; recursion; scaling; selfsimilarity and infinity. However before these terms are defined and contextualised, I will first describe the mathematical derivation of the fractional dimension which will lead to its definition. It is quite common knowledge that a line between two points has one dimension and a plane has two dimensions but what isn’t very well known is the maths behind this phenomena which is crucial to understanding the nature of the fractional dimension. However for the sake of simplicity, this description will only provide the logic behind the mathematical formula rather than an explanation for how it has been derived. Number of equal length divisions Original Line (iterations) made from original line. Four in this case log(div) log(4) =1 log(mag) log(4) New NewLine: Line:11 New New Line: Line: 2 2 New Line: New Line:33 NewLine: New Line:44 Maginification factor: how many times you Therefore a line has would need to magnify any new line in one dimension order to achieve the original line (length) Figure 3 Diagram conveying logic behind one dimensional lines (Source: Personal Collection) As you can see from Fig3 a line can be said to have one dimension as a result of the relationship between the number of times you can divide it into equal lengths and the amount by which you would need to magnify such new length to regain the original line’s length. This logic is carried on in two dimensional space where a polygon such as a square can be described as two dimensional as a result of the relationship between the number of times you can divide it into equal squares and the amount by which you would need to magnify such new square to regain the original squares length and width (see Fig4). If we were to continue and carry this logic into the fractal geometry where the number of new polygons created as a result of a single iteration is exponential (not linear), we can calculate the fractional dimension of any fractal geometry (such as the Siepinski triangle in Fig5). This is useful not only to determine whether or not a pattern or geometry is fractal but can also have functional properties as will be discussed in a later section of this dissertation. 6 Original Polygon New New Polygon: 1 Polygon: 2 Can also be written as... log(4) log(n ) 2log(n) = = 2 log(2) log(n) log(n) Desribing the relationship between Therefore a polygon has New New the numerator and the denominator two dimensions Polygon: 3 Polygon: 4 Figure 4 Diagram conveying logic behind two dimensional shapes (Source: Personal Collection) Number of new triangles created as a result of iterative process New polygon: 1 log(3) Fractional dimension is always = 1.585 between one and two log(2) Maginification factor: how many times you New New would need to magnify each new triangle polygon: 2 polygon: 3 to achieve the size of the triangle from which it was spawned Original Polygon Sierpinski Triangle Figure 5 Diagram conveying logic behind fractional dimension (Source: Personal Collection) Geometry can also be said to be fractal if it exhibits recursion, which, as described by Ron Eglash “is a loop where the output at one stage becomes the input for the next” (Eglash 1999). If you notice the three new triangles in created as a result of the first iteration of the Sierpinski triangle in Fig5 you will notice that this process can be repeated infinitely within each new triangle spawned. This loop pattern is only possible where the new shape created is identical to the original shape it spawned from at a different scale. This leads to the next essential component of fractal geometry: scaling, which is eloquently described by Eglash as a property where “enlarging a tiny section will produce a pattern that looks similar to the whole picture, and shrinking down the whole will give us something that looks like a tiny part” (Eglash 1999). This concept is closely linked with the cosmological phenomena of macrocosm and microcosm where a part of whole is just as important and encapsulates the whole itself. Next we consider what is known as selfsimilarity which Eglash divides into two categories. That which is ‘statistically self similar’ meaning not exact but has a great enough similarity to be considered fractal. This is more the case with naturally occurring fractals such as the branching alveoli in the lungs that are not identical to the whole (lungs). The other being ‘exact self  similarity’ which is sometimes more the case in manmade or conscious efforts towards fractal geometry or mathematical models that have been trained to produce fractal geometry with little margin of error. And finally, the last essential component of fractal geometry is the concept of infinity where a recursive image or process can seem infinite (and mathematically is) but in reality “is limited to a finite range of scales”(Eglash 1999). 7 Fractal Geometry in Vernacular African Architecture Apart from the research conducted by Ron Eglash in his book, African Fractals: Modern Computing and Ingenious design, very little is known about the relationship between fractal geometry and the social organisation of precolonial African tribes. This is largely due to the impact colonialism and the TransAtlantic slave trade had on West Africa causing an incomprehensible loss of traditional values, abandoned settlements and destruction of heritage in general. Nevertheless, the settlements and architecture that have remained and or have been documented can give us an insight into how these societies utilised fractal geometry to create a self organised and sustainable ecosystem. It is however important to note that although several vernacular African settlements exhibit this fractal nature, there remains an ongoing debate of whether these communities, artisans and builders truly made use of fractal geometry based on its pure mathematical properties or rather its applied mathematical properties and aesthetic result. That is using a form of algorithm to generate such complex geometry and having knowledge of why such geometry could be generated as a result or rather having limited knowledge of how fractal geometry works but knowing that it can produce optimal results for specific functions and aesthetic preferences. Eglash is adamant in saying that “unconscious structures do not count as mathematical knowledge, even though we can use Mathematics to describe them” (Eglash 1999). There is however, no substantial evidence to prove either of these arguments. Yet the fact that such an argument exists creates intrigue and propagates discussion and analyses of these society’s settlements. This dissertation will focus mainly on one of such settlements as a main case study which is the Ba’Ila settlement located Southern Zambia (as mapped in Fig9). Zambia 0 1000 mi 0 1000 km Ba’Ila Settlement Figure 9 Map depicting Africa and location of Ba’Ila settlement within country of Zambia (Amended from Google Maps, 2019) 8 Fractal Nature of The Ba’Ila Settlement The Ba’Ila settlement/village that was of roughly 2000 inhabitants is located in southern Zambia near the Namwala District inhabited by the Ila tribe who are known for raising livestock for subsistence. This settlement is the upgraded permanent village used by the Ila tribe who prior to to the Ba’Ila were also known to set up temporary villages “built primarily for defensive purposes as enclosures” ("Low Rise, HighDensity HousingDigitális Tankönyvtár" 2019) known as ‘Kraals’. The word Kraal (an Afrikaans & Dutch word) is used to describe an “enclosure for cattle or other livestock, located within an African settlement or village surrounded by a fence of thornbush branches, a palisade, mud wall, or other fencing, roughly circular in form” ("Kraal" 2019). Figure 10 Aerial image of The Ba’Ila settlement, Southern Zambia (Google Images: Mary Meader, 1937) Figure 11 Diagrams depicting iterations of fractal geometry of Ba’Ila settlement starting with seed shape going left to right (Source: CSTD 2019) In order to determine whether or not this settlement can be classified as fractal we can go through the checklist of essential components of fractal geometry mentioned in the ‘What is Fractal Geometry’ section of this paper. Recursion in the geometry of this village is self evident. As conveyed in Fig10. We see that there is an iterative function taking place that describes the relationship between the part and the whole. One ring like structure of a family home is surrounded by about 24 other ring like family homes varying in size depending on social status. These now 25 ring like structures form a ring that is surrounded by another 24 ring like structures forming a ring within rings within rings (an inception of sorts). We can describe the iterative function as dividing each ring by a factor (n) and repeating this process twice in order to achieve the fractal geometry depicted by the plan of the Ba’Ila settlement. The second component is self similarity, and since each ring resembles one another yet is limited by the smallest possible unit  the seed shape (the seed shape being the family unit which is the limit of 9 this fractal geometry), we can establish that this village is statistically self similar on varying scales and can be mathematically perpetuated to infinity. Finally we can calculate the fractional dimension of the settlement to be roughly 1.5 as explained in Fig12. Interestingly, this falls just on the edge of what University of Wisconsin researchers Deborah J. Aks and Julien C. Sprott refer to as an optimal dimension as their studies “indicate that the aesthetic reactions peak when the natural settings or the fractal pattern underlying it, have an intermediate fractal dimension (around 1.31.5)” (Joye 2007). This could possibly contribute to the debate of whether such emergent organisational patterns could have mental health benefits or alert viewers to certain elements that would otherwise go unnoticed. f g h e i d j c b k a l x m v u n t s o r p q Figure 12 Diagrams and calculations determining fractal dimension of Ba’Ila settlement geometry (Source: Personal Collection) (a+b+...v) x log(number of divisions) = avg length = magnification factor = fractional dimension 25 avg length log(magnification factor) (a+b+...v) 295.281 = 8.61 log(25) = 34.31496 = 1.49 25 34.31496 log(8.61) Average length of new shapes Magnification factor found by Fractional dimension found by using created found by adding all their dividing original seed shape length logarithmic formula lengths together then dividing by 25 by average length of new shape(s) Environmental & Economic Sustainability For the Ila tribe, a people who are self subsistent — only “growing enough food to feed their families” ("Ila People" 2019)— relying heavily on raising cattle, optimising day to day life through their architecture in a harsh climatic environment was crucial to prosperity and survival. The semi arid plains of Southern Zambia (as depicted in Fig13/14) has a temperate climate with dry winters and hot summers reaching up to 40ºC and a low of 5ºC (a high diurnal range) with an annual rainfall of between 500  1400mm that can cause flash flooding which can have a devastating impact on (stored) crops and livestock. It is therefore critical that these factors need be considered when constructing a home or a settlement. and as I will soon describe, the Ila people have found ingenious methods of construction to protect them against such environmental factors in a form of implicit algorithm (teachings and traditions that have evolved over time to provide optimal results that respond to a contemporary context without the need of complex engineering or mathematical knowledge). 10 Figure 15 Diagram depicting space use of Ba’Ila settlement (Google Images: Meader, 1937) Much similar to Sudano Sahelian architecture in West Africa, the Ba’ila village is constructed of natural biodegradable materials such as adobe mud, sticks, thatch, reeds, grass, dung and termite mound. “Men collect the outer sticks and place them in a circle on the ground. The women bind and thatch the structure using braided split reeds and grass. A central tree trunk acts as a support and the door is made low so that any foe has to stoop before entering. Dung and termite mound is mixed to a thick consistency and spread to form the floor which sets rock hard and may be polished to a mirrorlike finish using a polishing stone. The same material is used to form a raised hearth near the central pole. The hut is very stable, warm in winter and cool in summer. Smoke from the fire escapes out the door or through the thatch that has the effect of constantly fumigating the hut.” ("Zulu Culture  Building The Zulu Kraal" 2019) From the materiality of these structures we can begin to infer their environmental performance, sustainability and implicit functions. For example the mud used to daub the walls of the enclosures which is made of adobe clay has a high thermal capacity that can absorb heat during the day and dissipate into the interior space in the night to keep occupants warm. Its sustainability is self evident as the soil used in the production of clay is locally sourced (red sandveld soils similar to red laterite soils found in West Africa). And the water mixed with the soil to produce this thick mound is collected — even during the dry season — in ditches called ‘dambos’, a technique also present in Sudano Sahelian architectural construction where water is collected in ditches called ‘kuddibbipi’. There are also implicit functions that can be inferred from the construction of these kraals such as the use of termite mound as a floor and wall coating. Termite mound is known to be hydrophobic (repels water) and therefore protects the kraals (and the occupants, livestock and food storages) from water damage given the high rainfall events during the rain season (as seen in fig). 11 Figure 13 Climate classification map for Zambia (Source: Wikipedia) Figure 14 Graphs conveying temperature and rainfall profiles for Zambia (Source: Wikipedia) Spatial & Anthropological Organisation Architecture as a language can allow us to communicate our daily routines, bare necessities, symbolic and religious amenities, and social interactions through the spacial organisation and journey we experience in our built environment. And so architecture not only manifests the functions that take place within it but also becomes an artefact of the people who journeyed through it. The form, organisation and structure of the Ba’Ila settlement encapsulates not only the activities and programmatic requirements of the Ila tribe but also conveys the tribe’s insecurities and social hierarchies all through its fractal geometry. To begin with we can see from the plan of the settlement in Fig15 that its overall shape is of a ring. Not a square or rectangle, not a triangle or ellipse but a relatively circular fashion. This is, as described in the original text of Meader/Light, “Constructed in the form of a circle with the entrance on the downwind side so that the cattle (5000!) do not bury the place under dust when they come in… In those days lions were a constant threat… Nowadays the villages are no longer built like this because [of] its protective function, especially against lions, is no longer needed.” (Smith 1949) In other words, similar to the defensive form of Fujian Tolou in China, its very geometry on the urban scale has a direct relationship with the threats the tribe faced and its orientation provided an optimised route for cattle to be herded in and out of the village. And as we begin to dig deeper into the geometry of the individual units and their relationship with eachother, we can see a fractal pattern that forms as a result of the negotiation between social hierarchy and programmatic requirements. As Eglash describes the settlement 12 “Toward the back of each pen we find the family living quarters, and toward the from is the gated entrance for letting livestock in and out. For this reasin the from entrance is associate with low status (unclean animals), and the back end with high status. This gradient of status is reflected by the size of the gradient in the architecture: the front is only fencing, as we go toward the back smaller buildings (for storage) appear, and toward the very back end are the large houses. The two geometric elements of this structure — a ring shape overall, and a status gradient increasing with size from front to back — echoes throught every scale of the Ba’Ila settlement.” (Eglash 1999) Moreover the emergent self organisation of the village manifests itself in the geometry of the architecture. Below in are diagrams that depict the gradient of social hierarchy (Fig17) and also a social syntax mapping depicting the interconnectivity of the village based on plan images of the settlement (see Fig16). This map is placed in comparison to a typical contemporary high rise six storey apartment village proposed to be built in Hackney Wick. Both maps have been generated using the Gephi Open Graph Viz Computer Software. We can see from first glance as a comparison that an urban settlement such as that in Hackney Wick is built vertically as opposed to the Ba’Ila village which is spread out Laterally has less interconnectivity within its spaces. The branches between the nodes of the Ba’Ila network show that everything is connected from the food storage to the individual units to courtyards. All connected by the main courtyard seen upon entry to the village. B38 Balcony B41 Balcony B38 A39 Balcony B41 A39 B40 Balcony B40 F6 Lift & Hall A42 A36 A37 A42 Balcony A36 Balcony A37 Balcony B33 Balcony Mini A32 Balcony Village 1 Main Central Central Space B33 A32 Space A30 Balcony Main A30 Central Space F5 Lift & Hall B31 B31 Balcony B34 A29 A35 B34 Balcony A29 Balcony A35 Balcony A22 Balcony B27 Balcony A22 B27 B24 Balcony B24 F4 Lift & Hall A28 A28 Balcony A25 A23 B26 A25 Balcony A23 Balcony Figure 16 Diagrams depicting spacial interconnectivity of Ba’Ila village on urban scale and zoomed in portion B26 Balcony of mini village (above) and modern residential building in Hackney Wick (right). Dark orange representing open, public or social spaces and light orange representing private Wellings (Source: Personal Collection) B19 Balcony A16 Balcony B19 A16 B17 Balcony B17 F3 Lift & Hall B20 B20 Balcony A21 A18 A15 A21 Balcony A18 Balcony A15 Balcony B10 Balcony A8 Balcony B10 A8 B13 Balcony B13 F2 Lift & Hall A11 A11 Balcony A9 B12 A14 A9 Balcony B12 Balcony A14 Balcony A7 Balcony B5 Balcony A7 B5 A4 Balcony A4 GF Lift F1 Lift & GF Reception Hall B3 B3 Balcony A1 B6 A2 A1 Balcony B6 Balcony A2 Balcony Figure 17 Diagram conveying social status gradient within zoomed in section of Ba’Ila village (Source: Personal Collection 13 Supplementary Case Studies LogoneBirni The LogoneBirni commune is located in north Cameroon on the west bank of the Logone River. Fig 19 conveys an aerial photo of the chiefs palace which exhibits fractal geometry. As Eglash explains, “The Kotoko people founded this city centuries ago and used local clay to create huge rectangular complexes… each complex is created by a process often called architecture by accretion, in this case adding rectangular enclosures to preexisting rectangles. Since new enclosures often incorporate the walls of two or more of the old ones, enclosures tend to get larger and larger as you go outward from the centre… A man would like his sons to live next to him… and so we build by adding walls to the fathers house.” (Eglash 1999) Something also quite intriguing that Eglash explains in one of his online TED talks is how the geometry of the complex also relates to the social hierarchy exhibited as you transition through the spaces. As the throne room is in the centre and the eldest of children and family members are closest to the throne, there is a hierarchy of formality that is experienced as one travels through the maze like structure (similar to the social hierarchy created by the fractal geometry in the Ba Ila settlement). This sort of direct correlation between geometry and ecology is a prime example of why fractal geometry can be used for social and spatial optimisation. The diagrams in Fig 18 demonstrate the iterations necessary to generate the resultant geometry. The simulation is described to be a ‘golden rectangle’ that can be recursively subdivided into self similar rectangles at infinitely smaller scales. Also quite interesting is the fact that the path to the throne in the middle forms an approximation of the Fibonacci curve or golden spiral. Iteration 1 Iteration 2 Iteration 3 Figure 18 Diagrams depicting iterations of fractal geometry of Logone Birni starting with seed shape going left to right (Source: CSTD 2019) 14 Figure 19 Logone Birni aerial veiw (Eglash 1999) 15 Figure 20 Logone Birni spacial syntax and Fibbionacci spiral geometry (Eglash 1999) Contemporary Evolution of a Synthetic Vernacular Today, there are several examples of architectural approaches that hinge on the property of implicit algorithms exhibited in African vernaculars. The notion of implicit algorithm suggests that a system of organisation is formed spontaneously. This occurs through passed down generational knowledge and tradition that is evolved to suite contemporary challenges and a constant interaction between the factors involved with the process of self organisation (in this case the human inhabitants, their social requirements, the environment and subsequent materials at their disposal etc). Such implicit algorithms can be therefore defined as computing without computers. An example of such a contemporary approach to creating a synthetic vernacular can be seen in the works of renowned architects Fabrizio Caróla (a contemporary Italian architect who devoted most of his career to exploring bioclimatic architecture in Africa) and Paolo Cascone (a Neapolitan architects raised in East Africa who has devoted his career to the research and development of an interdisciplinary design methodology in the field of ecologic design) ("Archittura" 2010) . In an article titled ‘The Fourth Ecology’ (alluding to the philosophical chronology exploring how capitalism must be considered as a cause of a global ecological crisis, titled ‘The Three Ecologies’ by Félix Guattari) , Cascone presents a concept developed with his mentor and team partner, Caróla, of a new method of designing “where new technologies integrate processes that have been passed down for centuries to make them still more sustainable and reproducible on different scales” ("Archittura" 2010). The processes not only acting as input parameters for spacial organisation but also formal influences of the dome typology in Subsaharan Africa and its environmental benefits regulating sunlight and prevailing winds. Figure 21 Fourth Ecology project simulations and diagrams("Archittura" 2010) 16 “The design process we developed starts from the initial genotype of Fabrizio’s 2007 project. From it we abstracted what Deleuze calls the ‘material system’ ( a series of principles governing morphological, tectonic and bioclimatic aspects) and then developed it according to a recursive, evolutionary process of its morphology. The restraints set by Fabrizio’s initial idea on the development of a series of cupolas, linked together around a central space, guided the creative process. The result is the development of a series of successive generations (phenotypes) of design solutions through what I call ‘contextual algorithms’. The help of parametric instruments and environmental simulations enabled us to generate and test families of different solutions in a correlated way… The objetive of this strategy is therefore to alternate a sequence of semicovered patio/impluviums in clusters of terra cotta brick cupolas, differentiated in their dimensions and forms on the basis of the various activities’ spacial requirements.” ("Archittura" 2010) Another contemporary example of a synthetic vernacular can be seen in the work of a formidable Austrian architect by the name of Peter Trummer who leads the Associative Design programme in at the Berlage Institute in the Netherlands. The aim of the project was to “develop a synthetic vernacular; a form of housing that evolves from its historical heritage, its site specificity, and at the same time able to present alternatives to tabular rasa urbanism… [as a result of China facing the difficulty of] how to develop a housing environment which is not a modernist type purely applied to accommodate the mass housing problem” ("Associative Design @ Berlage « Dysturb" 2007). As a team member to the research group goes on to describe: This project tries to learn from the spatial organisation of the vernacular models, using parametric design technique to explore possible model of modern Chinese living, offering alternative strategies for middle income people. The neighbourhood model is based on the construction of a series of associative protocols, transformed and developed by local economical forces, housing policy, ecological environment, and cultural or social demands of Chinese people. They are developed mainly on 3 different scales, housing units, housing clusters, and the whole neighbourhood. Figure 22 Associative Design diagram("Associative Design @ Berlage « Dysturb" 2007) 17 Figure 23 Associative Design diagram depicting node changes(“Associative Design @ Berlage « Dysturb" 2007) Figure 24 Associative Design diagram depicting spacial qualities of created courtyards(“Associative Design @ Berlage « Dysturb" 2007) Moreover we begin to see that one of the greatest attributes we can learn from vernacular architecture or rather architecture that precedes our modern urbanised cities are the implicit algorithms manifested in their spontaneous generation. Whether it be spacial optimisation through fractal geometry or associative forces related to economic and cultural requirements, it is crucial to learn from the past in order to generate a synthetic vernacular. 18 Conclusions: Optimisation Through Fractal Geometry Moreover in this dissertation, I have explored the nature of fractal geometry, its use within the context of architecture specific to the Ba’Ila settlement in southern Zambia and explored how fractal geometry can enhance sustainability, facilitate scalability and can be used to negotiate spatial arrangements based on social factors. In order to establish the aspects of fractal geometry that can be used to provide optimal results in an architectural design approach, again I will refer back to the five essential components of fractal geometry devised by Ron Eglash. Fractal Dimension: Studies conducted by leading researchers at the University of Wisconsin suggests that stress (among other detrimental mental and emotional strains) can be reduced with a reaction to fractal patterns with an intermediate fractional dimension (around 1.3  1.5). This study is thought to be onbrought by evolutionary biology hardwired to the human brain as Yannick Joye explains that settings with a high fractional dimension could contain hidden dangers, such as ambushing predators, while those with a low fractal dimension probably do not contain enough elements, in order to off protection and sources of food. Hence we will be more aesthetically attracted and more relaxed in environments with an intermediate fractal dimension. Furthermore we can conclude that it would be important to consider that any architectural design approach based on fractal geometry should lie within this intermediate range if its purpose were to provide comfort and decreased levels of stress in its occupants and viewers as does the Ba’Ila settlement. Recursion: From the Ba’Ila settlement — which has two iterations of its fractal geometry — we learn that the number of iterations is not the most significant factor but rather the seed shape that defines the success of the geometry’s optimisation. That is, whether or not the seed shape, in the case of the Ba’Ila village, can sustain a family or store enough crops or provide enough room for cattle. Similarly a seed shape developed for a contemporary use of fractal geometry in perhaps a residential block can consider the minimum requirements for the smallest possible studio apartment. After the seed shape has been determined, recursion can occur as many times as new spaces are required. Yet it is also important to remember that in some cases, the more iterations made can mean the further the distance from the final iteration to the initial seed (or perhaps the studio apartment from a main courtyard in the example given earlier). Self Similarity & Scaling: Self similarity and scalability allows for ease of assembly and sustainability as each of the elements of the geometry is more or less configured in the same manner with small tweaks for enhancements or programmatic requirements. Use of homogenous materials that can be locally sourced (which isn’t a necessary criterion for fractal geometry) add to the scalability and allow the local community to feel that the architecture has been built for them by them. More importantly is the question of statistical self similarity or exact self similarity (where the Ba’Ila village is statistically self similar). Since exact self similarity is mostly only found in mathematical models, I would say that it is more organic to produce statistical self similarity where computer algorithms can generate an exactly self similar form and an architectural designer can begin to tweak it for further optimisation thereby resulting in statistical self similarity. Infinity: Although the concept of infinity with regard to fractal geometry is only really relevant when discussing pure mathematics, I feel that introducing the concept to the architectural discipline (within the context of fractal geometry) would complement the component of scalability. That is, if a form were to be designed based on fractal geometry to be modular, then being able to perpetuate its construction indefinitely would in many ways add to its value. A building that can be infinitely manipulated can have infinite possibilities. 19 Informing Design Programmatic Starting with the programme for my project which aims to create a cultural centre for Black Africans in Hackney Wick comprising of galleries, entertainment spaces, a learning centre and food court, I explored different ways in which my spaces could be organised in order to provide an experience that integrated learning, doing and buying, similar to the market environment found in West African countries. I explored fractal geometries that were inspired by those I researched whilst undertaking this dissertation. Figure 25 Spatial layout diagrams (Personal Collection) Figure 26 Spatial layout diagrams (Personal Collection) 20 Figure 27 Spatial layout and connectivity diagram indicating connectivity to central food court or courtyard similar to Ba Ila settlement (Personal Collection) 21 Formal Figure 28 Initial design form finding process (Personal Collection) Fractal geometry is also in consistent use during my initial form finding process as I start with the initial geometry of an umbrella (alluding to universal market typologies) and begin to evolve the geometry into a more complex form by alternating component scales using fractal geometry as demonstrated in Fig28. Figure 29 Design development sketches (Personal Collection) 22 Figure 30 Diagrams indicating control variables of generated geometry to suite different programmatic and environmental conditions (Personal Collection) Figure 31 Sketches and diagrams demonstrating spatial and environmental potential (Personal Collection) 23 Figure 32 Collage demonstrating potential market layout scheme for design proposal (Personal Collection) I then begin to imagine control variables that can be used to optimise the geometry for different programmatic and environmental conditions in Fig 3032. Through conducting this dissertation, my goal is to develop a design proposal that emulates a synthetic vernacular with its roots in fractal geometry that also celebrates African culture, technology and materiality as I develop into the next steps of my project. 24 Bibliography "Great Mosque Of Djenné". 2019. En.Wikipedia.Org. https://en.wikipedia.org/wiki/ Great_Mosque_of_Djenn%C3%A9. Eglash, Ron. 1999. African Fractals. Rutgers University Press. Joye, Yannick. 2007. "Fractal Architecture Could Be Good For You". Nexus Network Journal 9 (2): 311320. doi:10.1007/s000040070045y. "LowRise, HighDensity HousingDigitális Tankönyvtár". 2019. Tankonyvtar.Hu. https:// www.tankonyvtar.hu/hu/tartalom/tamop412A/20110055_low_rise_high_density/ ch03.html. Random House Unabridged Dictionary: Kraal: "Origin: 1725–35; < Afrikaans < Portuguese curral pen" "Ila People". 2019. En.Wikipedia.Org. https://en.wikipedia.org/wiki/Ila_people. "Zulu Culture  Building The Zulu Kraal". 2019. ZuluCulture.Co.Za. https://www.zulu culture.co.za/zulu_kraal_building.php. Smith, Edwin William. 1949. Addendum To The "IlaSpeaking Peoples Of Northern Rhodesia" Dh[Microform]. "Archittura". 2010. Domus La Nuova Utopia, no. 940: 4749. http://www.codesignlab.org/ attachments/article/176/Domus%20n%C2%B0%20940%20%E2%80%93%20Sept. %202010.pdf. "Associative Design @ Berlage « Dysturb". 2007. Dysturb.Net. http://www.dysturb.net/ associativedesignberlage/. 25 View publication stats
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