Extended Abstract

Algorithmic Tree-inspired Design

A link between manual and performative methodologies

José Maria Rodrigues de Freitas

SupervisorsProfessor Doutor António Menezes Leitão

Professor Doutor Miguel Amado

July 2019

Abstract. Architects throughout time have been always enthralled by the mechanisms por-traited by nature in its ecosystems. They have explored how to mimic these models and be-haviors, translating them into design solutions. First, decorate their creations and, then, asa mean to solve structural problems. Humans have always been drawn to follow nature andits patterns, so architects are bound to search for inspiration in nature, mainly trees and othervegetal shapes. As such, many examples of tree-like designs can be seen depicted in differentstyles of architecture, in different ages.

Recently, a more formal approach to these natural mechanisms - Biomimicry - has emerged,leading to the development of new design methodologies. In an increasingly performance-focused environment, many of these new methodologies are focused on the performative char-acteristics of these natural elements. They produce complex shapes, coined tree-inspired (ordendritic) structures, optimized to answer structural, cost or production-oriented objectives.However, they distance themselves from traditional approaches, provoking changes in the wayarchitects design, that can be difficult to adapt to, and usually require a loss of the creativefreedom exerted in the early stages of design.

Algorithmic Design presents itself as a possible methodology to incorporate performativeawareness into the early design phases, without the loss of creative freedom. Despite theinitial time required to create the rules and relations between the elements that define thearchitectural concept, the architect can build a program that defines its own creation. As aresult, he has the chance to find designs that were hidden before, but now surface has possiblesolutions to answer his conceptual needs. Furthermore, algorithmic design is a portable tool,capable of reproducing these algorithmic descriptions in diverse analysis tools, allowing for thestudy of the performative behavior of a design.

The present investigation combines algorithmic design and analysis tools in search for tree-inspired designs, as a method of linking traditional approaches and newer performative method-ologies.

Keywords: Biomimicry, Tree-inspired Design, Algorithmic Design, Performance

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IntroductionThe term Biomimicry first appeared in scien-tific literature in 1962, growing in popularityamongst scientists in the 1980s. It is definedas a new science that studies nature’s mod-els and imitates these designs to solve humanproblems (Benyus 1997). By mimicking andemulating nature in its analogies and patterns,Biomimicry allows the most distinct fields andareas of research to learn from the largestdataset of information available to humanity -nature.

Since the Greek-Roman period, wheremaster builders’ built columns inspired in nat-ural shapes, architects have drawn inspirationfrom trees and plants. Moreover, trees are or-ganisms with an inherent structural rational-ity. As specimens that stand on their own,they are exposed to different types of externalloads, to which they systemically adapt theirshape. Recently, as the interest in biomimicryis renewed, so these tree-like structures ob-tain a new terminology, dendriforms, or den-dritic structures.

This renewal in the study of nature ele-ments was proppelled by the growing con-cerns with sustainability and the rise of the dig-ital tools. As a result, a plethora of computer-supported algorithmic (Terzidis 2006) andparametric techniques (Woodbury 2010) pro-vide now the tools for the design and construc-tion of these dendritic structures. The popular-ity of these tools has created a shift in the wayarchitects design, as they offer the possibilityof model generation and create a wide rangeof variations almost effortlessly.

Furthermore, an increasing emphasis onbuilding performance - kindled by the possi-bility of future innovations and technologicalprogress in construction (Hensen and Lam-berts 2012) - is influencing the processes andpractices in building design, by blurring theboundaries between appearance and perfor-mance (Kolarevic and Malkawi 2005). Thisled to the development of several simulation-based analysis tools and optimization meth-ods. One of the challenges in performance-driven design methodologies is the effectiveintegration of simulation and optimization tech-niques with parametric design and generative

procedures (Rivka Oxman 2008).

For this dissertation we introduce a tree-inspired approach supported by algorithmicdesign to pursue a performance-driven frame-work that functions as a tool for design. Ourgoal is to merge advantages existent in thesethree distinct fields, understand their potentialsand narrow their limitations. At the same time,it is essential that the architect retains its abilityto hold power over the design intentions, for-malization, and development. As such, perfor-mative architecture should focus on form andfunction, efficiency and sustainability, whilepreserving the intentions portraited by the de-signer. The proposed methodology allows ar-chitects to model and explore their ideas, us-ing a parametric description to define their hi-erarchies and relations. Moreover, a connec-tion to analysis tools, early in the design, letsthe architect project with a performative con-sciousness.

Biomimicry in ArchitectureBiomimicry was defined by Janine Benyus inher 1997 book Biomimicry: Innovation Inspiredby Nature. As a new science that applies na-ture’s models to human problems, Biomimicryaims to promote "nature as a model, measure,and mentor" (Benyus 1997).

A biomimicry-oriented design typically fallsinto two distinct categories: (1) the Top-Downapproach (Design Looking to Biology), wherea human problem is formulated, and then a so-lution that can be correlated is sought in na-ture; and (2) the Bottom-Up approach (BiologyInfluencing Design), where the study of differ-ent features in nature can then be translatedinto a solution for a human problem (Knippersand Speck 2012; Helms, Vattam, and Goel2009).

Besides these approaches, there are threedifferent levels of Biomimicry that can be ap-plied to design problems: form, process, andecosystem (Zari 2007). These levels repre-sent three different scales of mimicry: (1) theorganism level mimics the characteristics of anorganism, the way it looks or what it produces;(2) the behavior level mimics a certain behav-ior of an organism, or between organisms; (3)the ecosystem level, which is defined by the

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mimicry of a characteristic of a whole ecosys-tem. Each scale can be stratified into five dis-tinct dimensions: form, material, construction,process, and function.

In the article "Tree-inspired dendriformsand fractal-like branching structures in archi-tecture: a brief historical overview", Rian andSassone 2014 present a detailed review oftree-like structures, one fo the primary appli-cation of biomimicry to architecture, which wasessential in the redaction of this chapter.

BIO-INSPIRED STRUCTURES

Humanity has been fascinated with naturesince its been able to comprehend naturalshapes and meanings. "Several ancient cav-ern painting arts, from the pre-historic ages,have been found depicting figures of trees andplants" (Rian and Sassone 2014).

In the period of the Ancinent Egypt (3000B.C. to 600 B.C.) an accentuated inspiration invegetal shapes can be seen in structures rang-ing from palaces to pyramids. Sculpted capi-tal built in sandstone can be seen emulatingpapyrus plants (Figure 1a) (Shaw 2003). Ad-ditionally, in the Classical and Greco-Romanages, capitals of the Corinthian and Compos-ite order, some friezes, and most aestheticalembellishments, use the acanthus plant as asource of inspiration, replicating its intricateshapes and enriching the architectural orna-ments.

Nevertheless, only later would start thebiomimetic pursuit that led to the emergenceof tree-inspired designs. Two thousand years

away from us, the Chinese Dougong Bracketscan be considered the first true tree-inspiredstructure. Inspired by the organization of treebranches as a cantilever, the Dougong is an"assemblage of structural cantilevers placed inbetween the column and the beam, that car-ries the load of the beam and the overhang-ing roof into the column" (Rian and Sassone2014).

Later in the medieval period, cathedralswere one of most common typologies to bebuilt at the time. In their interior, this formaltendency also manifested itself through tree-inspired fan vaults. One of the first exam-ples appeared in the Sainte-Chapelle churchin Paris in 1248 (Figure 1b) (Leedy Jr 1978)and were characterized by ribs which formeda conoid shape, "that provided both compres-sive forces along the entire upper edge ofthe conoid, and stress equilibrium, as well asgranting structural strength" (Rian and Sas-sone 2014).

From the late 19th century up until the 20thcentury, during the period that represented"the crowning of the decorative arts in archi-tecture" (ibid.), the Art Nouveau, some tree-inspired structures can be seen in the designsof Antoni Gaudí, like the Sagrada Familia, inBarcelona. He resorted to physical models, in-spired by mechanical and structural character-istics of nature, to find the most suitable form.

Throughout the 20th century, there was apredominance in the use of steel to constructnew buildings. Though, the structural signifi-

Figure 1: (From left to right) (a) Ancient Egyptian columns inspired by a bundle of papyrus plants in Luxor Temples, Egypt, built in1400 BC; (b) Saint Chapelle in Paris, built in 1248; (c) Dendritic structure in Stuttgart Airport, built in 1939.

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cance of dendritic shapes was not addresseduntil the study of lightweight structures by FreiOtto. (Nerdinger 2005), who methodically re-searched the structural aptitude of branchingstructures for the Stuttgart Airport (Figure 1c)(Stuttgart, 1939).

Performative Architecture

Performative architecture can be defined as anarchitectural approach focused on the project’sperformance. However, this concept is not en-tirely new. For instance, entites like AntoniGaudí and Frei Otto were already exploringform-finding techniques that maximized perfor-mance.

Pioneer in experimenting a form-findingapproach, Gaudí studied the loads in a struc-ture "by suspending it inversely with cables,letting gravity portrait the structural potential ofthose shapes" (Kilian 2004).

Otto’s lifelong research was into lightweightstructures, i.e., objects with very little mass,carved to withstand great loads. That led himto be inspired by a natural philosophy that fo-cused on a relationship between architectureand nature, and their performance. Otto con-ducted experiments with lightweight tents andsoap films, suspended constructions, domeand grid shells, and branching structures (Fig-ure 2b).

Nowadays, as digital technologies are as-suming a prominent role in performance-

based design, these form-finding methodolo-gies have converged into simulation and anal-ysis tools available to any architect or engi-neer. In fact, they have allowed for the re-definition of a term that has now become oneof the techniques most frequently associatedwith performance – optimization (Rivka Ox-man and Robert Oxman 2014).

Optimization defines the process of mak-ing something, such as a building’s design, asfunctional or as effective as possible (Nguyen,Reiter, and Rigo 2014). To this end, the opti-mization process requires parametric design,so that multiple variations of a design can beevaluated. Due to its intrinsic parametric na-ture, algorithmic design can be combined withsimulation tools to better perform an iterativecycle, capable of optimizing the building’s per-formance (Rivka Oxman and Robert Oxman2014), while pursuing the preferred design.

Algorithmic Design

Algorithms are sets of rules, which translate in-structions given by a human, and can be per-formed by a computer, in order to solve a prob-lem (Burry 2011), in this case, a design prob-lem. Algorithmic Design (AD) is the creationof architectural designs through these algorith-mic descriptions (Gerber and Ibañez 2015). Afundamental difference in this new paradigmis the necessity of "relating and repairing hier-archical relations between the different parts

Figure 2: (From left to right) (a) Suspend chain model of Gaudí’s catenoids; (b) Frei Otto’s Stuttgart airport suspended model; (c)Typical algorithmic design and analysis workflow: (1) the algorithmic design tool generates the model in a 3D modeling tool, (2)the model is exported to the analysis tools where the architect can visualize the results and/or, (3) the results are retrieved forfurther processing.

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of the design" (Branco and Leitão 2017), in-stead of adding or subtracting elements to newiterations of the same design. This type ofapproach to digital modeling allows the userto explore a variety of different ideas withouthaving to rework on the model for every duechange (Woodbury 2010).

Additionally, new tools start to incorporatethese algorithmic rationalizations into a pro-gramming environment capable of convertingthem into a modeling tool, enabling the archi-tect "to visualize and iterate his design at theearliest stages" (Branco and Leitão 2017) (Fig-ure 2c).

Proposed Methodology

Biomimicry is now a well-established area ofresearch within the domains of architectureand engineering, expanding the limits of de-sign and construction. Inherently sustainablein its nature, it allows for the pursuit of themost diversely performative designs, inspiredin the potentialities found in nature (Figure4.1). Performative Architecture rapidly be-comes entwined some aspects of our livesand it functions as the conduct wire betweenthe present and future. Most newfound ap-proaches press onto following performativegoals and demands, and the design processis shifting to accommodate to the new needsof the built environment. Algorithmic Designshows a promising future in design explo-ration, and the correlation of multivalent pro-cesses and typological transformations. Itpresents itself as an antidote to the repetitiveand time-consuming tasks of production of de-sign (Burry 2011) and a mechanism for fasterand cost-effective fabrication.

Given these developments, complexity isnow a trend amongst researchers, and newapproaches show promising sculptural de-signs. However, a disparity between re-searchers and manufacturers is growing asthese methodologies require certain produc-tion methods (Bialkowski 2015) that are notyet available to most construction companies.As a result, these methodologies are limitedto their use in the academic environment, dis-missing the possible advantages of having

feedback from actual manufacturing compa-nies. Additionally, new methodologies pro-pose intense shifts in the architectural prac-tice, leading to a stagnant relation between theactual approaches and new methodologies, asarchitects may struggle to adapt to the newtechniques.

Our main goals with the development ofthis thesis is to explore how can biomimetic ap-proaches be applied to a performance-baseddesign in architecture, whilst corresponding tothe needs of the contemporary manufacturers,and current architectural practices. We pro-pose a methodology based on developmentof a tree-inspired design that is described bya computer script that can not only generatethe model in the intended visual tool, but alsoconnect to the required analysis tools, to ef-fectively produce a performance-based form-finding framework. It takes advantage of den-dritic shapes and their natural structural fit-ness, and promotes a way of designing thatallows the architect to freely create.

The proposed framework aims to covera gap in the industry, where biomimetic andalgorithmic methods are neglected insteadof more production-oriented approaches, fail-ing to reach their full potential. Despitethe growing focus on performance, the earlyphases of the design can still be lackingthe tools to help architects generate a moreperformance-based design since the concep-tualization stage. For the evaluation of themethodology we started our investigation byapplying it to an already existent building thatpossesses characteristics that are directly re-lated to a biomimetic-oriented design. To fur-ther prove the viability of the proposed frame-work, subsequent original creations were de-signed.

Case Study

The chosen case is a tree-inspired design thatbenefits from an algorithmic-based approachand form-finding optimization, due to its geo-metrical complexity, and structural fitness. TheOriente Station is characterized by its canopy-looking structure, resembling a grove of trees.Like many other Calatrava projects, it is a dy-

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Figure 3: (From left to right) (a) A render of the case study: Oriente Station; (b) Table of the parameters defined for the OrienteStation.

namic structure, meant to merge sculpture, ar-chitecture and engineering.

In order to create a parametric interpreta-tion of Oriente Station adapted to this frame-work, it was essential to set objectives. Initially,we defined a baseline for tree-inspired struc-tures, so that new designs could be achieved.Secondly, we connected the geometrical rulesof the already built Calatrava’s Oriente Sta-tion, to understand the feasibility of the tree-inspired framework. Most tree-inspired struc-tures can be stratified into three main sections:(1) the trunk, represented by one or more mainbranches, usually convergent to a central pointclose to the ground; (2) the crown, where thefoliage, in this case the roof resides; and (3)the twigs or the interconnecting branches, re-sponsible for connecting the other elements.

The trunk functions as the main centralstem, responsible for the growth of the treein height, its structural fitness, and distribu-tion of branches and leaves, so they can re-ceive light to encourage a healthy growth. Thisphenomenon is called Apical Dominance andis defined as a self-correcting and counter-

gravity growth process (Mattheck and Kubler1997). The branches connect the main stem tothe crowning foliage. They support the leavesand transfer the momentum to the main stem,allowing the tree to withstand greater loads.

In Oriente Station we can find elementsthat represent each of these components thatdefine trees. The main trunk is representedby four thicker columns that meet at the bot-tom in a thicker individual column, responsiblefor the weight distribution of the smaller beamsand most of the structural fitness of the struc-ture. The crown can be divided into two parts:(1) the roof elements, composed by the pro-tecting shell, laid on top of the structure; and(2) the roof beams, where the external loadswill be applied, functioning as the link betweenthe roof and the trunk of the structure (Fig-ure 3a). Lastly, we chose the parameters thatwould define these shapes (Table 3b). Theyare intrinsically related to the structural simu-lation and evaluation.

Tree-inspired DesignAfter understanding what characterizes a tree-

Figure 4: (From left to right) Renders of the tree-inspired designs: (a) Trees; (b) Mushroom; (c) Hexcentric; (d) DNA.

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inspired design, and how a framework can bebuilt around it, we created some designs, rang-ing from simpler to more complex designs:Trees, Mushroom, Hexcentric and DNA (Fig-ure 4), each with one main defining char-acteristic, that would help us further ensurethe viability of the framework. Furthermore,tree-inspired designs tend to produce a forest-like canopy, where many structures are con-nected to each other in a grid, so they cancreate a dense shell, that can support its ownweight and external loads, while covering theground. In the following designs, we createdthree types of grids, that usually define theroof configuration of each structure: rectangu-lar, hexagonal and diamond grids (Figure 5).

Figure 5: Grid organization of the tree-inspired designs: a)Rectangular Grid; b) Hexagonal Grid; c) Diamond Grid.

The resemblance between the differenttree-inspired designs is palpable, as they allshare common characteristics. Nevertheless,it is important to consolidate and compareeach design to preconceived notions that canfurther enhance the validity of the framework.To this end, we created a comparison table(Table 1) that shows the similarities and differ-ences of each design, in relation to the others.The categories were based on the character-istics found in trees, such as (1) the numberof steams, (2) the position of the main stem tothe overall design, (3) the canopy grid shape,and (4) how the branches are connected.

Table 1: Summary table comparing the different tree-inspireddesigns and their relations.

Performance Analysis

A structure is considered to perform well interms of structural fitness if it has the neces-sary strength to withstand the internal and ex-ternal loads to which it is subject on a dailybasis. Considering our framework, which pro-duces canopy-like structures with a roof shellcovering the whole, most of the external loadswill be applied on the roof. Therefore, differ-ent roof areas will have distinct external loadsapplied and a different structure weight. For-tunately, algorithmic approaches can disclosewhich parameters are related to the size of theroof and connect them to the external loadsinput inserted into Robot. This promotes anautomated process, avoiding the necessity tocalculate the external loads applied for eachdifferent roof surface.

There are several advantages of the use ofalgorithmic design and analysis into the earlydesign stages. Firstly, the cyclic iteration thatis generated provides performative feedbackin the conceptual phase. Secondly, the archi-tect is more aware of the structural strengthsand weaknesses of his/her own design, whichresults in a more structurally conscious de-sign. Thirdly, the portability of the algorith-mic design software allows the architect to pro-vide the same analytical model to the engi-neers in a later phase of the design, allowingthe specialty to further optimize the structure.Furthermore, the time-consuming task of pro-ducing the analytical model out of plans andsections is no longer necessary. Fourthly, theparametrization of the design can be made toanswer to multiple objectives, depending onthe focus of the architect. This, for example,not only assures the structural feasibility of thedesign but can also diminish material usageand maximize cost efficiency.

Evaluation

A tree-inspired framework using algorithmicdesign to pursue performance-driven designcan be very different from both traditional man-ual approaches and contemporary topologicalmethodologies. Moreover, as algorithmic andperformative approaches start to envelop themore conventional ones, a transitional frame-

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work helps with the introduction of new tech-nologies to the already established architects,engineers, and manufacturers.

The framework presented in this disserta-tion does not intend to transform the currentdesign process into a form-finding methodol-ogy, but rather to inform the architect in theearly phases of design, about domains thatusually appear later in the design process. Inorder to understand the validity of the frame-work, metrics related to both traditional andperformative methodologies have been tested,presented in the following subsections.

STRUCTURAL FEASIBILITY

The integration of analysis tools into the earlierphases of the design is slowly becoming es-sential in the current performance-driven pre-rogative. Nevertheless, most approaches ei-ther use them in the final phase of design,where changes turn into time-consuming pro-duction tasks, or do not exist at all. Contrarily,our framework is supported by a direct con-nection between the algorithm and the analy-sis tools, since the birth of the concept, wherethe rules and relations are defined within thealgorithm.

As such, different designs were producedand analyzed at two different scales: a macroscale, considering the width of the roof andheight of the structure, and a micro scale,where the radius of the main stem truss barswas examined. At the macro scale, the struc-tures present themselves structurally fit. De-spite their distinct array of parameters valuesin height and width, the great majority of the re-sults is within the legal boundaries. At a microscale, the results retrieved were examined af-ter the initial analysis at a macro scale. Thus,the results are all within the boundaries estab-lished as the legal values allowed. The resultscan be seen and compared in Table 1a and 1b.

Figure 6: (From up to bottom) Table of analysis results at a(a) macro scale and (b) micro scale. The max displacement -Dmax - changes according to the width.

DESIGN ORGANICITY

Complexity is the trend of contemporary archi-tecture. New methods and construction tech-niques have allowed architects, engineers,and designers to create intricate shapes andspaces, where distinct design intentions cancommune in harmony, or in contrast. Techni-cal advancements in the manufacturing indus-try have led designers to push the boundariesof what was thought to be possible.

Our framework finds common ground be-tween traditional approaches and the perfor-mative methodologies. For instance, it allowsthe architect not only to be fully in control of thefinal design solution, but also to be knowledge-able about its structural fitness. It incorpo-rates structural analysis into the early designprocess as a tool, instead of a form-findingmethodology, where the architect is dependenton the final solution.

Nevertheless, the framework still lacks theorganicity seen in the newer methodologies.Our intention is to develop a tool that gener-ate designs that can be produced using sim-ilar manufacture techniques to the ones usedin manual approaches. Thus, in our specificcase studies, the designs created are condi-tioned by the usage of steel truss bars, whichcan pose as a limitation to the complexity ofthe design morphology.

THE ARCHTECT’S ROLE

The role of the architect has shifted throughoutthe years, as new methods are conceived andnew technologies are developed. The digitalera brought us computerization, which gave usthe ability to take advantage of digital tools toproduce rigorous drawings within a managabletime frame. New methodologies focused onperformative goals require initial design needsthat may remove the ability of the architect tocreate freely. At the same time, new methodsusually require an initial time investment. Nev-ertheless, performance is becoming one of thedriving forces behing architecture, and there isa need to adapt.

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We establish a link between the tra-ditional approaches and the performance-focused methodologies. Firstly, tree-inspireddesigns assure a basis for a performative so-lution. Then, the architect can move towardsmore complex ideas, as he/she structures theconcept into logical relations, and lets thecomputer present him/her new unfound so-lutions. Afterwards, the architect can ana-lyze the structure in the analysis software, andmold his design to better correspond to its in-tentions. By pursuing a tree-inspired design,with the aid of algorithmic design, the architectcan pursue new objectives without changinghis role in architecture.

TIME DISTRIBUTION IN DESIGN

Design entails many intricate and complextasks, ranging from creation to production.Most architects start by examining the cultural,economic, historical, and topological contextof the building site, its surrounding, and theproject needs. Afterwards, a formalization ofa concept is made, supported by the contex-tual study and the architect intentions. Newermethodologies are more optimization-focused,merging the concept with performative goalsand conditions. The geometry is usually bentto answer the design’s performative needs andthe designer can end up neglecting the cre-ative process to pursue the best performance.

Our framework focuses on the balancebetween the ability to be in charge over thedesign decisions of manual approaches, andthe pursuit a performance-based design ofthe newer methodologies. By taking advan-tage of Algorithmic Design, the architect caneliminate the need of producing elements foreach iteration of the design. the parametricdescription is connected to the structuralanalysis tool, allowing the architect to be moreaware regarding the structural feasibility of thedesign. As such, the architect can balancethe aesthetics and performative needs onhis own accord. Furthermore, tree-inspiredstructures mostly ensure a basis for a struc-turally feasible design, so the architect isfree to explore more complex designs thatcan enhance his design intentions and cor-respond to the functional needs of the project.

ConclusionIn this dissertation, we proposed a solutionthat integrates Biomimicry into Algorithmic De-sign and Analysis, in order to promote a tran-sitional framework between the current man-ual approaches and the newer optimization-focused methodologies. The detailed frame-work combined the strengths of designing witha performative mindset - by having perfor-mance feedback in the earlier design stages -with the automation mechanisms provided bya parametric description. Additionally, it did notshift the role of the architect as the decidingfigure in terms of intention and concept formal-ization, allowing him/her to balance his/her de-cision with more performative awareness.

FUTURE WORK

1. Focus on Manufacturing Processes: ourframework could be enhanced by further con-necting the building design to the productiontechniques;

2. Extended Materiality: our methodologywas focused in steel truss bars but it wouldbe interesting to explore concrete-based solu-tions;

3. Design Organicity: Klemnt (2015) showedus it is possible to control the organicity of thedesign. Exploration into controling the level oforganicity of the design should enhance theframework;

4. Precise Structural Control: the frameworkfunctions as a tool to help the architect un-derstand the structural capabilities of the de-sign. Connection to an optimization algorithmshould help us understand the limitations ofthese structures;

5. Practical Experimentation: as a mean toevaluate the framework in a real scenario, andbetter attain the advantages the tool can offerto architects.

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