3 2 Analytical Study of Urban Development Projects that Use Parametric
2.1. Mathematiciansâ Contribution to Architectural Design
Research shows that the pinnacle of mathematical ingenuity was reached duringthe Timurid Dynasty in the fourteenth century when the strong relationshipbetween mathematicians and architects first began. Although the Seljukâs andthe Mughals excelled the fields of art and construction, Islamic scholars areresponsible for the development of these domains. The height of intricateornamentation used to decorate monuments was under the Safavid Dynasty, asseen in the use of geometric ratios to embellish the Nezam al-Mulk dome in theGreat Mosque of Isfahan. After the Safavid period, the use of mathematics inarchitecture declined due to the arrival of western methodologies thataccorded greater importance to philosophical and theoretical issues.  Figure 1 represents the most outstanding example of the advanced used ofmathematics in construction. The double-shell mausoleum dome, located in thecity of Sultaniyah in central Iran, is 45 meters high and 24.5 meters indiameter. In spite of its huge size, only a small number of pillars supportit, and there are no struts or beams. This obviously required a calculation ofconstruction weights prior to building, confirming the use of advancedmathematical applications. | Figure 1. Uljaytu Sultaniyah Source:www.archnet.org/sites/1671 —|— Regarding shapes and formation, Islamic architects excelled in producingprecisely formed, intricate decorative shapes that can be easily translatedinto mathematical equations, making it possible to categorize the rules thatgovern formation processes and to organize the minute geometric components ofeach decorative element. Illustrative examples will be analyzed later in thispaper. Mathematics is an abstract science that involves the use of symbols to expressrelationships between non-material things. It is a scientific discipline borneof human intellectual ingenuity and innovation. Mathematicians are artists;their medium is the mind and they produce ideas. The most important attributeof mathematics is that it is a research method that depends on logic andmental processes. The study of different ancient civilizations reveals thatartists resorted to mathematical functions to create regularized geometricshapes, starting with the ancient Egyptians, then the Greeks and Romans and,finally, the Islamic civilization (the most precise and comprehensive incomputational design interpretation). After its discovery, the Golden Ratioconcept and its influence on the ability to recognize and assimilatearchitectural facades became widely used. We will proceed to review some ofthe civilizations whose architecture depended on purely mathematicalfoundations. 
2.1.3. Islamic Architecture
| Figure 4. Taj Mahal, India: Application of the Golden Ratio to the buildingand its components â the intricate tile decorations, produced in the middleAges, exemplifies the use of geometric patterns by Muslim architects, Source:Abu El Ela, Salwa (2017) —|— New technologies and the digital revolution concepts emerged as a continuationof previous trends. The digital revolution affected all aspects of life,particularly architectural design. Architecture is a mirror that reflectssocial change and development; it can be used to discern social conditionsclearly. New techniques born of the digital revolution produced differentconstruction and design methods used in the treatment of materials, formationsand functions. The innovative and creative qualities they added toarchitecture came to be known as âdigital architecture. The digital revolution is the outcome of the extensive integration and overlapbetween several technological revolutions. The first revolution was theinvention of the personal computer, the second was the World Wide Web and thethird is the tremendous advances in media technology.  Parametric design is one of the modern computational / digital design systems.It is a process based on algorithmic thinking that is able to coordinatedifferent data and types of information, which are introduced into the programto be translated into formulae that are then applied to the design. 
2.2. Parametric Architecture
Parametric architecture refers to a number of parameters (variables) relatedto a specific design. By changing the values of these parameters, one cancontrol and modify the designâs shape and proportions. Parameters can alsobe altered to produce an infinite number of similar designs producing a finalarchitectural product that is coherent in aspect. Parametric designs aresimply architectural designs produced with the help of complex mathematicalprograms that interpret parameters and perform complicated calculations thatthe human mind is incapable of, to produce the formation, or the apparentshape of the design. The relationship between design elements and parametersin the built structure is presented in a complex geometric relationship.  Parametric design can also produce metamorphic forms (Para Morph) that appearto be moving in space, but whose components are structurally stable.Parametric architectural forms are expressed through a set of algorithms.These highly complex formulae cannot be managed by the human mind alone;complex parametric equations are handled by computer algorithm programmingtechniques to produce the required formation. 
2.2.1. Parametric Architecture Examples
| Figure 5. Illustrative images of the complex initial configurations ofparametric design, how they are related, and their ability to move within acontrolled frame, Source:http://www.aecbytes.com/newsletter/2016/issue_82.html —|— As explained above, parametric design enhances a designerâs creativity byproducing thousands of designs that explore non-conventional shapes, which adesigner is unable to imagine on his / her own. It also makes it possible fordesign systems to choose among the several solutions and ideas resulting fromthe process. This is done within a highly rigid framework determined by thescope of the problem and the requirements that the design needs to fulfil.Nevertheless, parametric design is most apparent in problems related to shapeand form, for computers are very effective tools for creating differentdesigns and providing an endless number of solutions and alternatives, such assimulating natureâs behaviour in formation constructions. | Figure 6.Illustration of Parametric Thinking in FaÃ§ade Design: Abu Dhabi Tower,Source: https://draftsman.wordpress.com/ —|— | Figure 7. Illustration of Parametric Thinking in FaÃ§ade Design: The GrandMacao Hotel, Source: https://issuu.com/albenaa/docs/issue_325/60 —|—
2.2.2. Parametric Designâs Ability to Simulate Nature
In appearance, parametric shapes resemble organic and non-organic naturalphenomena that result from the self-development of natural elements. Contraryto the shapes produced by previous design movements, parametric designproduces shapes that resemble nature in appearance and structures that imitatethe biological functioning of natural elements. Known as Bio morphism, thisdesign approach is the result of using an algorithm that simulates natureâsbehavior (a genetic algorithm) to produce structural forms. | Figure 8. OceanWave Formation: An Example of Non-organic Natural Shapes, and Internal BoneStructure Formation: An Example of Organic Natural Shapes Source:  —|— It is also possible to pull architectural shapes away from nature by usingindustrial forces that simulate natural forces, such as gravity, wind,sunlight, push and weight forces that are governed by laws and affect shapes.Interactive computer programming scripts are used to produce these kinds offorces.  Parametric forms in nature include many models and patterns, some regular andsome irregular. They depend on parameters that are defined repetitively orsystematically and are based on the repetition of a given element that iscompletely identifiable in nature. Examples of parametric models and patternsin nature are presented in the table below. | | Table 1. Parametric DesignPatterns, Source:  — This section of the paper has presented an overview of the origins andthinking that led architecture to resort to using calculations and equationsin design. Natural forces and the ideas of ancient architects and artistscontributed to this development and the outstanding part played by technologyenabled architectural design to reach an advanced level, capable of expressingmotion and flexibility, which can be used to support various differentorientations. The next section of the paper will analyse a number of parametricarchitectural and urban models and examine more closely the mathematicaldetails that produced this type of architectural thinking and its applicationin a number of different forms that are more developed than the originalversion of parametric architecture.
3.1. Analytical Study of Types of Parametric Design in Ancient
Civilizations The numerous studies conducted in the field of architectural formations havemade it possible to identify the design elements that are most responsive toparametric design i.e. Islamic design elements. This is because the symmetryand standardization of Islamic shapes and formations mean that they have manyof the repetitive qualities for which the program can create parametricmodels.  Numerous experiments have been carried out using the basic units oftraditional Islamic design elements, which range from cells to patterns. Manydiscrepancies were found because the parametric process allows designers tomanipulate entire patterns. The most important aspects, or levels, of Islamicarchitecture, categorization and description have been analysed.
3.2. Analytical Study of Urban Development Projects that Use Parametric
Design Since the emergence and spread of architectural applications and the attemptsto use algorithms to introduce parametric methods and design intoarchitecture, parametric design has become a source of many uses and benefitsthat are most effective when applied on a large scale, i.e. at the urbanlevel. The works of Zaha Hadid and the writings of Patrick Schumacher areamong the most important experiments in this field.  This approach also provides great potential for modifying plans and producingdifferent alternative planning solutions in any given location by altering theangle of rotation of individual buildings or districts. | Figure 14.Planning Alternatives for the Same Design, Produced by Parametric Design,Source:  —|— Certain types of algorithms can also produce planning alternatives for anurban area. One example is Cellular Automata (a group of cells that areorganized on a grid according to a standard determined by the designer,thereby producing alternative designs for a given urban site).  The above analysis shows how algorithms and parametric design can be used toassess solutions. Below is an overview of the most notable urban projects thatuse parametric design to achieve the required output.
AP Polytechnic Lecturer Syllabus 2019: Architectural Engineering
Engineering Mechanics | Landscape design and site planning —|— Basic Design | Building Services Building materials | Sociology of human settlements Building Construction | Economics, Estimating and costing Architectural Drawing and Graphics | Town Planning Introduction of art and architecture | Building Acoustics History of Architecture | Advances construction Water supply and Sanitary Engineering | Professional Practice Climatology | Computer applications
AP Polytechnic Lecturer Syllabus: Chemical Engineering
Process Calculation and Thermodynamics | Instrumentation and Process Control —|— Fluid Mechanics and Mechanical Operations | Plant Design and Economics Heat Transfer | Chemical Technology Mass Transfer | Chemical Reaction Engineering
3.2. Bio-Based Architecture
Enliven the building is one of the main tendencies of this kind ofarchitecture. Charlie Luxton one of the pioneers in the field of Bionicarchitecture says the main point of this architecture, is best using materialswhich cause the strength of building and architectural flexibility andvariety. Bio-based architecture on the here considered authors, as inarchitectural design inspired from nature, which is focused on the rules oflaws that govern nature. In fact, Bionics architecture is engineering designprocess based on the new systems which are available in nature.
4. Bionics and Tall Buildings Design
Design a building as the result of detailed studies and the process iscomplex, with many challenges surrounding such as structural, mechanical andelectrical, cooling, shell building, protection, and security and so on. Sincethe beginning of human life, a world of mystery of nature has been a goodinstrument for solving these challenges and bionics bridging the gap betweennature and technology. Construction is usually based on a common simple system such as: column, beam,electrical and mechanical ducts. But the nature is based on sustainabledevelopment of complex systems. As mentioned, bionics is knowledge ofcombination of different concepts of Natural Sciences, Engineering, formedwith the study of complex biological systems, living organisms, natural forms,respond well to solve the technical problems of structure engineering. Bionicsstructures with caused a revolution in technology development and itsassociated structures in the world of science that is still being developed. |Figure 4. Shanghai Bionic Tower based on bionics model of the tree root —|— Bionic Tower is the natural model for use in structural design model offers asmart feature. Application of Natural templates for tall buildings structuraldesign, focused not only natural, and so much more to be said, the buildingshell can both be involved so it intelligence.
5.1. The Structure of the Body as a Model for the Design of Tall
Buildings Define a building as tall buildings, the proportion of building height ordiameter that determines the type of geometry, which is high in thesecategories is given in Table 1. According to this definition, for a man beconsidered, H, and D averaged 180 and 40 cm, so H / D value of 4.5 isobtained, the human body among the structures is long to very long.| | Table1. High Definition based on Ratio of height to cross section — | Ratio of height to cross section H/D| 1.5Ï| Ï| 0.5Ï| 1/3Ï —|—|—|—|— Building Type| Very Tall| Tall| Average| Short | Figure 5. Height ratio of the cross section scale for high levels —|—