Generative system Research Papers

A Recursive Algorithm for the Generative Study of Seljuk Muqarnas in Kayseri and Sivas

2024

Recent developments in archeological research extend diverse technological methods for the geometric deciphering and cultural understanding of various historical building components. One of the emerging methods in this field is the... more

Fig. 1 The research scope of Seljuk structures between Kayseri and Sivas regions in Turkey. The silk road trading routes are shown in yellow lines while the red dots indicate the extensive locations of Seljuk structures ; Bottom left the location of Sivas and Kayseri in Turkey

Fig. 2 Workflow diagram showing the integration and development of computational tools for the archetypal investigation of muqarnas

Fig. 3 The mugarnas gate inventory extracted from Kayseri in Sivas showing diverse morphologies in vlan During the first phase of our research, all the selected structures are visited and documented using photogrammetry to extract the physical conditions and geometric configuration of the structures. Due to the orientation of muqarnas structures, the 3D forms of muqarnas gates can be captured from the ground plane by combining numerous pictures in Agisoft. The schematic explanation of photogrammetry, used data, and details of the model preparation, are explained in earlier work on structures found in Kayseri (Gdkmen et al. 2022). Table 1 shows the studied photogrammetric data of scanned muqarnas structures. These models are used for the reproduction of architectural drawings and refined 3D models in Rhinoceros.

Fig. 4 Top General images of the muqarnas; Bottom photogrammetric models of the Haci Kilic Mosque andthe Gevher Nesibe Madrasah in Kayseri and the Sifaiye Madrasah, and Cifte Minareli Madrasah from Sivas

Fig. 5 Muqarnas proportions juxtaposed according to ‘silver ratio’ (d, ) using unit measures extracted from_studied structures. By assuming a=1 as a unit measure, the following values are found: b = 2 —V/2.0=./4 — 2/2, d= V2 —1e= V2, f=1— 22, g= V22 A common approach for the geometric analysis and modeling o f mugarnas structures is established through planimetric drawings (Alagam et al. 2017; Agirbas and Yildiz 2021). As a stacked dome structure, muqarnas are composed of through triangular or quadrilateral pieces that can be compared through trigonometric angles, ratios and tile types. A fundamental characteristic of mugarnas is determined through the symmetry of the overall muqarnas that can follow or dodecagonal patterns—all of which can form quasicrystal be hardt 2007). While the cities of Kayseri and Sivas present examples of all the radia types (Gékmen et al. 2022), in this paper the focus will be on the identification o ayers that are formed octagonal, decagona havior (Lu and Stein

In Sifatye Madrasah mugarnas (Sivas) the computational analysis of its geometry, symmetry and growth shows that there is similarity in the development of the muqa- rnas in every three layers where muqarnas branch along the diagonal and orthogonal axis(Fig. 6). This is further supported by the secondary growth axis (green) that con-

Fig. 8 Computational analysis of the Cifte Minareli Madrasah in Sivas with the identification of muqa- mas symmetry groups, growth rules and 3D propagation of muqarnas showing quasicrystal develop- ment in plan

A Recursive Algorithm for the Generative Study of Seljuk Mugarnas in... Fig. 9 Computational analysis of the Gevher Nesibe Madrasah in Kayseri showing the identification of muqarnas symmetry groups, growth rules and 3D propagation of mugarnas that shows patterned development in plan

Fig. 10 Recursive rules extracted from the studied muqarnas structures

A Recursive Algorithm for the Generative Study of Seljuk Mugarnas in... Table 2 Recursive application of growth rules for the generative modeling of the Haci Kilic muqarnas. The dark grey rules show the growth rules that are applied for the current layer

Fig. 12 Parametric permutations of the studied muqarnas with growth rules. The variations are achieved by substituting syntax rules and triangle connections based on growth patterns extracted from case studies

A Recursive Algorithm for the Generative Study of Seljuk Mugarnas in...

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Beyond Flat Surfaces Parametric Derivations of Historical Islamic Geometric Designs

by Sema Alaçam

2023, Architecture and Planning Journal (APJ)

This paper sets out to identify a guiding methodology and define algorithms to extend the existence of Islamic geometric designs beyond flat surfaces. The paper discusses two computational approaches to deriving various non-flat geometric... more

Muqarnas, a vaulting decorative component, shows some of the earliest attempts to employ Islamic geometric design to generate a three-dimensional composition from two-dimensional design blueprints, as shown in the Topkapi and the Tashkent Scroll (figure 2) (Necipoglu, 1996). Karbandi is another possible employment of geometric designs to derive forms beyond flat surfaces, such as the ribbed dome that exists at the Great Mosque of Cordoba (figure 3). Unlike Mugarnas, the geometry is curved as if it is being projected into a round surface (Mohammadi et al., 2018). Fig.1: Contemporary examples of IGP on non-flat surfaces. Left: Cambridge Mosque (Image credit: Wikimedia). Right: Louver Abu Dhabi (Image credit: authors).

Fig.2: Left: page from the Topkapi scroll showing a 2D blueprint of a Mugarnas (Image credit: Wikimedia). Right: Mugarnas in the Iwan of the Shah Mosque in Isfahan, Iran (Image credit: Wikimedia).

Fig.3: The interior part of the dome of the Great Mosque of Cordoba (Image credit: Wikimedia).

Fig.4: Historical examples of the employment of Islamic geometric patterns on non-flat surfaces. Left: the dome of the Karatay Madrasa (Image credit: Wikimedia). Right: the dome of the Sultan Qaytbay Funerary Complex (Image credit: Wikimedia).

Fig. 5: shows the possible designs that can be derived from the same polylines by changing the employed symmetry (from top to bottom: rosettes, periodic, or quasi-periodic structural order). Rosettes patterns are formed by applying rotational symmetry to a particular geometric composition around a specified axis. This type of patterns can have several axes that goes from 1 to oo (Shubnikov 1974). Rosettes patterns have two types: cyclic and dihedral; cyclic is formed by applying rotations to the geometric compositions, while dihedral includes using reflection geometry in addition to the rotational symmetry.

Muqarnas is an exemplar case of the EPE method. Figure 6 shows an example of this method with a simple design. Fig.6: Square-based, Islamic geometric design was employed to generate the muqarnas-like form shown above through the manipulation of the z-coordinate of the points on different geometric patterns.

7ig.7: Left: shows example of a projected 2D Islamic Geometric Design on a curved surface. Right: tiling the derived form with the original 2D Geometric Design.

The Islamic geometric designs parameters are the symmetry type, points count, poin coordinates, and polyline intersections, all of which can explore the latent design space of a 2D Islamic geometric designs. The migration method parameters differ based on the employed method. For instance, the parameters in the Euclidean Point Extrusion are the Z-coordinates of the points and the shape of point connections. However, the parameters in the Curve Projection and Curve Mapping are primarily based on the shape of the HS. When combined, the two sets o parameters allow exploring the latent design space of Islamic geometric designs on a non-fla surface (figure 10). Fig.8: Curves Mapping method applied to a dome-like HS. Top: shows the process of unrolling the equivalent surface, inserting the desired design within, and mapping back the design to the hemisphere. Bottom left: perspective view illuminates the distortion occurring at the bottom edge of the HS when using the Curve Projection method. Bottom right: using Curves Mapping to fit a design into the hemisphere.

Fig.9: Computational process for exploring the latent design space of Islamic geometric design on non- flat surfaces.

Fig.10: Design variations were created using a fourfold Islamic geometric design and the Curve Projection method.

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Graphical Smalltalk with My Optimization System for Urban Planning Tasks

by Reinhard Koenig

2023, eCAADe proceedings

Based on the description of a conceptual framework for the representation of planning problems on various scales, we introduce an evolutionary design optimization system. This system is exemplified by means of the generation of street... more

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A generative design case study for UAV-based assembly and fabrication: parametric analysis and synthesis of Iranian-Islamic Muqarnas

by ERFAN ZAMANI

2023, Open House International

PurposeThis study proposes a DfMA (Design for Manufacture and Assembly) based on unmanned aerial vehicle (UAV) and uses Iranian-Islamic Muqarnas as the main case study due to their geometric modularity. In Islamic architecture, different... more

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Parametric Iranian-Islamic muqarnas as drivers for design for fabrication and assembly via UAVs: parametric analysis and synthesis of Iranian-Islamic muqarnas

by ERFAN ZAMANI

2023

This study proposes a DfMA (from design to assembly) based on Unmanned Aerial Vehicle (UAV) and uses Iranian-Islamic Muqarnas as the case study due to their geometric modularity. In Islamic architecture, different geographic regions are... more

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Graphical Smalltalk with My Optimization System for Urban Planning Tasks

by Reinhard Koenig

2022

Abstract. Based on the description of a conceptual framework for the representation of planning problems on various scales, we introduce an evolutionary design optimization system. This system is exemplified by means of the generation of... more

our evolutionary algorithm (EA). The main argument for EA is their flexibility in dealing with the problem representation, which is crucial for the problems de- scribed above. below.

Graphical Smalltalk with My Optimization System for Urban Planning Tasks Author(s): Koenig, Reinhard; Treyer, Lukas; Schmitt, Gerhard N.

left-hand network in Figure 6 we find that there is no single bottleneck, and at least one other populated route. As a result this network has the worst fitness of the three. the diagrams in the bottom row in Figure 7 is similar to that of the corresponding diagrams in Figure 6. This indicates that both fitness functions direct the search process in a similarly efficient way. Our third example is based on the initial sce- nario with two defined sub-areas as shown in the right-hand image of Figure 5. In Figure 8 the central sub-area is shown as a dotted ellipse and the quiet sub-area as a dotted rectangle. To include the spatial aspect in the fitness function, we have to define how to represent the graphical objects that represent the sub-areas with the corresponding specified proper- ties. The fact that the three best networks have differ- ent maximal fitness values (diagrams in the bottom row of Figures 6 and 7), indicates that the evolution- ary optimization process explores different parts of the search space each time it is run. But despite the small differences in the maximum fitness values of the variants, they all fulfill the requirements relative- ly well. When we consider the random points (repre- senting randomly generated variants) we can clearly see the advantage of using the evolutionary search process compared to randomly generated solutions. The best variants are improved continuously over the 50 generations and reach a level, which cannot be achieved by a random generation process.

for residential usage, we want to have only streets with low choice values in it. Therefore we sum all differences of the choice values from the street seg- ment ci that are located inside the quiet area A and the maximum choice value of the network cmax. The average of this sum is used as the second part of our fitness function: solution in the left-hand image of Figure 8. Here the maximum choice value is at the edge of the central area and there is a relatively populated road in the quiet sub-area. Maybe the optimization algorithm could have found a better solution with more gen- erations. But the combined fitness function may be hindering the improvement of this variant. We will discuss this problem in the next section.

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Graphical Smalltalk with My Optimization System for Urban Planning Tasks

by Reinhard Koenig

2022

Based on the description of a conceptual framework for the representation of planning problems on various scales, we introduce an evolutionary design optimization system. This system is exemplified by means of the generation of street... more

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Generating Urban Morphologies from Ontologies

by Stefano Pensa

2022

Abstract. The paper presents the ongoing research work on a software system for supporting the exploration of the numerous and often interrelated factors that can affect the urban design. The present implementation of the system supports... more

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