Parametric modelling and fractal geometry share a lot of similarities between each other. They both focus on the idea of self similarity and replication of geometry to create and extend the design process from one single, and mostly simple geometry.
Parametric modelling is a methodology for exploration of possible designs generated from the use of one single model. Initially intended for the aeronautical industry, they were introduced into the architectural domain due to their ability to support a powerful framework for the conception of design. As Carlos Barrios had described, “a parameterization is presented as a fundamental tool for design exploration, which allows the reproduction of original shapes..., and the generation of a large set of new designs.”[1] Parametric modelling also presents a freedom to the restrictions normally presented in traditional CAD systems, it provides parameters of the geometry to be freely modify, to satisfy the idea of design exploration.
Fractal geometry is geometry whose spatial form is not even nor fluid, hence irregularity across many scales in its structure. It is a portrayal as geometry of nature. This is evolved from the hypothesis which objects with geometry whose structure is irregular in terms of Euclidean geometry, but within this irregularity lays a pattern which is as order as those in simpler objects composed of straight lines. Fractals are based on the notion of repetition and scalar ambiguity, any part of fractal, regardless of size and scale, presents more or less the same structure of geometry as a whole, the architectural forms or urbanistic models that are derived from them are characterised by a scalar ambiguity.
The one rule of fractals is that fractals are always self similar, or at least in some general sense. Self similarity is the idea of replication of one single geometry, across many scales although not down to the exact details, but in a very general and broad idea. Therefore on an enlarged or reduced scale, ad within a given range, you examine a fractal, it will always appear to be similar to the whole, with some degree of irregularity. In fractals, the whole will always be manifest in the parts. A great example is looking at a piece of rock that broke off from a mountain. You will see the mountains in the rock to some degree of familiarity.
The idea of self similarity is very related with parametric modelling, in terms of its notion of repetition. Parametric modelling suggest and conceive design concepts based on alteration and modification to one single modular component replicating and developing the idea in a parallel fashion. Whereas fractals focus on the similarity of structure within its geometry, to create order within seemingly irregularity. Both concepts relies on the idea of replication to broaden their design concepts. Due to the nature of parametric modelling, the process which each modification yields a result, contrasting with the traditional CAD modelling, each modification applied to the geometry produces an instance of the newly created geometry, so it is evident the similarity between the original geometry and the newly created geometry differed by only the applied configuration.
This leads to the fractals’ concept of hierarchy. Sometimes, fractals are portrayed in terms of a hierarchy of self similar components. Fractals, in order to display the order within its irregularity, presents a hierarchy structure that ‘regulates’ the geometry. Hierarchy of fractals can be seen across many scales and tree is a very classic example of ‘branching out’. Being a literal interpretation of the term ‘hierarchy’, it presents the most fundamental structure of fractals. Looking at twigs and its structure will create a familiarity with the branch structure, even if twigs is a partial form of a branch. Similarly from branches to trees, one branch of a tree will resemble the structure of a tree.
Other interesting example is the structure of cities, as Michael Batty and Paul Longley explained in their book, “Fractal Cities: A Geometry of Form and Function”, the structure of cities seems to be unordered and seemingly without regulated structure, but at closer examination, districts of cities creates a self similarity between themselves. As the writers described, “The organisation and spacing of cities as central places is such an order while the configuration of districts and neighbourhoods, and spatial distribution of roads and other communications are hierarchically structured”[2], if roads and neighbourhoods are turned into geometry, ignoring the materiality of the buildings and constructs, we can easily identify the repetition of structure within cities.
Referring back to parametric modelling, parametric models are often seem irregular at first examination, but each individual geometry is spawn from a previous geometry, and the relations between the two geometry can be explained and visually described. This idea of modelling, similar to fractal geometry, provides a relationship between multiple geometries. Since a parametric model is created from one simply geometry, for example, a twisted tower is spawned from one single enclosed shape, copied and transformed into multiple instances of the shape, then joined create a loft between the shapes. Each section of the tower will create a familiarity between each other, because each section is originated from one single enclosed shape. Similar to the hierarchy structure of fractals, where twigs resembles branches, and branches resemble the tree.
Both of the ideas, fractal geometry and parametric models, after the discussion of hierarchy, gives an impression that it is very rigid in process and not very maneuverable. But in fact, both ideas present a very flexible system of creating geometry. Parametric model is modelling based on parameters of geometry, such as length, control points, and surfaces. We can apply modifications to the geometry as long as it is defined within the parameters, thus creating a theoretically limitless amount of configurations from using one single geometrical component. Fractal geometry, as discussed before, based on the idea of self similarity. This is similarity is not restricted down to exact detail, therefore allowing freedom to creativity to the construction of fractals within a particular boundary, restricted by only purposes of the design and the intention of the designer.
The intersection of fractal geometry and parametric modelling are mostly based on its idea of familiarity between each section of the geometry, each newly created instanced of geometry are similar to the previously created geometry, differed by only the modification applied to the component.
[1] Carlos Barrios, Transformations on Parametric Design Models: A Case Study on the Sagrada Familia Columns (2006) Department of Architecture, Massachusetts Institute of Technology, USA p. 1
[2] Michael Batty, Paul Longley, Fractal Cities: A Geometry of Form and Function (London, Academis Press Limited, 1994) p.60
Unreferenced Sources
· Carl Bovill, Fractal Geometry in Architecture and Design (Birkhäuser Boston, 1995)
· Shaoming Lu, Hidden orders in Chinese gardens: irregular fractal structuve and its generative riles (Environment and Planning B: Planning and Design 2010, volume 36, pages 1076-1094
· Stephen Demko, Laurie Hodges Bruce Naylor, Construction of Fractal Objects with Iterated Function Systems (New York, USA, Proceedings of the 12th Annua conference on Computer graphics and interactive techniques, 1985)
· Jonathan Chapuis, Evelyne Lutton, ArtiE-Fract: Interactive Evolution of Fractals (International Journal on Artificial Intelligence Tools, 2006)
· Mai Abdelsalam, Digitizing Architecture: Formalization and Content [4th International Conference Proceedings of the Arab Society for Computer Aided Architectural Design (Manama, 2009) p. 297 – 304
· Tristan Al-Haddad, Parametric Modulations in Masonry, (CAADRIA 2008) p.221 – 228
· Fabrizio Apollonio; Marco Gaiani; Cristina Corsi, A Semantic and Parametric Method for 3D Moels used in 3D Cognitive-Information System (Zurich 2010) p.863 – 872
· Ayman Almusharaf; Elnimeiri Mahjoub, A Performance-Based Design Approach for Early Tall Building Form Development (Morocco, 2010) p.39 – 50
· J.S. Gero and F. Sudweeks (eds), Shape pattern recognition using a computable shape pattern representation, (Artificial Intelligence in Design '98, Kluwer, Dordrecht), pp. 169-188
· Ediz, Özgür, “Improvising” Architecture: A Fractal Based Approach, Computation: The New Realm of Architectural Design, (Istanbul (Turkey) 16-19 September 2009), pp. 593-598
