function & form

Vortrag: ITU institute of science and technology, Istanbul; 08.11.2010

DI Wolfgang E. Lorenz
wolfgang.lorenz (at)

November 8th, 2010,

Fractal Characteristics and Architecture

In the year 1975 Benoit Mandelbrot introduced the term Fractal as a possibility to distinguish self-similar natural or artificial objects from smooth Euclidean objects. Since then Fractals have been identified in many fields. Under the presupposition of the new Geometry of Fractals mainly two kinds of architectural compositions can be differentiated – with nuances in between. Those buildings offering self-similarity are close to Fractal Geometry and distinguish themselves from the smooth Euclidean Geometry of Modern architecture that is reduced to a few geometrical objects. But buildings are no Fractals in the same sense as mathematical Fractals.

Fractals are defined by their characteristics – self-similarity, generation by iterations, rough surfaces, infinite complexity, dependence on starting parameters and common features with nature. But often the only way to describe Fractals is through their Fractal Dimension. With regard to this definition, architecture and façades in particular can be described according to visual criteria whether they offer fractal characteristics or not, examining various levels of scale. Limits are imposed by certain influences that are inherent in buildings, ranging from materials used over purposes to specific sizes of certain details. In nature such influences are amongst others caused by weather and climate, which changes the idealized fractal structure. The factor of chance is then what turns the outcome of such computerized simulations into realistic models. Hence fractal characteristics such as self-similarity of natural and artificial objects are difficult to describe precisely. As an example, Robie House by Frank Lloyd Wright offers self-similarity on different scales using the horizontality of the surrounding nature as a concept that is translated into the building with regard to purpose, material and construction. The horizontally stretched façade consists of widely protruding, longitudinally stretched roofs and stretched storeys, where the storeys themselves again consist of level window-strips and horizontal parts of walls, with the walls again being structured horizontally by emphasized back mortar beds and flush brought narrow header joints. But how can this concept be measured?

Graduate Studies in Building Science and Technology

Computational Geometry


1 VU ... 3,0
March, 2005 to June 27,2005 and
March, 2006 to June 27, 2006
Course description:
This course introduces methods in geometry and geometric modeling. It offers a hands-on in-depth possibility to acquire the necessary skills for dealing with complex geometry. Topics include free forms, fractals, morphology.
Georg Franck-Oberaspach / Wolfgang Lorenz / Stefan Leopoldseder / Michael Hofer

Concentration: Digital Architecture

Evolutionary Algorithms and Fractal Geometry in Architectural Design

Lecture: university of east london, London; 02.02.2005

DI Wolfgang E. Lorenz
wolfgang.lorenz (at)

February 2nd, 2005,

  • Before all, self-similarity leads to some kind of recognition. Each scale has its own details and the whole offers a similar roughness as its parts. This also applies to a similar roughness of the coast and its bays.
  • The conscious use of self-similarity can provide a possibility for orientation by using a variation of a motive on different scales. Covering different and simple orders leads to complex geometries.
  • The variation of the environment can bind the building more closely to its environment. Examples are the contribution for the competition of Cardiff Opera House by Greg Lynn or Falling Water by Frank Lloyd Wright.
  • Quality may also have something to do with using fractal characteristics to get a contrast to smooth Euclidean objects. ‘Fractal’ architecture has a similar roughness and remains interesting. Information or details are held together from the whole to its parts. This is expressed by a similar fractal dimension across certain scales. We get a complex architecture that is not confusing.
  • Fractal geometry also deals with the question of a balanced ratio between order and surprise. Too much order is boring while too much surprise would be confusing.

Self-Similarity in Architectural Design

Lecture: Aedas Architects Limited, London; 03.02.2005;

DI Wolfgang E. Lorenz
wolfgang.lorenz (at)

February 3rd, 2005,, London

How is self-similarity achieved at Robie House, Chicago from 1909?

  • As the overall view of Robie House by Frank Lloyd Wright shows, horizontality is continued by the alternation of the oblong garden wall, the parapet of the south balcony and the window-strip. On the next scale the long stretches of stone of the copings and sills underline this tendency. Even the bricks and the image of the joints stress horizontality. The mortar beds are of ordinary cement and tilted back from the face. In contrast to that, the narrow header joints are of red-colored cement and in line with the face.
  • Furthermore, the form of the three-cornered living room prow is repeated on different scales: in the slope of the roof, in the design of the iron gates to the garage court and in the glass designs of the doors and windows. Again a couple of variants can be found, from the triangle to the parallelogram. But also the form and the design of the lamps of the living room and the dining room reflect the prow.

The concept of the basic idea is not only found in examples that are close to nature. It is also true for Schröder House by Gerrit Rietveld built in 1924. This building belongs to de Stijl. This time lines and disks of different functions, characteristics and scales can be found.

Schröder House by Gerrit Rietveld

  • The biggest elements are the large flat, white disks. They form the spatial and constructive structure of the building.
  • They are followed by smaller flat gray or white disks – such as the balcony. Linear elements are used for horizontal and vertical accents. Smaller elements are then inserted into the holes that are left out by the previous elements. These are windows, doors, railings and the ladder to the roof outside.
  • Looking at the furniture this combination of disks and lines in different sizes is once more repeated.

Fractal Geometry in Architectural Design

Vortrag: Forschungsseminar Bauphysik, Vienna; 15.01.2004

DI Wolfgang E. Lorenz
wolfgang.lorenz (at)

January 15th, 2004,

Fractals and Fractal Architecture

Vortrag: archdiploma 2003, Kunsthalle Project Space, Wien; 07.10.2003; in: "archdiploma 2003", (2003), S. 94 - 95

DI Wolfgang E. Lorenz
wolfgang.lorenz (at)

January 13th, 2004,

Special Issue
"From Fractal Geometry to Visual Intelligence in Architecture"

The Special Issue is aiming for contributions that deal with new methods of fractal based analysis and/or generative design suited to the field of architecture. With architecture in the center of interest, research in related fields, as well as interdisciplinary perspectives on this specific subject, is required, and architects, civil engineers, product designers, mathematicians, computer scientists, and others are invited to this Special Issue. ...

Vertical Green Utopia

kleines Entwerfen SS2023

Das kleine Entwerfen mit dem Titel „Vertical Green Utopia“ verbindet die Planung von vertikalem Grünraum mit digitalen Entwurfsstrategien. Die Stadt Wien steht gehört zu jenen Städten Europas, die durch die globale Klimaerwärmung stark unter Druck steht. ...


eCAADe 2022:
Multilayered Complexity Evaluation within Configurators for Design

Multilayered Complexity Evaluation within Configurators for Design – Responsible Collaborative Systems for Architectural and Product Design
Talk and Proceeding: eCAADe 2022 – Co-creating the Future: Inclusion in and through Design (KU Leuven Technology Campus, Ghent/Belgium | conference)

This paper describes the concept of integrating several complexity evaluation methods, previously developed and tested by the authors, into one product configurator through a technical prototype. ...

eCAADe 2022:

NoMoTown – An agent-based model of transport mode choice
Talk and Proceeding: eCAADe 2022 – Co-creating the Future: Inclusion in and through Design (KU Leuven Technology Campus, Ghent/Belgium | conference)

In most cities, cars remain the dominant mode of transport. This is a huge problem not only because of obvious effects such as congestion and pollution, but also because it causes health issues for commuters themselves which lead to further costs for the community. ...

Kindergarten meets Easy Rider

kleines Entwerfen WS2022

Kindergarten und Motorrad? Was auf den ersten Blick nicht zusammenhängt, ist beim näheren Hinsehen ein spannendes Gegensatzpaar, aus dem sich ein Denken „out-of-the-box“ ergeben soll: ...

Fractal and Fractional:
Multilayered Complexity Analysis in Architectural Design

Multilayered Complexity Analysis in Architectural Design: Two Measurement Methods Evaluating Self-Similarity and Complexity
Journal Paper: Fractal and Fractional, 5 (2021), 4; S. 1 - 25.
DOI 10.3390/fractalfract5040244