At the end of the 19th century William Bateson developed the theory of symmetry and of discontinuous variation. It says that where information is lost or mutated, growth returns to simple symmetry. As an example Bateson analyzed possible mutations, e.g. that of additional thumbs at a hand, and he found out that the abnormity has a higher measure of symmetry in the form of an additional plane as a mirror between the new and the original thumb. This means that the “normal” thumb, which is asymmetric to the four fingers, is replaced by a symmetric part of another four fingers, see picture 31.
picture 31: Mutation of a thumb
The right picture shows an analysis of a human thumb mutation. Due to a loss of information, the thumb gets a symmetric mirror image within the asymmetry of the hand. In the other picture of a finger mutation analysis by William Bateon four fingers replace the thumb.
In general mutation may mean additional information with regard to higher symmetry and reduction of heterogeneity but also, as Bateson thought, that the reduction of asymmetry and the growing homogeneousness was the result of a reduction of information.
According to Bateson, genes regulate the simple bilateral symmetries by adding heterogeneity and differentiation as a form of organization - information hinders symmetry, as information can be a reaction to genetic or environmental disturbance. Therefore a breach of symmetry does not mean a loss but an increase in organization in an open, flexible and adaptable system. In this sense symmetry is a lack of organization resulting from a lack of interaction with stronger external forces and surroundings. But in this sense typologies are then reduced, empty and false: Organisms cannot be related to one idealized reduced type, they are the result of dynamic non-linear interactions of internal symmetries with changes of a disorganized context. An alternative to typologies may therefore be an internal system of indeterminate growth differentiated by general and forecast able outer influences, which results in unforeseeable, dynamic and new organizations.
5.4.1.a Cardiff Opera
In "Arch+ number 128" the question of symmetry is discussed in connection with a competition for the opera in Cardiff in an article by Greg Lynn, written in addition to his contribution. The competition had two main tasks: first the project had to get a symmetrical horseshoe hall and second there should be a connection to the surroundings, the historical harbor basin. This meant that on the one hand the resulting opera should correspond to the environment and on the other hand it should have a new identity. The interesting aspect brought up by Greg Lynn was the thought of standardization of the surroundings with harbor and basin and the new opera through processes of differentiation rather than simplification. It was an attempt of a transformation of existing information into the new context. Mutation and differentiated growth was the key to the sketch. The idea behind the concept was that the resulting object should not be determined from the beginning, and therefore should not be reduced to the internal rules of the object itself and external outer relations. Symmetry should be found at each level of the sketch. In this connection theories by William Bateson from 1894 were mentioned: the loss of information goes hand in hand with the growth of symmetry, and homogeneity is equality or lack of differentiation, see picture 32.
picture 32: Cardiff opera
competition contribution by Greg Lynn and Ed Keller
In this example the starting form of the opera is generated by a transformation, a rule similar to mathematical fractals, in which the starting body is replaced by three parts, each similar in form but rotated and/or reduced. The final sketch is again transformed through the idea of function, construction and form.
The construction rule of the basic Fractal.
The fractal is changed and the volumes are newly arranged because of the requirements of e.g. the foyer, the opera house, the stages and the dressing rooms. Below, the structure of fine walls, supporting the Opera House volumes, is presented, which follow several existing site alignments, including the light rail line, the highway and existing edges of buildings and the Oval Basin. Below right, the final configuration of the lathed oval volumes is given, with the adjustments to program and with the differential faceting based on scale.
Aerial perspective of polyp volumes - plan of level one.
Fractals are symmetrical in the one or other way: e.g. elements at different levels - scales -, are symmetrical to one another by bilateral symmetry, translation or by combinations of symmetry. In Bateson’s thoughts this would mean that they include less information, which may be expressed by few production-rules. But nevertheless there is a high degree of differentiation because of different scales, that is self-similarity, which, however, leads to complexity. Moreover according to Bateson’s article true mathematical fractals do not take up outer influences - there are first of all none be found in the computer -, which leads to systems that can only be compared to natural forms by their underlying principles. In this way Mandelbrot introduced the possible fractal forms of coastlines by the Koch curve, in order to show the principle of self-similarity, complexity, generating-rules and roughness. To get more "nature-like" fractals the factor of randomness can be added or even better natural influences such as weather, resources, availability, population, natural barriers, depending on the system, e.g. plants, coastlines or cities.
In architecture the concept of self-similarity has very often been used in the case of the “golden section”. Showing this self-similarity first a rectangle is drawn with the larger side length being "a" and the other "b", with the “golden section” being defined as the relation a/b=b/(a-b). In the second step a square of the shorter length "b" is put into the rectangle. Next again a square is drawn, this time in the remaining part of the “a-b”-side length and so on.
The resulting image is a self-similar spiral of rectangles, produced by a cascade of self-similar proportions, see picture 33.
picture 33: "Golden section"
The picture below left shows the principle of the construction of the “golden section”, the one below right a cascade of self-similar rectangles.
The rhythm, developed out of symmetry, is found in architecture in many examples like the distribution of windows, with the distances and sizes being interrelated. But also the bilateral symmetry with the mirroring axis in the middle front door, which has its heyday in the villas by Palladio, is always present. Sometimes this strict use leads to contradictions as with the oratorio of the Filippines by Francesco Borromini (1637-1640) in Rome.
In this building the main entrance is not in the middle but to the right and the outside contradicts the inside asymmetry, see picture 34.
picture 34: Borromini - Oratorio of Filippines/Rom
The architect Sachio Othani, who belonged to the circle of students around Kenzo Tange, used the other kind of symmetry, namely self-similarity in form of oblique concrete posts as the main theme of his first larger building, the international conference-center in Kyoto. Though no room is identical, the basic theme is always present, the oblique posts, and this helps for orientation purposes, see picture 35.
picture 35: Sacchio Othani - Conference-Centre Kyoto
 Lynn Greg, Das erneuerte Neue der Symmetrie, Arch+ number 128 (1995), Arch+ Verlag GmbH Aachen, ISSN 0587-3452, p.49.
 Lynn Greg, Das erneuerte Neue der Symmetrie, Arch+ number 128 (1995), Arch+ Verlag GmbH Aachen, ISSN 0587-3452, p.50.
 Lynn Greg, Das erneuerte Neue der Symmetrie, Arch+ number 128 (1995), Arch+ Verlag GmbH Aachen, ISSN 0587-3452, p.48.
 Bovill Carl, Fractal Geometry in Architecture and Design (1996), Birkhäuser Bosten, ISBN 3-7643-3795-8, p.2.
 The reason lies in the demand of city planning in form of an existing church to the right side, which Borromini wanted to subordinate. Jencks Charles, Die Architektur des springenden Universums, Arch+ number 141 (1998), Arch+ Verlag GmbH Aachen, ISSN 0587-3452, p.37.