Identity of Generated Objects – Gain and Loss Along Transformational Chains.


Prof. Dr. H. Dehlinger

Department of Product Design, Kunsthochschule Kassel, Kassel, Deutschland.



Dipl. Des. O. Werner

Department of Product Design, Kunsthochschule Kassel, Kassel, Deutschland.






Simple transformations applied to a structure may have dramatic effects on the visual appearance and other properties of the structure. They may result in an increase or in a loss of properties contributing to the “identity” of the structure. Starting from some objects (generated and adopted), such gain and loss of identity along transformational chains is experimentally discussed and demonstrated. Many questions are raised and some hypothetical conjectures are attempted. This is work in progress.


1. Part One: construction and reconstruction of identity


To prove our identity, we possess an ID card, a passport or some other sort of document, usually with a picture, with information about height, the colour of the eyes and other information of personal characteristics. The „proof of identity“ is presenting such a document issued by an authority. Sometimes a fingerprint, voice samples or an analysis of the genetic code is used. If identity is to be ascertained, coordinates of identity  (I1, I2, I3, ... In) are compared and checked against the pretended identity. They are listed and are compared, until a certain threshold of doubt is eliminated and we are persuaded that the presented coordinates proof the pretended identity. Identity is uniqueness. The Greek root, eidos, idea, also signifies form. If all things possess identity, then the relevant knowledge from which we draw the comparative coordinates belong to a very large domain, and this knowledge is structured on the ground of historical / cultural reasons in a certain manner. One can postulate that the modus procedendi of constructing / reconstructing an identity will depend on the logics one chooses to follow. The analysis of the trains of thought which lead to the construction / reconstruction of identity as a result, puts the identification of rules of the nature of this action to the task. Its concern is a common problem to be found in the work of engineers, planners and all kinds of designers: the generation of a design.


The construction of identity can be formulated as an imperative:


(i) Design an object Oj that has an identity like object Ok.


Such an object Oj is in some way partially identical with the reference-object Ok. By pointing to a reference  Ok, which may be analysed subsequently, a list of coordinates of identity may be arrived at. It remains however open, which ones are chosen by the designer to fulfil the demand for identity. For most design problems however, at least for all the ones that „matter“, there is no reference object whatsoever.

Partial identity may be measured on an ordinal scale e.g. from weak to strong, and arbitrary weak partial identities may be constructed.

Instead of relying on an arbitrary set of identity coordinates, we may demand that a limited, but specified subset of characteristics is fulfilled exactly:


(ii) Design an object Ok, that has exactly the identity coordinates (I1, I2, I3, ... In).


Or, in a weaker form: 


(iia) Design an object Ok with has identity coordinates similar to (I1, I2, I3, ... In).


The search for relative identity is not easy to grasp. It can lead via associations / terms of reference to conceptional units, which are located far away from the starting point, and it can lead into remote corners of the search space. It is not unrealistic to assume that very innovative ideas have a very large conceptional distance from the established knowledge structure of a field. An innovative designer then has to produce "conceptional chains" (associative transformations) over large classificational distances, which (possibly) become the more fruitful; the more daring they ignore the established borders.


A more exact  view of the term “identity” and of the scales on which it can be measured and compared, leads to different possibilities of logical distinctions with regard to degrees of identity. They are to be outlined in the following considerations.


(a)    In the sense of a binary decision, and in a not further specified manner, Oi and Oj may be claimed identical or “of the same identity”

(b)   Comparatively one can say: Oi has more from the identity of Oj than from Ok .

(c)    This can be differentiated further, if we introduce discrete levels (absolutely  identical, very identical, a little bit identical ...) or use a scale from 0 to 1 as a measure of "relative identity". We then can formulate statements (see above) like: Oi and Oj are “relatively identical”, with reference to the identity coordinates I1, I2, I3 ..., In.  Oi and Oj share a common set of coordinates.


Still further types of identities can be distinguished, e.g:


(d)   Structural identity. Two objects are structurally identical, if they can be decomposed into structural components with a common mapping.


(e)    Complementary identity. Two objects are complementary identical, if they fulfill their function only together and in coexistence.


(f)     Substitutive identity. Two objects are substitutive identical, if one can replace the other. If the possibility of the substitution refers only to partial aspects, one can speak also of partial substitutive identity.


(g)     And others more.





Designers usually and gladly fall back on the type of unspecified identity, which can only be measured on a binary nominal scale as "is existing" or "is not existing". In this way the fog of mystery, surrounding the creative act is maintained, which appears to be intended. If one tries to find a code for the construction of identity, the only way seems to be the one to explicit define the coordinates of a certain and specific identity. In the following parts 2 and 3, some experiments will be discussed which point into this direction.



1.    Part two: Transformations and Complexity


Abb1. Rotation und Teilung


Abb2. Rotation und Teilung


Abb3. Rekombination


Abb4.: Schnittmengen



The designer is constantly struggling to arrange himself between the world of concepts and ideas - all which is before his mental eye only - and the world of explicit public presentation of this ideas to everyone. There is always the problem to confront him and the others with a presentable explicit picture of things, which do not exist yet at all at a given time frame. It requires a fundamental understanding of spatial relationships and arrangements in abstract terms without direct seizure of an object. The ability to order three-dimensional things mentally, to present them, is a condition for performing the act of representation. Only which is existent as a conception already, is also representable, and presentations are an indispensable aid in the design process. Understanding of the premises is linked with our experiences and it is based closely on the availability of certain arranging and explaining information. Spatial representations with the aid of the computer presuppose an accurate imagination of the objects to be constructed.

If a construction is however  "entered" into the machine, it can be changed and supplemented fast, without much effort, and under a great variety of objectives. This is the big potential of the computer-aided representation. It is simply and instantly available. The representation process itself does not have to struggle with the actual construction of the object as compared to a process, carried out by hand. The structural division between presentation of a visual image and construction of the visual image in the machine, allows to generate images of objects without having a clear picture of the generated image at all. It is conceivable then, to write down or to plan an abstract sequence of construction-operations (we can call this a preconceived programme), without having in advance a clear idea about the outcome. Only on the screen will this idea be formed by the generated results.  Such a preconceived programme, carefully designed and tested, is a form-generator, which is required in all generative design approaches. We assume here such a generator to be a highly interesting instrument to engage in a game of exchange between human imaginative power and visual calculative representation on the screen.

For the example presented below, we use a "programmme" which essentially consists of a sequence of geometrical operations, which can be carried out in short time and directly in front of the screen. On the basis of a simple two-dimensional figure, we generate increasingly more complicated three-dimensional objects.


The two questions in which we are interested are: Is it possible for us, to imagine the identity of the generated objects solely on the basis of a given rule of transformation?  And, vice versa: Is it possible by looking at the result, to identify the transformational rule responsible for the result?


[Please refer to the German version of the paper regarding all figures.]


The experiments [1] show, that our imaginative power is surprisingly limited, which we will demonstrate with the following sequences of images.


The basis for all the constructed figures is the regular and well known “star” with six spikes. It is constructible with a simple rule from an equal sided triangle: Draw on the middle third of each side again an equal sided triangle [Abb. 1. Fig. A / Abb. 2. Fig. B]. In a further step, three-dimensional objects are generated from this figure by rotations on two axes of symmetry [Abb. 1. Fig. A-1 / Abb. 2. Fig. B-1].


If we cut the generated object along the planes of the coordinate system, we get two identical objects each [Abb. 1. Fig. a-1, Fig. a-2, Fig. a-3 / Abb. 2. Fig. b-1, Fig. b-2, Fig. b-3].

The existence of identical planes after cutting, allow new combinations of either equal or different parts. A multitude of new and surprising objects may be generated. Abb.1 is showing a combination of Fig. a-1 with Fig. b-2.

The forms of Fig. A and Fig. B are now merged into one Volume in 300 resp. 600, and the new object is calculated. The new object is formed from the volumes shared by both of the figures we started off with.

·         Fig. AB-1: merged from Fig. A-1 und B-1, angel of rotation 30°

·         Fig. AB-2: merged from Fig. A-1 und B-1, angel of rotation 90°

·         Fig. AA-1: merged from Fig. A-1 und A-1, angel of rotation 30°

·         Fig. AA-2: merged from Fig. A-1 und A-1, angel of rotation 90°

·         Fig. BB-1: merged from Fig. B-1 und B-1, angel of rotation 30°

·         Fig. BB-2: merged from Fig. B-1 und B-1, angel of rotation 90°


For the generation of those rather complex forms only two operations are necessary (one rotation, one Boole operation each). Keeping this in mind, the destructive power of longer transformational chains on the identity of the object, as well as the fast emergence of new identities for generated  objects becomes apparent.


2.      Part Three: Transformations and Identity

Abb1.: Beispiele für gefundene Trockenformen aus der Natur, die in ein Diarähmchen eingespannt wurden [2]


Abb.2: Blatt und Blattraum [3]


Abb. 3 „Formen 1“  [4]

Abb. 4 „Formen 2“  [4]


Abb. 5 „Kugel“       [4]


Abb. 6 „Stadt-Raum“ [5]


Abb. 7 „Hochhaus“     [5]


Abb. 8 „Gebäude“       [5]


Abb. 9 „Explosion“[6] 


Abb.10 „Blattfiguren“[6] 




Forms from nature impress us frequently by their constructional sophistication and their visual complexity. The wealth of form of nature is a constant source of inspiration for designers. And, moreover, they usually can be clearly identified as "forms of nature", i.e. they definitively possess  "identity". In the following experiments we refer in each case to an object (or a part of it) from nature. They are collected in the fall or wintertime, when vegetation rests, as dried forms. They are usually small finds [see Abb. 5], and they are prepared between the two glasses of a photographic slide. The “slide” is then scanned in a digital scanner The material received this way is the raw material for the digital (student) experiments which we want to discuss the following section.


From the collected and digitally prepared natural forms, three-dimensional objects are generated, using any of the CAD-systems commen in designing. The students work with different programs and tehey were used in the experiments. For the production of the three-dimensional objects only selected and prespecified transformations are allowed. They can however be used repeatedly and in any order.


Strictly only the following transformations are allowed:

  1. Extrude contour (or plane)
  2.  Scale, rotate, shift
  3. Duplicate, add
  4. Cut


The goal is, to generate three-dimensional, sculptural objects, which stimulate “architectonic fantasies”

We regard the results of each transformational chain now under the criterion of the preservation or the destruction of "identity. The simple, however difficult to answer question is: Is there something remaining in the produced spatial object, which can be recognised in its identity and attributed to the natural form it started from? Since the transformational chain may be bridging many steps, we can also ask: After which step do we recognize, that the object has clearly departed from the starting form? We begin with a simple example [Abb.2].


The programme has seven steps and the identity of the starting object is somehow recognizable. The programme is as follows:


  1. Vectorize the leave and fill plane
  2. Cut along axis of symmetry and erase left part
  3. Extrude
  4. Scale
  5. Rotate and copy
  6. Construct a vertical swinging line from copied elements
  7. Rotate this line around vertical axis and copy 40 times


A different Situation is shown in the following figures [Abb. 7, Abb. 8, Abb. 9], which each show a generative sequence. Especially the Fig. 9 is showing in towards the end of the sequence a complete loss of the identity of the starting figure.


In the following sequences [Abb. 10, Abb. 11, Abb. 12] some „architectural“ images are emerging, but, despite their complexity, it seems to be possible to identify their origin from the given starting point. A similar situation is encountered in the last two examples [Abb. 13, Abb. 14] too.


The following observations from the experiments may be notable:


1.                  The generated images have an own identity. In all cases this identity is somehow unique.

2.                  Only in some cases a transport of identity from the start object to the final object is observable

3.                  The images are of a nature, which would be difficult to achieve deliberately

4.                  Surprisingly few transformations are needed to arrive at the final object

5.                  Only very basic transformations – off the shelf of standard software – is needed

6.                  There is no specific and obvious use of the generated images. They are digital games

7.                  The results are however highly inspiring and a practical use can pop up any time

8.                  It is difficult o formulate rules, in the sense of recommendations to follow a preferable sequence of transformations

9.                  The discussed “experiments” (student work), have a deficit with respect to mechanisms of controlling the experiment

10.              In most cases it seems the students were “carried away” as they proceeded

11.              It seems possible, with a little experience, to manipulate the results into wanted directions





[1]       First constructed by Ottmar Körzell, then by Ole Werner

[2]       Martin Güntert,
[3]       Susanne Hermann,
[4]       Christian Poppel,
[5]       Anne Schmitz,
[6]       Jens Otten,