Code, a password to infinite


Prof. Enrica Colabella.

Generative Design Lab. Politecnico di Milano, Italy



This paper tries to investigate around the concept of code, as identity of a theme, and of variations, as results of a generative process. The hypothesis is that infinite rises in a borderline between a visionary world and an interpreted reality with a strong connected dualism. As in Nature the first gets from a dynamic centre, in endless variations until the border, the second by using diachronic matrixes moves unsteadily toward a static centre for delineating open systems of transforming rules. This is a creative route in the site of the Myth of Sisyphus.


 1. Aims: To investigate in a creative process, by getting into focus how to define an idea/code for building endless variations.



Fig.1Tiziano, Il mito di Sisifo


The site of the Myth of Sisyphus.

If we image that Sisyphus rises his eyes and looks to his reality at a distance as in another contest with a new imaginary borderline, by feeling not only what happened, but also how is exactly the frame of his life in a new consciousness of human beings, we can see a freedom root. The endless repetitions become variations of the theme toward infinite. These are like frames of a new complex reality, in which memory can loose its domain and hope can rise.


      2. An hypothesis 

By learning to discover reality it is a visionary procedure that defines the dual structure between a discovered reality and a new  idea of transformation as a coherent open system.


  2.1 First step: At a distance

…. A spatial distance….. by discovering a viewpoint.


In “Zibaldone” Leopardi said : “It exists in human beings an imaginary ability that can conceive things that are not and in a way in which real things are not… man goes wandering in an imaginary world and he figures things that he could not if his vision extended in all, because  reality excluded imaginary.” (12-13/07/1820)


Interpretation is an essential condition of a visionary process that starts by choosing a viewpoint.

In Perspectiva Artificialis working from 3d to 2d we can define theoretically all the points of space as points of view, but when we choose a point and an horizon we build an artificial scenario that is starting inside infinite. So we can realize endless representations of the same space in a dynamic approach.

 It is also possible, as i.e. in this (Fig. 2) “Ovale della prospettiva della Piazza Granducale” by Bernardino Gaffurri (Firenze 1606), to manage a complex system running from two different viewpoints. This ambiguity is a strong tool to open mind toward a possible interpretation.


Fig 2


       3.2  Reverted vision

If we work from 2d to 3d using a reverse perspective process, we can design generative codes of transformation with a set of possible 3D results that start from each 2D shape. More in general we can use the multiplicity of results made by the passage from a dimension to the upper dimension. In other words, a two-dimensional image, as a photo or a sketch that represent a possible our imaginary, is really extremely useful when we move from a dimension to a more high one by following our interpretation. This procedure finds again in a substitution group the generative potentiality of describing unexpected configurations of the author’ idea/code.

We can define a point of view but only in a coherent system, that works as a supreme invariable. This is a binding condition to recognize the figuration.  The dynamical  interchanging as interpretative hypothesis is only on choosing a point on the line toward infinite. So we have a limited combination, also if in a big number, of the2d picture. This happens because the relationship structure of the picture is the product of a historical fixed imaginary.

In “ The not Euclidean Image” Celestino Soddu wrote about his experimental work in defining 3D interpretative models with a reverse perspective.



Fig.3 “Il bambino azzannato dal lupo” by Simone Martini, 1328

Fig.4  Two axonometric views of 3D models, as results of 2 different view points of a reverse perspective



Fig. 5/6 Perspective representations of the identical model by using in sequence a horizontal rotation of 22,5 degree. In this passage, all the possible three-dimensional structures that are generated are able to represent, in their multiplicity, the discovered visions inside the previous two-dimensional one.

  3. 3 Anamorphosis and not Euclidean perspective

By analysing Van Gogh, Celestino Soddu defined first algorithms  directly connected to natural vision and after he used anamorphosis  for representing the totality of the space in a temporal vision.

Fig.7 The room of Van Gogh           Fig.8 A curved perspective

Total Perspectives with a viewpoint inside the room



Fig. 9  The viewpoint is closed to the bed

Fig. 10 An oblique vision in a side

Fig. 12 And in the other side

Fig. 12 A total perspective traced on a cylinder in axonometric representation


1.3.2        Natural infinite 

Leonardo defined philosophy as “images of mental talk” by drawing a deep parallelism  between  Nature and Reason. Luca Pacioli suggested Leonardo to read the V book by Euclide. This was a basic point that he extended with genial intuition, by using proportions also in time, space, sounds, weights, sites etc. By this scientific investigation  he discovered  “… varie e strane forme fatte dalla artificiosa Natura…”

( ..variant strange shapes made by Artificial Nature..), that he fixed in sketches  and used later as codes in his works.

His scripts edited only in 1881 were pressed as a simple first draft on a wax table in only one passage, by using a Roman technique. These were written all in a reverse way. It is possible to read them only in front of a mirror, for emerging a similarity between natural process and interpreted reality.  

Fig 14 Mechanical wing by Leonardo

Fig 15 Hands drawings by Leonardo


Hand can use a double direction to write vision.

From left site to right, from east to west, the vision of God in human beings as connection between result and matrix.  A centripetal vision that works for uniqueness and defined quantity. In this configuration it is also a way from up to down, toward an unchanging centre as permutations of an eternal set. 

From right site to left, from west to east, the maternal vision toward human beings as natural infinite in a centrifugal process. Leonardo with his reverse scripts describes this process, by representing the maternal vision.


Fig. 16 The right hand of Madonna litta by Leonardo

Fig. 17  The nearly profile of Madonna

Fig. 18 The right hand and look of baby


   1.2.2 Second step: A temporal distance


  1.2.2 …. A coherent time…..



An allegory

Time, Real and Imaginary

An Allegory

by Coleridge

On the wide level of a mountain’s head...

Two lovely children run an endless race,

              A sister and a brother!

              This far outstripp’d the other;

Yet ever runs she with reverted face,

And looks and listens for the boy behind:

                  For he, alas! Is blind!

O’er rough and smooth with even step he passed,

And knows not whether he be first at last.





If we define a code, as open strata of diachronic matrixes, we can generate new endless variations.

If we see the generative work by Celestino Soddu about “Medieval Towns Morphogenesis” , we can discover codes and matrices that work to produce endless variations of the same identity.


Fig 19/20 Four different Scenarios of Medieval Towns generated from an interpretation of frescos by Giotto and Simone Martini


Also in  “Old Chicago”, we can discover new generated Scenarios in perfect harmony with ancient environment, such as to seem with the same cultural time code.


Fig. 21/22/23 Different Scenarios of generated sky scrapers in Chicago of the beginning of the last century




1.2.2 ….a reverse time…


Some days ago people got the news that after seven centuries the tomb of Petrarca  will be opened for rebuilding his physiognomy with VR. But it might be for his DNA too


The question is: a Petrarca clone will be a Poet? In a strong temporal distance the same code will rise a great poet in another contest? If yes, the code is the whole, but if we read this fragment:

“If we were not something more than unique human beings, if each one of us could really be done away with once and for all by a single bullet, story telling would lose all purpose.  But every man is more than just himself; he also represents the unique, the very special and always significant and remarkable point at which the world’s phenomena intersect, only once this way and never again.  That is why every man’s story is important, eternal, sacred; that is why every man, as long as he lives and fulfills the will of nature, is wondrous, and worthy of every consideration”.  Hermann Hesse, Demian (1917)

We can simply deduce that story telling are losing all purpose. So the clone of Petrarca cannot be a poet. But this is not enough.

5. Conclusions

 We can only say

  1. The visionary world can rise only inside a natural infinite.
  2. The cloning is a 2D point (temporal dimension is zero). 

In "Zibaldone" Leopardi said:" It is infinite a labor of our imagination… infinite is an idea, a dream not a reality: at least we have not any proof of its existence, not even by analogy."



G.Leopardi, Zibaldone, Newton Compton, Roma 1997

H. Hesse, Peter Camenzind, Gertrud, Rosshalde, Demian, Newton Compton, Roma 1992

C.Soddu, "L'immagine non euclidea" (The not euclidean Image), Gangemi, Villa San Giovanni(RC), 1987.

C.Soddu, "L'idea di spazio nelle rappresentazioni d'arte", (the space idea in Art representation), in "Critica d'arte" magazine, n.16, Firenze ,Gennaio/Marzo 1988.

C.Soddu, "Citta' Aleatorie", (Random cities), Masson., Milano 1989

C.Soddu, E.Colabella, "Il progetto ambientale di morfogenesi", (The environmental design of morphogenesis), Progetto Leonardo, Bologna 1992