GENCITIES AND VISIONARY
WORLDS* *

** **

**Celestino Soddu.**

*Architect, Professor of Architectural Design*

*Generative Design Lab, Department of Architecture
and Planning.*

*Politecnico di Milano University*

*e-mail: celestino.soddu@polimi.it*

Abstract

When we
look at clouds transforming themselves with the help of the wind we interpret
them following our subjectivity and own cultural references. We use the same
transforming logics, the same anamorphic logical approach for building our
subjective system of codes that we use for recognizing and facing the events
surrounding us.

This
system of decoding, unique because it fits our subjectivity, mirrors our
creativity and imprinting as artists and designers. Generative artworks spring
from this subjective morphogenetical engine. Forms are only a subsequent
step.

Investigating
on these transformation logics and the subsequent anamorfic approach we can
construct our generative engine reaching a strong identity and recognizability
of our works.

One of
the most interesting fields for investigating these logics is the generative
engines coming from moving from different dimensions, from 2D to 3D and back,
using different perspective approaches.

Each
physical city, mirroring their own Ideal City and the multiplicity of its visionary
variations, will be, finally, not clonable but unique, unrepeatable and
unpredictable, natural and harmonic.

1.
Forms, identity, recognizability and morphogenesis

We
recognize a form if we identify it as similar or, however comparable to those
already experienced. We recognize only a form through the memory of other
forms. But they are not singly remembered forms, neither sequence of different
events. The memory is structured in system built activating a logic that
reflects our subjectivity linking and associating different forms by
identifying particular aspects of them. We could affirm that each of us builds
and identifies a proper morphogenetic code in associating different forms
together. This code is direct expression of our way of seeing, of our cultural
references, of our identity.

There
are many and different ways of experiencing and of recognizing the physical
world. Some people identify and build the code through the logical-geometric
reconstruction of the process of realizing the forms, other people approach it
by recognizing, structuring and following the subjective satisfaction of
particular needs, from practical to aesthetical or symbolic requests. Everyone
identifies and progressively sharpen during their life a series of recognizability
codes, a structure of species that fits their own subjectivity and that
progressively identify themselves following the increasing of own experience
and of own culture. Everyone, therefore, has a unique approach in recognizing
and appreciating the events surrounding him. Besides, each person identifies,
following his personal way, what appears as normal (inside the species) and
what as exceptional. Every system of subjective codification allows people,
however, to share identifications with other people and to find the possibility
that each form simultaneously belongs different species. Looking at a stool, we
could affirm, for instance, that the object belongs to the "chairs"
species, with the exception to have not the back, or that it belongs to the
"tables" species, with the particularity to have a reduced dimension,
or to the "staircases" species with the exception to have only a
step...

If we
consider the field of creativeness and of design, the investigation on species
and on possible approaches activated by each people to build their codes of
recognizability of forms is very useful to explain the logical structure of
creation. This investigation expressly identifies different creative ways
bringing to the conceptual creation of the idea and its structure and the
specificity and identity of the creative approach of each one.

For
instance, let's take a pyramid: a physically existing pyramid like the Pyramid
of Cheope. Each people have a memory of this form and he associates it to other
forms. If we call these forms as "pyramids" all people could agree,
because an individualized geometric common concept exists for all people with
the name of pyramid. Instead, if we want to go ahead, each of us could also
associate the pyramid of Cheope to other events whose logical structure belongs
to the species that each of us built for recognizing the pyramids. These logics
can conceptually be very different, and they allow us to produce groups in
which it is possible to overlap similar events. Some examples. A first logical
approach could be defined by considering the pyramid as a solid cube from which
a whole series of pieces has been removed through plain cuts. This vision for
subtraction of the three-dimensional solid is the characteristic vision of the
sculptor. Michelangelo affirmed that the statue already exists in the stone; it
is only necessary to remove what is superfluous. If this logic is adopted for
building a species of forms, any form that can be identified as what remain of
a cube after cutting away some pieces, it belongs to the same species of the
pyramids.

A second
logic could be constructed starting from a plain matrix that produces spatial
events. A square with two diagonals, when the center and intersection of the
two diagonals is "lifted" and moved in the space produces pyramids of
which that of Cheope is only one among endless possibilities.

A third
possible logic still could be born from the cube. If the superior face is
magnified or reduced smaller, this transformation produces a whole series of
solids where the pyramid is the moment in which the superior face is reduced to
zero, while the trunks of pyramid and the hourglasses are the moment when the
dimension of the superior face is positive or negative.

We can
identify a fourth possible logic considering the pyramid as a solid generated
by the following facets of a half-sphere. If we progressively divide the
half-sphere in triangles we produce a whole series of solid that, departing
from one almost-half-sphere with a large number of triangles we reach the
square based pyramid as next to last step before the tetrahedron.

A fifth
logic, that we could call zigurrat, considers the pyramid as an overlap of
squared based prisms. The range can start overlapping two prisms and can go
ahead increasing the number or prisms when each one becomes more and more
thin.

But we
could continue imagining the pyramid as one individual of a species in which
each event is inside the progressive transformation from the cone to the triangular
based pyramid or to the triangle itself, imagining this last event as a pyramid
with the base constructed with two or only one side.

Which is
our subjective logic for declaring that an event is a pyramid? If we find us in
front of the pyramid of Cheope anybody have no doubts because this pyramid is a
common point of reference. But if we are looking at an event whose form is not
so axiomatic, because it contains, for instance, also some curved surfaces or
it has not peak, and so on, who will identify it as pyramid, even if particular
and on the boundaries of this species? Perhaps only who conceives the pyramid
as an event inside the progressive transformation of a half-sphere, or of a
cone. The other people will associate the form to other morphogenetic
species.

Every
form, when losing its geometric axiomatic aspect, that is when no one can
incontrovertibly associate it to only one geometric species, becomes anamorphic
shape. It becomes a form changing meaning, changing character, changing
"species" according to the subjective approach of the observer. In
other terms it is possible to associate each complex form to different species
of events using different logics and association codes. These differences
define the subjective recognizability, the matrix of reference based on own
personal cultural background. We could define these approaches to forms as
anamorphic interpretations, as the results of subjective anamorphic
logics.

These
approaches normally happen when we are fascinated by the contemplation of the
clouds, interpreting their forms in multiple ways; or when we find human
expressions in the form of some rocks or in the plot of a carpet.

The
anamorphic logical approach is different from anamorphosis because it doesn't
happen through an artwork, where the author stratifies meanings, but it happens
when we look at complex forms, also natural forms, using our memory and our
subjective codes of recognition. The anamorphic logical approach is the
creative speculation on possible different readings of the existing form and of
the possible variations of its image, meaning, and structure. Each of us
implements this approach with the awareness not of the ambiguity but of the
stratification of possible affiliations to different species, to different
functions, to different aesthetical, symbolic and functional structures. In
this sense, the anamorphic logical approach can be considered one of the bases
of the creativeness, of the design imprinting and of the style. Following their
subjective logic, each artist makes his artworks recognizable. His approach to
interpreting forms is an essential part of the identity of his idea.

Generative
Art has discovered the anamorphic logical approach as one of the possible
motors able to produce endless possible events through the activation of codes,
of morphogenetical logics. Generative Art also discovered the not-eludeble
strength of species. Generative artists need to realize their creative identity
in the endless generated artworks. Each artwork, also unexpected, must be
recognizable not only as single results but as belonging to a species, to the
artist's identity and style. If not
Generative Art will be confused with Random Art. Nothing is so far and
different as Generative Art and Random Art.

2. The
passage from a dimension to another.

The
field of reference is the relationship between the three-dimensional form and
its two-dimensional image in its manifold variations. But we could consider
also the image and its possible forms, in its manifold interpretative
variations. The "generative" reciprocity between the form and the
image of the form where every form "produces" a plurality of images
and where each image "produces" a plurality of forms, in an endless spiral,
is one of the principal fields of construction of the Generative Art, of the
art that was born from expressing ideas as morphogenetic logic.

First of
all, a difference of dimension can exist between the form and its image. Often
this difference exists by considering the form as a three-dimension event and
its image as a two-dimension representation. But this is only one of the
possibilities. We can get a 3D representation from an event having a lot of
dimensions or we can increase the dimensions of the representation in comparison
to the dimensions of the event, when we, for instance, try to represent the
image of a jewel pending from the neck of a noblewoman in a seventeenth-century
portrait by building a three-dimensional object that interprets the image of
the painting. In this case only one of the possible two-dimensional
representations of the constructed 3D event will fit the original image.

If we
like that the result of this moving through different dimensions can be
considered totally acceptable, it would be necessary that each point of the
form corresponds to one point of the image and that the structure of the
form-system will have the same topological logic then the image-system. This
obviously is not possible in the passage from a dimension to another. The "perspectiva
artificialis" of Piero della Francesca is only one of the possible
two-dimensional representations of three-dimensional events. With this approach
a lot of information are lost. The inverse run, from the perspective
representation to the three-dimensional event is, in fact, only a reasonable
hypothesis. This passage could be considered as acceptable only if we built
this three-dimensional event on the base of a lot of further knowledges (what
we don't find in the image) as the point of view used in the representation. If
we don't know previously it, we could identify it only through a subjective
interpretation; therefore every interpretation "produces" different
forms.

More. We
can reconstruct only what we see and not what is behind or what is inside the
represented events. As Florenskji said, the perspective image represents only
the skin of the three-dimensional event approaching the three-dimensional event
to the two-dimensional representation. But, also with this consideration, the
bending of the skin won't be ever sufficiently represented in the plain sheet
of the sketch. The relationship between bending of the skin and plain sheet can
be compared to the relationship among Euclidean geometry and not-Euclidean
geometries.

Not
only. We have to operate a further interpretation choosing among the different
techniques of perspective representation that we suppose could have been used
for producing the two-dimensional images. These techniques are manifold and we
could synthesize them in three types, each of which links the form to its image
in different way:

1.
Perspective - 1*1.

Perspective
with only one point of view and only one direction of the look. The observer
and the represented event are faced.

It is
the "perspectiva artificialis" of Piero della Francesca: only a point
of view, therefore only one eye and not two, and only one direction is
considered. This direction becomes also the point of central escape in the
geometric construction of the image.

*Piero della Francesca, “Flagellazione”.
If you reconstruct the represented space, as L.Ragghianti did, you will find a
very long space, different from your expectation. *

2.
Perspective - 1*N.

Cylindrical
and spherical total perspective: these perspective technique considers only a
point of view but manifold directions of the look, up to cover 360 degrees in
horizontal (cylindrical perspective) or also in vertical (spherical
perspective). The observer is the center of the system.

The
curved perspectives follow the naturality of the vision. In fact, if we are
inside a space, for instance a rectangular room with the parallel walls and
with the plain ceiling, and we look toward a side we will see all the parallel
sides to the constructed image converge toward a point (the fire). Then, if we
turn the eyes and we look at the opposite wall, we realize that the same lines
converge toward another point, opposite to the first one. Quickly turning our
look from one side to the other, we could realize that these parallel lines
converge in two points of the image that we are building in our mind. A bundle
of parallel straight lines converge in two points only inside a non-Euclidean
geometry system. The amazing aspect is that if we pass from a perspective built
inside a Euclidean geometric system to a perspective built inside a
non-Euclidean geometry, as spherical geometry, the mathematical representation
of the transformation, the algorithm representing the passage from 3D into 2D
becomes, mathematically, very beautiful being possible to represent all through
the measure of the angle. I have experimented these non-Euclidean total
perspectives twenty years ago. These experimentations and the algorithms that I
wrote for building and representing the "total perspective" are at
the base of my generative software. They configure a generative engine able to
generate endless possible results starting from a single image. (C.Soddu,
"L'immagine non Euclidea" non-Euclidean image, 1987, Gangemi
Publisher)

*Generated Castle by C.Soddu
represented in Total not_Euclidean perspective in two different views, the
first one with horizontal sight and the second inclined, using the software
designed by the author.*

* *

*Generated Castle realized with
rapid prototyping using 3D STL model directly generated by Argenia and the
Cstle of the other images represented with anamorphic total perspective using
the software designed by the author.*

* *

3.
Perspective - N*1.

Reverse
perspective by Florenskji. This approach considers a multiplicity of points of
view, the two eyes and their various possible motions, and only one target of
the look.

The
represented event is the center of the system.

This
perspective intends to contain in one two-dimensional image the multiplicity of
different visions. The practice construction of this perspective approach can
be realized through an interesting conceptual overturn that I have experimented
in my software. If the target of the look is unique and the points of view are
different we can capsize the total perspective, that has only one point of view
and different targets, setting the point of view in the target and the
directions of the look in a lot of "eyes". The realized images could
be assimilated to a representation of the skin of the object seen by the
inside. The reverse perspective has been identified and explained by Florenskji
looking at the Russian icons. Being sacred representations the fundamental
choice is setting the represented event as center of manifold looks. In these
two-dimensional images the representation of the face of the Saint is,
according to my hypothesis, represented as seen by the inside of its same head.
Since, as Florenskji affirms, we represent only the "skin" of the
physical event we can capsize the face. Its projection on a sheet will result
similar to the representation in reverse perspective of the Russian icons. In
other terms I like to affirm that the reverse perspective is the overthrow of
the spherical total perspective and not the overthrow of the" perspectiva
artificialis" of Piero.

*Russian icon with Christ
represented in “reverse” perspective.*

The
passage from a dimension to another, and particularly from the
three-dimensional to the two-dimensional events through different perspective
logics, but above all the reconstruction of the object 3D using different
perspective-visual logics introduces fields of variation owed to different
factors inherent in the dimensional transformation and in the type of used
representation. These fields of variation belong to the subjective
interpretation of the image or better, to the interpretative reconstruction of
the parameters that could be used for the production of the image, and of the
reconstruction of the parts that are not represented because not in sight
because behind or inside to the volume of which the skin is represented.

The
hypothesis of reading an image decoding it through the perspectiva artificialis
when instead it had been built through the Florenskji reverse perspective can
produce unpredictable forms. For instance a cube could be reconstructed as
pentagonal prism. This happens because, with the inverted perspective, the two
opposite faces of a cube are represented as "in sight" together with
the face in front of the observer. The reverse perspective of a cube is able to
show three faces in sequence because you can see the cube both from left and
from right. This happens everyday when we look at a very small cube and we
approach it to the eyes. An eye sees the right face and the other the face on
the left. The resultant image is the synthesis of the two sights. The mental
image reconstructs a cube representing three consecutive faces. If we look at
this representation with a canonical Euclidean perspective approach we need to
suppose something different from a cube. The space "behind" appears
too much ample and the re-constructive interpretation of the three-dimensional
form can bring us to imagine more than a hidden face, for instance two, and
therefore to generate an acceptable reconstruction of a prism with five or more
consecutive sides. The cube, through these following passages of dimension (3D
- 2D - 3D) is turned into a pentagonal prism.

These
transformations are born from our interpretations: It is a "natural"
construction of generative motors that mirrors our creative identity, our
cultural references.

The idea
of an architect doesn't base on forms but on transformations. This is a
transforming approach able to see the existing world as a dynamic world, and
able to generate visionary scenarios and their endless variations. The
generative engines are the structure of the designer's idea. They work on
morphogenetic codes fitting the oneness of the approach; they are the
anamorphic logics that allow the designer to generate endless visionary worlds
by mirroring, in their multiplicity, the design idea.

*Generated castle by C.Soddu,
represented in elevation and in two different “reverse” perspective, using the
software designed by the author
following the Florenskji approach.
*

3.
Construction of generative morphogenetical processes: subjectivity and
variations.

The
identity of an artwork exists if people can recognize it as belonging to a
species. So, if we like to build the identity of our artworks we need to
identify its species and to realize it designing an artificial Dna. This
approach is Generative Art: building a
series of logics of transformation able to generate endless possible results
recognizable through the morphogenetical paths used for their creation and
through the reference to possible anamorphical logics belonging to our creative
and cultural identities.

The
results, in terms of quality and extended appreciation, are the best where the
anamorphic logics produce answers pertinent to different subjectivities,
therefore where the generated complex system don't give only the possibility to
be understood as axiomatic structure of a shape or of a function but its
complexity performs the availability to subjective and unpredictable uses. This
usability is realized and appreciated when the suggestions, the logics of use
and the aesthetical appreciation of each user is related to the complexity of
the designed system and to the potential anamorphic interpretations that this
complexity makes possible.

Not
only. The identity have to belong to a species without denying, rather
strengthening the identity as individual, as unicum. It brings to consider that
the design of morphogenetical paths rather than of shapes doesn't remove
anything from the final results identity but strengthens then, especially
because of the parallel presence of "variations". As happens for the music, from Bach to
Mozart and to jazz. Variations are built consolidating different forms in
different moments, but these results are reciprocally congruent because of the
common morphogenetical paths that, from the detail to the whole, are at the
base of an idea. These "endless" variations could seem aesthetically
less strong and functionally, less recognizable than only one result chosen
because considered the best at the end of the optimisation of the form-function
relationship. This approach is misleading. The affiliation to a species, with
the possibility of mirroring each result in the infinity of the parallel
variations, creates two congruent layers of recognizability and identity that
are strengthened one each other: the identity of the species and that of
individuals.

*Two variations of ”Cordusio”
project by C.Soddu. All these 3D models are fully working in the field of
functional and structure system and are completely generated by Argeněa.*

*“Cordusio” project by C.Soddu. the
aim of this architectural projec was to fit the Futuristic cultural reference
of Milan buiding an architecture able to fit the Milan identity as represented
by the cordusio square in the beginning of last century. This because the
twenties of ‘900 were really important in construicting the “idea” of Milan.
2005.*

This
approach find the quality also in the oneness conjugated with the
recognizability. For instance the oneness of a painting of Van Gogh is also
appreciated through the possibility to recognize it as painted by Van Gogh, as
belonging to a species with unique characters and unrepeatability. This happens
in the appreciation of the Nature where the multiplicity of the variations
mirrors the multiplicity and oneness of every one.

This
process of appreciation happens not only on the aesthetical layer but also in
the aspects more directly related to the functionality. The use of the object
becomes "intuitive" really because linked to subjective runs of
appreciation and recognizability. As, for instance, sometimes happens in the
structure of software interface. For using a function, manifold
"logical" runs are designed mirroring different and subjective
possible approaches.

*Four more visionary variations of
“Cordusio” project for Milan, realized by the author usig “Argeněa”, his
generative software. Milan, 2005*

4.
Generation versus Cloning.

In a
production process of individuals belonging to a species, the copy doesn't
exist and, we could say, it is not possible. We are able, in fact, to copy an
object, to reproduce it until the least details, but we are not able, with the
same tools and with the same philosophy to copy a species. This because the
anamorphic logic that has been activated during the design of the species is,
for its own nature, different from the anamorphic logics of whom analyses an
object, or also a series of objects belonging to the same species. The
subjective and interpretative component is so strong and involves the passage
from a conceptual system to a plurality of physical events that is not possible
to "reconstruct it"; it is possible only "redesign
it". A "generative" design is not reproducible departing from
the results. It is possible to produce only "clones" of single
variations. The only certainty that we can acquire is the feasibility of the
generative project, because someone has already realized it. We cannot copy it.
We can recreate it only ex-novo using the personal subjectivities and interpretative
ability. But it will be another project, however.

5. The
generative city and the visionary worlds

The
future of the ideas and their realizations is a city living of unique events,
unrepeatable and anamorphic events able to answer in pertinent and recognizable
way to a plurality of citizens with their unique identity. But also a city that
progressively discovers its own identity approaching to the Ideal City that is
in the mind of who lives and designs it. As each ideal city and the visionary
worlds representing it, also every physical city could be, surprisingly,
unpredictable, not homologable neither clonable and therefore, finally, natural
and harmonic.

References

[1]
Celestino Soddu, “L’immagine non Euclidea”, (not-Euclidean image), Gangemi
Publisher, Rome 1997

[2] Celestino Soddu, "Generative Design / Visionary
Variations - Morphogenetic processes for Complex Future Identities" in the
book Organic Aesthetics and generative methods in Architectural design"
edited by P. Van Looke & Y. Joye in Communication&Cognition, Vol 36,
Number 3/4, Ghent, Belgium 2004

[3] C. Soddu, "Meta-Code, Identity’s Borders" in
"Generative Art 2004", proceedings of the International Conference
GA2004, Aleadesign Editor, December 2004

[4] C.Soddu (interview to), "From gene to design:
Prof. Soddu and his Generative Design", pag. 6-13, Magazine
"Designer" n. 1, 2004, Changsha, Hunan , China

[5] C. Soddu,
"变化多端的建筑生成设计法"
(Generative Design), article in the magazine "Architect", December
2004, China.

[6] C. Soddu, “Milano, Visionary Variations”, Gangemi
Publisher, Roma, May 2005.

[7] C.Soddu, “Generative Art in Visionary variations”,
“Art+Math=X” proceedings, University of Colorado, Boulder, 2005.

[8] C.Soddu,
“Visionary Variations in Generative Architectural Design”,article in Chepos
magazine number 003, TU/e, Eindhoven 2005.

[9]
C.Soddu, E.Colabella, “A Univesal Mother Tongue”, Leonardo Electronic Almanac
Volume 13, Number 8, August 2005