Introduction by the Editors

Foreword by Christopher Alexander

Images of Community

Review of Alexander's The Nature of Order

The Architects and City Planners:





Andrés Duany


Léon Krier


Images of Public Buildings


The Scientists:


Philip Ball, Brian  

    Goodwin, Ian



A Response by


    Alexander: New

    Concepts in


    Theory Arising

    from Studies in



Images of Neighbourhood




Built Work of


   Alexander and his



* Examples of






The Kind of


   Architecture is:

   Jane Jacobs,



   and Since


The 1982 Debate



   Alexander and

   Peter Eisenman


Images of Comfort




Nikos Salingaros:   

   Design Methods,

   Emergence and




* Brian Hanson and

   Samir Younes:  

   Reuniting Urban

   Form and Urban



Images of Building Details


* Michael Mehaffy:

   Meaning and the 

   Structure of Things



  Alexander: Our

  New Architecture

  and the Many

  World Cultures


Nikos Salingaros:

   Fractals in the New



Brian Hanson: 

   Architecture and

   the “Science of



Images of Landscape and Gardens


Michael Mehaffy: 

   Codes and the

   Architecture of Life


Nikos Salingaros: 

   Towards a


   Understanding of

   Architecture and



Brian Hanson:   

   Science, Voodoo

   Science and



Images of Houses


* Michael Mehaffy:     The New Modernity



   Alexander:  Sober

   Reflections on

   Architecture in Our



Images of Drawings


Afterword by the Editors


       *       *       *

London Conference

Information  - NEW


Discussion Page




Previous Issues


Contact Us


Additional Links

And References


Katarxis Nº 3




A Primer on "Connective Geometry,"

and Some Additional Examples


This gallery is a work in progress, and emerging examples from

around the world will be added as time goes on;  please visit again later. 


You can also nominate additional examples. that you think would be appropriate.  The architects, designers and builders submitted may want to consider joining our growing global network of practitioners.


Tekke Ensi, 19th Century



Space, we now understand, is not an isolated collection of objects related in a simple Cartesian matrix.  Rather, it is a rich 4-dimensional field that includes time and process. 


The constituents of this vast structural field have been described in a number of ways by physicists and philosophers.  (See for example A.N. Whitehead, Process and Reality.)  The architect and physicist Christopher Alexander has developed a theoretical framework in which these constituents can be described as "centres." 


Such centres form regions that are amplified by other regions, forming perimeter fields with respect to the centres.  This system of centres is embedded in still-larger systems of centres, with both hierarchical and network aspects.  Each centre is in fact embedded in the totality of all centres, but with diminishing contextual influences. 



             A simple system of centres -              A much more complex system -

                 a cathedral plan                                    the urban fabric of Rome


Process is central to the understanding of how such centres are formed, and transformed.  The key process is what Alexander calls a "structure-preserving transformation."  (Mathematicians call this transformation "symmetry-preserving," and they refer to its counterpoint as "symmetry-breaking.")


The formation and transformation of centres results in a characteristic set of properties that are familiar to designers.  They are structures that resonate deeply with human experience.  The perception of such underlying order, in fact, gives rise to the human experience of beauty. 


Seen this way, beauty is less a "constructed" personal experience, and more a kind of symmetrical interaction between the person and the larger structure of things.  It is not, therefore, a purely "subjective" phenomenon, but can be discussed and developed as a collective art.  It is, above all, a perception of natural order.


Alexander identifies 15 such properties, discussed in great detail in his new book, The Nature of Order.  We can summarise them here as follows:





1  Levels of Scale                 2.  Strong Centres       3.  Boundaries           



4. Alternating Repetition     5. Positive Space             6. Good Shape



7. Local Symmetries           8. Deep Interlock          9. Contrast

                                              and Ambiguity



10. Gradients                     11. Roughness               12. Echoes



13. The Void                     14. Simplicity and             15. Not Separateness

                                          Inner Calm


The crucial point to grasp is that such a structure of centres forms a vastly complex connective network in space.  Beyond any symbolic meaning, this structure embodies real connective symmetries.  It does so through the exceedingly complex patterns of interactions between its constituents -- its centres.   This greater complexity arises is in spite of the fact that the steps of transformation can be deceptively simple.


Thus this very real connective structure carries real and definable (and discussable) attributes.  For example, one can vary the degree of connectivity, and the density of centres.  In so doing, Alexander argues, one affects the very life of the structure.


Alexander's aim is that architects and others can use these insights to structure networks of centres into more potent classes of connective geometry -- more beautiful, more coherent human environments.  This offers the ability to create a much richer kind of order in the built environment of the future.


Following are examples of  new dwelling structures that contain elements of these richly connective classes of geometry.


Homes in North Africa

    Courtesy of the Aga Khan Awards for Architecture


  Cottages in a New Village in Turkey

A Courtyard House in Texas

This structure follows patterns of house-making that are regional to the southwestern US.  As such, it incorporates common Mexican, Spanish and Islamic patterns, but applied in a completely unique way.  Note how this structure connects both internally and with external structures:  hillsides, sunlight, and so on:


   Views from the bedrooms:


   Views from the main bedroom:

    The building from below:


A Cottage in Texas

A cottage that incorporates the existing landscape, in a system of centres extending out into native areas:


   Projects in the Islamic World

   A major part of the larger world to which our efforts at a

   sustainable future must connect


   Houses in Bali