Ποιειν Και Πραττειν - create and do

Fractal Planning by Sue Tilden

There is work being done by planners, geographers and others to explain the growth of cities along the lines of chaos theory and fractal mathematics, including the resulting graphic expression of fractal patterning.

Michael Batty and Paul Longley, authors of Fractal Cities: A Geometry of Form and Function, point out that Jane Jacobs, well-known urbanist, has been saying for some time that cities grow organically and thrive on seeming disorder, and that attempts by architects and planners to impose a rigid geometric form or structure are unrealistic…”Fractals are objects with irregularities that form an image of the entire object and that repeat (sic) geometrically at different scales – the object is said to possess the property of self-similarity.” A mountain range is a fractal because it is made up of irregular boulders of different sizes, each of which looks like a mountain; a city is fractal because it is made up of neighborhoods of different sizes that look like small cities. Fractals are unlike smooth squares or circles – the standard fare of Euclidean geometry and Euclidean city planning…Fractal analysis may provide a new way to understand the power of physical form to determine the quality of life in cities, new ways to visualize the impact of decisions on cities, and new ways to plan. (H. Henderson book review in Planning magazine, July 1995.)

An article by Beverly Russell appearing in the May 1990 issue of Architecture magazine on the work of artist Frank Carson opens a synchronistic view to a new, or perhaps pre-Euclidean, geometry “which considers the spatial, coincidental and coherent aspect of proportion rather than embodying the linear and functional intensity of measurement. Measurement is objective, separate and orderly. Proportion is subjective, inner-related and harmonious.” Carson works with “a math of circles and curves” and a primary tool of his work is the use of the golden ratio: 1.6 to 1.

Pythagoras’ work 2,500 years ago explored this “golden section” and its “connection to musical intervals and harmonic vibrations and thus linked the understanding of harmonious visual and aural proportions.” Leonard Fibonacci in the 12th century explained the concept of a universal proportion mathematically, discovering that if you take any two numbers and add them up in a series, there is an inherent harmony in the series. The ratio between any of the two approaches a constant, known as Phi (named after Phidias the Greek sculptor who used it), or the golden ratio: 1.62 to 1. A later dissertation by Luca Pacioli, illustrated by Leonardo da Vinci, noted this golden ratio as the inherent, organic proportion informing everything that grows, including the human body. Da Vinci’s famous drawing enclosed this geometry within a circle and a square, thus uniting the rational and the non-rational.

It is from Fibonacci by way of Mandelbrot and others that fractal mathematics derives – the mathematical expression of chaos theory.

People in many different fields are investigating the applicability of chaos theory to their understanding of their disciplines. A fascinating linkage of the genetic code to the Chinese I Ching is explored through chaos theory and fractals by Dr. Katya Walter of the University of Texas in the Tao of Chaos, first published in Germany as Chaosforschung, I Ging und Genetischer Code.

Predating formal chaos theory, perhaps, was Marshall McLuhan, who, according to Gary Wolf’s recent article in Wired magazine, “was fond of repeating a slogan he claimed to have gotten from IBM: ‘Information overload = pattern recognition’.” This is ‘metonymy’: the part can stand in for the whole. McLuhan believed that metonymy, which can be represented graphically as a fractal design, or as a spiral, or as a web of concentric circles, is the natural mode of electronic communication. In the same vein as Jane Jacobs speaking of cities, he felt that “attempting to force linear, logical, coherent plots and arguments into electronic dramas or discussions creates unintentional comedy.”

The Greek artist, Nikos Hadsikyraikos-Ghikas, described his work as ‘lyrical geometry’. Speaking of the out-of-body experience he had, said he felt in them the total fusion of reality and dream. (The Athenian, October 1994.)

Much earlier, Nathaniel Hawthorn noted in The House of the Seven Gables that “all human progress is a circle, or rather in an ascending spiral” and spoke about “the charm of nomadic life…pitching dwellings where the sense of beauty dictates.”

Fractal imagery is beautiful. Natural replication and genetic growth occurs according to a harmonious progression. I have envisioned the form of a city as a woven construct, made up of many components, variously seen as an interplay of filaments, forming a web of human environment that can be soft or hard, beautiful or ugly, harmonious or unbalanced. Printed city plans are strikingly similar visually to American Indian hoop weavings and medicine wheel designs and also to the mandala images appearing in a variety of world cultures. This corresponds with ideas of the organic growth of cities and graphic characteristics of fractal patterning in general.

It is entirely appropriate that planning and poetry be linked, the technical and the artistic, both in our Myth of the City 1995 context and in continuing work on achieving livable cities.

From an open letter written to participants in the “Myth of the City” conference in Crete in September, 1995

Sofia Yannatou’s perceptions of the City, presented at the Tech Center outside of Iraklion, sparked a linkage for me with the very new exploration of fractal modelling in planning. This needs to be investigated as a way of understanding what is being “replicated” (and perhaps why) versus other possible choices for city form in modern times.

How is fractalization initiated and what determines its choice of replicable form?

How might this be driven? Selected?

Linking back to a proposition I postulated in the response to a tender soliciting new approaches to understanding and shaping urban form, I described a system of filters to guide component selection in the planning process. This in fact depicted the way in which rules and laws such as development guidelines direct and shape the way an area is formed. Fractally speaking, how could the application of such filtres allow only certain replicable components to be accessible as city-building choices? (This differs from actually pre-selecting the components rigidly.) How could a “natural” replication be instigated that self-determines and self-reinforces, and is this possible in today’s development environment?

It is here that poetic insights do indeed inform fractal planning. What is livable, what is humanly replicable, what resonates with people? Why do we have worldwide replication of “modern” cityscapes and edgescapes which are so inhuman – why are the outskirts of Iraklion much more like the outskirts of Athens and Los Angeles and Port au Prince than of the hinterland of Crete?

So another linked concept is the interactive relationship between city and hinterland. We had some fun coining the term “rur-urb” during the conference, as being further out than a suburb and referring to the rural scape. But it isn’t possible to be serious in planning for anyplace without taking an interactive approach regionally and even globally. And this loops right back into the compelling model of the Minoan-age 100 Cities described by Bishop Irinaios. In it we find a distributed system in which every social component has not been co-opted by a few major cities – in which people could distribute themselves according to a more evenly spaced population pattern across the landscape (including both urban and rural areas) while still maintaining access to necessary services and amenities.

The dignity of man living humanely in a harmonious environment is a replicable model eminently compatible with concepts of regional integrity, maintenance of culture and tradition and also with the emerging technologies of the electronic frontier. This hearkens back to Jeffersonian ideal which I might update to term: “fully actualized man in a rationalized countryside.” Crete might be a very good place to attempt this, as the people there are still in connection with their place in distinctly unmodern ways, while being aggressive and energetic enough to embrace new techniques.

What would a conjunct set look like, combining a filtered fractal growth model with the Minoan 100 Cities model? What could be self-limiting mechanisms or built-in “stop” points (much like genetic marker proteins) that indicate when a growth sequence should cease and creation of a new centrum begin? Do the “genetic messengers” have to be legalistic? Must they be minutely planned and selected to overcome the counterforce attractors of greed and “alien” development patterns? Or can they occur naturally, as the needs of the citizenry dictate? Is the hierarchical model of religious organizations’ distribution of services and personnel another valid pattern, one which is more driven by expressed human needs than market or bureaucratic forces?

In regional/urban planning we would be talking about such things as:

-          Maximum service area / capacity for district health centers, while maintaining quality of care

-          Local / regional educational facilities, especially in light of telecommunication capabilities

-          Libraries and resource centers

-          Courts and municipal services

-          (specifically for Crete) sustainable tourism development patterns

-          Commercial residential development, where and how it will be encouraged or allowed

…all developing and flourishing within the distinctive cultural and environmental context of a place.

Many times in planning, certain actions or initiatives do not work, the plan doesn’t “take” in a specific situation such as a downtown development plan that doesn’t result in a rejuvenated and lively downtown, or a commercial venture that fails to inspire investment or generate jobs.

We might ask – how does fractal replication occur?  Ripple effects are evident in such phenomena as gentrification or some special use development such as an area that seems to “attract” horseback riding related development, or the unplanned growth of a theater district.

There must be a Start Event …which must occur in a Receptive Medium. The Start Event should be strong without being cataclysmic, which can mean being sustained or repeated. It must have definite shape and characteristics, i.e. ready replicability. It can be devised through CAREFUL calculation or may be natural, seeming to arise out of the waveform of chaotic possibilities in a given place. Planned seed projects are planned Start Events and very often iffy propositions. Possibly the most likely to succeed in encouraging replication are planned reinforcers to naturally occurring Start Events, which in effect can be quite like using the Start Event as a naturally occurring filter prototype, which should be most suitable and appropriate for the place, but like any new growing thing, may need support and nurturing to thrive and spread.

In the example of an unplanned theater district, once the Start Event has appeared (one or a few theaters open in an area), planned reinforcers could be applied such as implementing zoning laws and development incentives which allow and encourage theater related activities: building of a municipal parking garage to serve theater patrons, municipality funded drama festivals or advertising assistance. Spinoffs which encourage the momentum to benefit a broader spectrum of the urban environment could be the eventual establishment of a pedestrian arts district encompassing the area; location of an arts high school there; or homestead type loan programs which might be able to take advantage of increased residential desireability toward effecting the upgrade of a downtown neighborhood.

There is a great difference between this type of planned reinforcement of naturally occurring Start Event and the imposition of a planned Start Event on a place. The latter has too often taken the form of selection of a development project from a palette of trendy possibilities used in other places. Insertion of yet another waterfront festival marketplace with mixed use development characteristics kicked off by building a new aquarium is more analogous to the arrival of a meteor in its effect on a place and actually may send an area off into an alien development pattern mimicking what’s happening elsewhere. It has very little to do with replication of the unique livable human aspects of a specific place. The richness and depth of any environment lie in its individual characteristics, which by definition cannot be imposed or entirely copied. Going with the flow of a naturally occurring Start Event is most truly expressive of the spirit of individual places.

With regard to Crete, I would propose looking at spontaneous occurrences manifesting themselves in distinctly Cretan form – this does not mean only copying traditional OLD ways. I believe that some of the things we saw on our trip qualify as positive Cretan responses to life and growth. Other things are perhaps a kind of morbid replication of an international development mode that is basically destructive of the unique integrity of the place in which it occurs. I do have photo examples which I would be glad to share and I do believe that there are unique opportunities for planned reinforcement of possible Start Event phenomena. The question previously raised of whether or not such a ‘cultural action’ as the conference in Crete held last year can fulfill the aims of comparative research could seem to be answered through the pursuit of some specific Cretan answers to the ‘fractal planning’ exploration questions posed above.


Comments on Evaluation Report of “The Myth of the City”, 9 – 15.9.95 (Draft: 14 November 1995) - Hatto Fischer

It seems to me that what we are involved with in “explaining” planning to non-planners often has to do with the impact of development and investment schemes. These are some of the most visible of planning efforts, as well as the ones upon which people in general (and, as you will remember, our poets in particular) are most likely to voice their opinions.

I wonder if this isn’t because all too often, such schemes ARE alien and noticeable? We seem to be all too ready to impose outside ideas and formulas rather than to “go with the flow.”

Particularly regarding page 3, second, third and fourth paragraphs:

There is a need to become more sensitive to impacts of certain and overall investment schemes since they are really the symbols of non-participation and thus alien to people living in those cities having imposed upon them ‘tough interventions’…

From the fractal perspective explained in my previous letter to which are responding, these alien, imposed interventions are “false”, non-indigenous and other-cultural patterns of development, which do not arise from the structural basis of the place as natural fractal patterns of development, but are like a stone thrown into the pool without continual external reinforcement. I don’t necessarily think that the term tough interventions would always be appropriate here, because such interventions are not by definition “tough” – simply inappropriate and incapable of a sustained life of their own in the subject environment – ultimately, “meaningless interventions” might prove to be the better description.

the original idea of the tender was to “web” cities…

i.e. restated in accord with my Tender model of the Woven City: “To weave together in a pattern of connection…”

that is by allowing to create human relationships at different levels…

In place of “create”, I might suggest substituting the word “enable” the “occurrence” or “birth” of human relationships, because this implies a naturally occurring event rather than one imposed or “created” by an outside force, rather like “enabling” the natural growth of crystals into their own original and beautiful shapes by providing the proper medium versus the building of a machine by a master builder from a bounded set of plans for a predetermined form and use.

so that mono-functional usages are avoided and informal-formal control mechanism allow for a peaceful complexity to develop…

“Peaceful complexity” is a very nice way of putting it – non imposed, natural intricacies of the pattern of connectivity, which grow without supervision.

for there is also the dimension of violence against cities

This could be a neat tieing-in of the Crete conference subject of violence and cities to the fractal model I hope to describe. Violence can be seen in the imposition of mono-dimensional development schemes and unbalanced planning initiatives on the fractal harmony of the indigenous structure underlying any culturally distinct place.

The old injunction to doctor: “First, do no harm,” can be invoked here as the basic evaluative criteria for any such schemes. This is done now in ways variously called “impact analysis” or “cost-benefit analysis”; these incorporate the use of inventories and impact studies as well as pro-formed financial analysis. The situation being considered in this way is a snapshot, a static image of how things “are”.

Looked at from the perspective of urban environments made up of constantly moving patterns with an ever-present potential for change, it becomes obvious that in order to properly model impacts, one would need to run active models – indeed this is done in traffic analysis. But if we try to properly account for the multi-dimensional complexity of a total human environment – not just one rather closed system as traffic – the model gets more and more difficult to run. In the same way that modeling global warming has proven to challenge the fastest of existing supercomputers, modeling factors such as population shifts due to refugees and other in/out migration, changing family demographics, economic effects of/on employer or consumer behavior, speed or delay in evolution of building codes, occurrence of natural disasters, and other factors about which we literally have no advance information, make it quite doubtful that we will ever have a “true” impact analysis of any proposed scheme.

So perhaps what we can do is to focus on the possibility of determining proper directions rather than proposing tidy solutions. Most planners actually do this; for instance, they hope to “stimulate investment” rather than “perform an economic miracle”. Better tools should be developed to assist in a truer understanding of a place and its human ecology and so point the way toward beneficial planning initiatives.

Hatto, I would like to work with you on extending my initial concept of components and filters which I proposed for our Tender offer as a key technique in the evaluation of the projects that you have told me about. And combining this within the perspective of a fractal planning model into a way for judging the appropriateness of a proposed development scheme and then monitoring its progress/success.

Kamilari April 1996


A chaotic reading list:

Prigogine, Ilya. Order out of Chaos: Man's New Dialogue with Nature. With Isabelle Stengers. New York: Bantam Books, 1984.

Peat, F. David. Sychronicity: The Bridge between Mind and Matter. New York: Bantam, 1987.

Walter, Katya. Tao of Chaos, Merging East and West. Austin, Texas: Kairos Center, 1994.

Jackson, John Brinkerhoff. Discovering the Vernacular Landscape. New Haven and London: Yale University Press, 1984


A Sense of Place, a Sense of Time. New Haven and London: Yale University Press, 1994.

Hawthorne, Nathaniel. The House of the Seven Gables. Toronto and New York: Bantam Books, 1981. First printed 1851.

Swan, James A. Sacred Places, How the Living Earth Seeks Our Friendship. Santa Fe, New Mexico: Bear & Company, 1990.

Hough, Michael. Out of Place, Restoring Identity to the Regional Landscape. New Haven and London: Yale University Press, 1990.

Mather, Cotton and George F. Thompson. Albuquerque, New Mexico: University of Mexico Press, 1995.

Wilhelm, Kate. Death Qualified. New York. Fawcett, 1995.

Garnham, Harry Launce. Maintaining the Spirit of Place, A Process for the Preservation of Town Character. Mesa, Arizona: PDA Publisher Corporation, 1985.

Hiss, Tony. The Experience of place. New York: Alfred A. Knopf, 1990.

Russell, Beverly. "Toward a New Geometry". Architecture, May 1990.

Dimotakis, Paul N. "Chaos Theory and the Greek Miracle".


Elliott, Sloan. "Ghika: The Origins of European Culture in Greek Reality" (Our Town Editorial). The Athenian, December 1990.

Wolf, Gary "The Wisdom of Saint Marshall, the Holy Fool." Wirded. 4.01.January 1996

Kenner, Hugh "McLuhan Redux" Harper's November 1983.

Henderson, Harold. "Bring Back Determinism" Planning, July 1995.

Cassidy, William L. "Feng Shui FAQ" copywrited, published and readable on the Internet.

Turner, Frederick. "Escape from Modernism"


Lapham, Lewis H. "Notebook, the Endorphin High." Harper's, November, 1983.

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