Thursday, March 17, 2016


Menneskesinnet trives aller best med en fraktal metning rundt D 1,4. Dette tilsvarer hva vi finner på de afrikanske savanner, hvor vår fraktale biologi ble evolvert. Faller den fraktale metningen for mye under D 1,4 blir vi engstelige, går den mye høyere kan vi fanges av en religiøs stemning og risikere å bli overstimulerte.

I Gamla stan blir jeg til stadighet fanget av denne religiøse stemningen, men allikevel ikke så mye at det kjennes ubehagelig. Et godt sted å reise til for å søke tilflukt fra en fraktalhatende modernisme, som dessverre i nyere tid har tatt til seg dette begrepet og pervertert det.

Personlig er jeg veldig var mitt fraktale sinnelag, og er derfor også en asfalt-hater. På samme vis som jeg er en brosteins-elsker. De vakre brosteinsmønstrene i Gamla stan gjør meg simpelthen høy til sinns, og slår inn i hjernekjemien med en langt større effekt enn det sterkeste anti-depressiva.

Mye av den angsten som har inntatt vårt samfunn skyldes utvilsomt all denne nådeløse og meningsløse asfalteringen. Jeg husker min sorg da de la ottadekke på grusvegen etter Kronborgsetergrenda, hvor jeg vokste opp.

Brosteinsmønstre knytter oss til jorden på en helt spesiell måte. Er man litt trist og bøyd i nakken blir man ikke trist av å se ned i Gamla stan. Nei, da løftes raskt sinnsstemningen, vårt fraktale sinnelag bruser av fryd. Brosteinsfryd!

Brostein i Stora Nygatan

- Pavements as Embodiments of Meaning for a Fractal Mind: 


By Nikos A. Salingaros.

Architecture has in the past felt a need for pavements that are either patterned, or that embody figurative art. Our perception of space is founded on a connection with the ground via design. In creating an artificial built environment to house themselves and their activities, human beings have always been careful to connect with the ground visually. Methods that connect a pedestrian to the floor, whether inside a building, or in an open space outside include pavements, tilings, textures, mosaics, etc. A pioneering study of interior pavements has been undertaken by Kim Williams [13]. The authors are in complete agreement with Williams that pavements are central to mankind's architectural -- and intellectual --development. Most twentieth century pavements are plain and empty, arguing the case that there is no functional need for either representation or pattern in a pavement. We will argue the contrary: that pavements can serve the crucial function of connecting an observer to all surrounding structures. The connection becomes necessary for larger spaces, so this effect is most dramatic in external pavements.

Everyday experience -- which calls upon visual scales between 1mm and 1m contained in the human body -- serves as the foundation for any fractal design hierarchy. We connect visually and psychologically to an area surrounding our feet. This region defines the first fractal scales in a pavement design, and these external scales become linked to internal scales within our consciousness. Without a deliberate design here, there is a chance that no connection will be experienced. Regardless of the smallest unit employed, whether it be a piece of mosaic, a brick, or a tile, contrast should be used to identify the smallest scale unambiguously. Nevertheless, most urban plazas, and indeed, brick and stone walls of all kinds built in the twentieth century, disguise the smallest scale by repeating a single unit monotonously (e.g., so-called bonded brickwork, which creates a uniform surface).

Spatial coherence requires internal definition on successively larger scales, going up to the size of the entire region. A patterned expanse needs to define several distinct scales to create hierarchical linking. Therefore, while a detailed pattern might connect to the user at the smallest scale, simply repeating the design indefinitely without using intermediate scales will fail to connect the user to the larger space. Successful pavement designs contain similar but not identical regions. An urban space lacking a hierarchical linking can never connect to surrounding buildings at a distance because the jump in scale is simply too large. For this to happen, the buildings must define an additional, larger scale in the same hierarchy. It is therefore necessary for the pavement texture, color, and design to harmonize with the surrounding structures. Similarity between the pavement and buildings relates the scales.


One of us has already discussed the properties of urban space, and how patterned flooring helps to define it. Commenting on contemporary examples, we said [14] (page 44):
Sidewalks, city streets, and street corners

An incredible opportunity to connect the pedestrian to the pavement has been missed all around the world, by using plain, featureless surfaces (even with expensive materials). The standard concrete sidewalk contains no visual information, and anyway, it is far too narrow. Even when brick is used for paving, perceivable patterns are usually avoided. Yet, patterns on the surface of pedestrian paths can make a great difference. Recall, for instance, all the wonderful mosaic and tiled pavements of the Roman world. Among notable historical examples are the pavement of the Piazza San Marco, and the Portuguese architectural tradition of lively sidewalk designs. Some of the most famous modern patterned sidewalks are in Brazil, a former Portuguese colony.
The design of flooring, as in an open plaza, has to obey the same principles as other, time-honored designs, such as oriental carpets. Methods for connecting different scales are outlined in a model of complexity by one of the authors [15]. The basic mechanism for linking among units separated either by distance or by scale is similarity in texture, color, and form. Similarity works via translational, rotational, reflectional, and scaling symmetries in the plane [16]. This is known by all sensitive artists trying to establish visual and emotional harmony. The coordination responsible for the visual coherence of the whole requires complex ordering, but not simplistic alignment. Symmetric arrangements on a plan do not connect elements across scales.

Great urban spaces were built before the twentieth century, before the wholesale replacement of traditional design criteria. Discarding techniques for connecting human beings to the built environment developed over the previous several millennia, architects now follow a design philosophy that values an emotionally uncomfortable novelty, and which disconnects people from surrounding surfaces [14]. It is therefore a welcome surprise to see successful contemporary plazas built by the British artist and urban designer Tess Jaray [17]. One sees in her designs a well-defined smallest scale; distinct yet connected designs on different scales; and careful harmonization with the surrounding buildings [17]. This paper tries to analyze why her designs are so successful, using the fractal encoding model outlined above. Jaray's pavements provide a satisfactory experience on a number of different scales.

From the informational point of view, an open plaza offers vastly decreased input from surrounding walls compared with a totally enclosed, roofed space. It is therefore critical to connect to the ground via geometry. Thus, the most expressive pavements are to be found in public open spaces around the world. When successful -- as in the case of Tess Jaray's pavements -- they connect the pedestrian to the ground, and thereby permit the psychological freedom to be alive and move around. This is what determines the success of an open space independently of other factors such as exposure, surrounding façades, and density of cross-paths.


We postulate that the intensity of fractal connection corresponds directly to the degree that human beings intuitively feel a space or design to be meaningful or "alive". This model therefore identifies the visual connection of designs and structures with a viewer's emotional state. It is becoming increasingly clear from neurophysiological research that the human conceptual system and the possible forms of reasoning are limited by the wiring of our brains [12]. Moreover, mental activity turns out to be emotionally engaged; i.e, it is likely that we actually feel our thoughts [12].

There exist subconscious processes going on inside our brains, which probably encompass the fractal connections discussed above. Our model of fractal encoding helps explain why we feel emotionally elated standing in a great historical plaza which is paved with some design that harmonizes with surrounding buildings. If all components work to connect and harmonize, we become an integral component of an enormous space because we link hierarchically with it. This could represent one of the greatest architectural-aesthetic experiences for an observer.

The corollary is also of interest. Urban spaces that conform to the contemporary design canon tend to be dead, because they fail to establish a positive emotional connection with the user. One can argue that this effect is not unintentional. A person feels ill-at-ease in such places, and consequently avoids them. This is not simply a matter of choice; as proposed in this paper, non-fractal structures clash with our perceptive process. Not only is our environment thereby impoverished, but the design rules that generate such environments deny and suppress fractal connections. We now have a widely-embraced design philosophy that ignores the need to create structures that elicit a sense that we are in a meaningful place, thereby severely narrowing the range of our emotional experience.

The environment is not separate from us, offering only objects and external sensations that we encounter: it is part of our being [12]. A balanced, healthy mental state requires an understanding of nature that is linked to our human emotions. The mind is much more than a computer; it is also passionate. How are we to understand our sense of belonging to a larger whole? In this paper, we have discussed the experience of meaning from the environment, yet our explanation is limited compared to what is described very well in mystical and spiritual literature. Connecting to a larger, all-encompassing whole can lead to ecstatic participation, or a spiritual experience. Such a state has frequently been described as transcendence.


We wish to concentrate on the perception of meaning coming out of visual complexity in the environment. Visual information presented as a coherent image or coded pattern is accessible in a direct manner. There is a mapping function between structures in the world and structures in the mind. When the mapping is faithful to the hierarchical linking (i.e., it preserves the information and its interconnections rather than any overall form), it creates an experience of meaning. Neural structures use information on connectivity to create meaning as an internal state: in our model, meaning is not assigned to external forms. The degree of conformal fit or coherence determines the strength of the sense of meaning and also the strength of the emotional experience. In its simplest aspect, meaning corresponds to a valence in emotion, which is either positive or negative. When two or more meaningful structures are linked together in a meaningful way, we begin to build a system of beliefs.

If an image is incoherent, then the information it contains cannot be perceived easily as a whole. There is less meaning because, even though there may be considerable information there, the information is difficult to synthesize. This in turn generates a negative valence which is manifested in negative emotions. Viewers are more receptive to information that is presented in a pattern that is strongly connected to them. Information structured in this way is typically called "natural" or "intuitive". One of us has previously argued that intuition is actually a process involving reasoning with structure [18]. By contrast, a viewer will not be receptive to information that is presented via a visual pattern (or lack thereof) that fails to establish a strong connection with the viewer. We believe that environmental structures need to be fractal to satisfy the human brain.

Our sense of understanding arises from the way we form conceptual structures in the mind. When a collection of ideas has coherence and a sense of relatedness among its elements, we perceive its structure. When we perceive the structure of thoughts and ideas as a coherent whole, we conclude that they are correct and that the construct is valid [18]. We remember it as a guide for further thought. We also use it to guide our behavior. Ideas that are neatly linked and have a coherent structure are judged to be valid or "true". The nature of intuition may be understood as the ability to match the structure of a present situation with the structures of problems that have been experienced before. Intuition represents the general ability to reach a conclusion on the basis of less explicit information than is ordinarily required to reach that conclusion [18].


Rules for creating a memorable open space can be abstracted from studying historical examples. The lesson from our fractal encoding model is that there exists a fundamental similarity between complex structures in the environment and structures in the mind. Designing an open space can be successful if one follows one's basic instinct to ornament, connect, and harmonize different levels of design. In principle, therefore, there is really no need for rules if one is guided by one's deepest feelings. Indeed, one can argue that the closer the match between the architect's felt intuition about a space and the structure that is finally created as an expression of that intuition, the greater will be the meaning of that space for the observer. In a sense, the built place becomes the vehicle for the mental structure of the architect to be instantiated as a mental structure in the observer.

Nevertheless, some pointers are necessary because of the plethora of negative examples of structures in existence. Even though the best pavements depend on engineering principles, they have to balance and synthesize so many factors that the result should be considered a "work of art". A successful pavement will have the following characteristics, and satisfy hierarchical linking:
  1. Human-scale design to connect immediately with a user. 
  2. The smallest units defined by contrast and symmetries that allows the units to be detected. 
  3. A smallest design scale that is compatible with human dimensions -- anywhere from 1cm to 1m. 
  4. Several levels of design before reaching the full extent of the open space. 
  5. Intermediate levels of design that are distinct yet strongly linked via similarity. 
  6. Larger levels formed from ordered combinations of elements on smaller scales. 
  7. Balance among all regions and scales -- every element acting as a connector for the other elements. 
  8. Harmonization at a distance to link all scales with the surrounding buildings. 
If these conditions are satisfied, then a user, on entering the environment, will experience a sense of meaningfulness as all of the scales in the view are seen as a unified whole. There is a fractal (i.e., hierarchical) connection to the entire space. The strength of the component connections determines the coherence of the whole. In a poor design, the smallest elements are not symmetric, and appear as amorphous smudges to which we cannot connect. The connection proceeds from the smallest scales to the larger scales, up to the largest scale which is defined by the surrounding structures. While our description of the connection process was sequential, the actual connection through perception is sudden. This experience is frequently dramatic, and creates a definite and sometimes intensely positive psychological and physiological state.

In conclusion, we have proposed a theory of pattern perception that can explain how patterns generate meaning in the environment. Although this theory is entirely general, it was applied here to discuss pavements. A strictly utilitarian approach to pavements requires no sign of any promise of destination or completion that attaches meaning to built forms and spaces. When the environment becomes more complex, the pavement becomes the guarantee that the environment is planned to embody destinations and connections. A pavement that is designed to have meaning ought to obey the eight rules given above. Pavements as a definition of space represent the highest order of mapping between an architectural theme and a theme that the human mind can understand. Meaning in the pavement thus allows one to "know" the place without seeing all of it.

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