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Category: Borders

  • Architectural Systems and Their Borders

    In a previous post, I discussed the fractal boundaries of two interacting systems. Whenever a natural system, such as a tree, a river, an animal path, or a cloud interacts with another, the border between the two will show self-similarity. This often takes place in both systems, and one may be the cause of the other.

    This is how Nature interacts with herself. With living systems, I believe it is because growth is algorithmically based. Growth is very much a self-replicating pattern, and that growth eventually must end at a border. Yet for non organic systems, such as atmospheric phenomena, turbulence or other chaotic behavior still exhibits self similarity when interacting with itself.

    Any beautiful architectural structure or any well-designed product will include fractals along its transitional border. This seems natural to us and it is obvious that a border that does not have a fractal of some kind will look incomplete.

    We can divide structures into systems. These systems are discrete elements with different functions and therefore use a different form that does not resonate with the other elements. In a house, for example, we will have the system of a roof, and another for the walls. Neither one of these has the same function and will be constructed differently. When these components unite, we find that the borders are different.

    Designers and architects have learned the art of combining borders to create a harmonious union. Intuitively, they use self-similarity to harmonize the borders, in other words, at the border you will find fractals.

    Systems:

    In my definition, a system is a grouping of elements that is necessary for the function of a building, or structure in general. It creates its own form.

    Examples of systems would be walls, roofs, doors, foundations, windows, floors and ceilings, columns and pilasters.

    Borders:

    In my definition, a border is the intersection of two different systems.

    Examples of borders would be window frames, molding, capital and bases of pillars and door frames. They link two disparate systems each with its unique form that do not interact harmoniously with another.

    Harmonious Borders:

    Below are a few pictures with harmonious borders. Notice how self-similarity is used. There is no fixed form for these borders and we will always find innovation and originality.

    Within these images, notice the intersection of the windows with walls, porches and the building wall and the division between floors. Note too that the border includes the building itself with the sky and the ground. Steps can be included with a building to ground border, along with a foundation. The border may include plants.

    Notice too that corners of a building usually do not display a border because it is an intersection of two similar systems and there is no clash.

    Additional examples of harmonious borders can be fences:

    Or the molding between a wall and a ceiling:

    Or the top of a pillar or pilaster.

    Disharmonious Borders:

    A disharmonious border does not resolve the clash between two systems. Modern architecture is rampant with these.

    Modern architecture will state that borderless systems are cleaner and borders are mere ornamentation. Modern architects and designers do not wish to resolve the clash between two differing systems. But this perspective creates unnatural designs. Intuitively we all know that is true.

    A disharmonious interior is very common in modern homes:

    Often, disharmonious borders are used to celebrate the artificiality of design, of a sense of human progress leading into a bold future. A casual look at old or new science fiction movies will almost always exhibit futuristic settings where humanity lives in a world without natural borders.

    The intention is to lead the person who experiences this to feel a sense of progress away from the so-called bounds of nature. The reality however, gives people an experience of anxiety and depression.

    Things to Come, 1936

    Conclusion:

    If we look at buildings as a collection of systems, where a system is a form based on a specific function, we see that the border between these systems requires self similarity in order to be harmonious. And it is important to include the ground and the sky as a border.

    Beautiful architecture will always have fractal borders.

  • A New Perspective on Ornamentation

    Over the millennia, ornamentation has been used in architecture and design for countless reasons. For some, the design isn’t complete until it has a few smaller pieces or a border attached to a main structure as a reinforcement of the design’s theme. This is very apparent in Louis Sullivan’s work, where the terra cotta decorations on his skyscrapers reinforced the organic theme of the building.

    Louis Sullivan’s ornamentation on the Van Allen building

    In classical design, one purpose of ornamentation is to reveal the elements of a building that were originally wooden, such as dentils.

    Dentilation used on a classical building

    Another purpose is to show the purpose of the structure. In churches and cathedrals, for example, the ornamentation is a display of Christian themes. 

    The central tympanum of Chartres Cathedral

    Despite the different reasons behind ornaments, one still finds that the borders are fractal. That is, they practice self-similarity. If one looks at the various elements of a structure, such as a wall and a window or a porch and a yard as systems, the merging of those systems requires a border. And the border is most beautiful when that border is fractal. Just as in nature, where two separate systems mix, for example, water vapor (clouds) and air, you will find fractals.

    Modernity Detaches from Ornament

    Many modern architects consider ornamentation as a superfluous addition to a structure or design that adds nothing worthwhile and can thus be discarded. They will point to Baroque and Rococo with their overly dramatic and emotionally intense additions. The purity of true, geometrical form doesn’t need any enhancements, they might argue. The origins of this philosophy began in earnest with Bauhaus, where it emphasized machine technology and function. O. B. Hardison, Jr. writes in “Disappearing through the Skylight”, on the idea that influenced Bauhaus’ founder, Walter Gropius:

    In 1916, Gropius identified the new aesthetic with industrial products: “Accurately cast forms, bare of ornamentation, having clear contrasts and consistency of form and color, become commensurate with the energy and economy of modern life.”

    Bauhaus in Dessau (1925-1932)

    As a result, the borders do not practice self-similarity. One suspects that architects today use these strong, utilitarian lines and mathematical functions to prove that we can move beyond the constraints of Natural Law. For example, Amazon is a trillion dollar company and its headquarters is a group of glass and steel towers rising in defiance of the fractal basis of Nature.

    Amazon headquarters

    Amazon, Virginia. Faustian Man defies Nature.

    This architecture is reminiscent of Spengler’s, “Faustian Man”, where humanity believes it will eventually divorce itself from the constraints of Nature and either reach out to the infinite unknown of space or to embed consciousness into the artificiality of a computer chip.

    Fractals as Ornaments

    In an earlier post I wrote that Nature’s borders are fractal. I believe earlier generations had a strong intuition regarding borders and knew that a building or any design needed self-similarity to soften its edges. They recognized how Nature worked. That is why today’s built environment is a stark contrast to natural forms. The strong, abstract lines, whether Euclidean or based on mathematical functions, clash with the lines of Nature when imposed without self-similarity. However, when a built structure gives way to Nature, such as a derelict or decayed building, you will see the strong lines softened by erosion and vegetation.

    This is one reason why we have intuitively added ornamentation to a structure or design. It makes the object look natural. Rather than having stark, utilitarian lines artificially project, we gently enhance the lines by using self-similarity of scale, or fractals.

    In my walk around Keene, New Hampshire, where older buildings still line the streets, one can easily see the use of ornamentation as a means to soften borders. Windows, porches, eaves, even chimneys all exhibit a self-similarity on the edges.

    Use of ornamentation to soften borders on older structures:

    Compared to modern buildings:

    On the other hand, the modern buildings leave only bare lines that clash with natural form.

    Not just buildings:

    The fractals can be found throughout all parts of exterior furnishings, such as signs and even fences.

    When creating a design, whatever pattern you desire to use, it will have much more resonance and power if you soften its borders with fractals. Use the principles in the design you’ve created and repeat it on the edges. It will be much more beautiful. And you will find that ornamentation, rather than being superfluous or irrelevant, adds harmony and beauty to your creation.

  • Order and Disorder in Architecture

    When we look at Nature, we take a snapshot of her with our mind. In a single moment, we see a glorious balancing act, both expansion and contraction, building and destruction. We experience her in the eternal present; and because this snapshot is frozen in time, we can easily forget the process that builds up to that moment and likewise recedes from it. Without time, all we see is equilibrium. All the forces disappear. Because of this we extrapolate the present into the future and the past and we think that everything emanates from our present.

    Far from an equilibrium, Nature is dynamic. She is a set of trillions of interactions ranging in different levels from the sub-microscopic to the cosmic. Time lapse images and movies reveal the reality of nature interacting through time. A video of clouds show a roiling tempest of atmospheric forces at work. A flower opens and closes before our eyes with the rising and setting of the sun.

    In physics we have a simple rule about the nature of equiibria, a rule which was independently established by three physicists: E. Mach, P. Curie, and W. Voigt. They observed that in a state of equilibrium, processes, or materials, tend to assume the most even and regular distributions of which they are capable under the given conditions. 

    Arnheim. Entropy and Art: An Essay on Disorder and Order, quoting Wolfgang Kohler

    This quote implies the tremendous number of forces that interact in positive and negative ways. Equilibrium between order and disorder is always in flux. How can equilibrium be in flux? Because it is in equilibrium at the moment, just like two people pulling a rope, one will have greater strength and pull the other towards him, but the other is always reacting.

    Thus orderly shape results from the balancing of the antagonistic forces.

    [65, p.110], Stanley W. Angrist and Loren G. Hepler. Order and chaos: Laws of Energy and Entropy. Basic Books, NYC, 1967.

     

    A building is also in a state of flux. We know this by looking at ancient ruins. Even a home built twenty years ago may already have decayed to the point where it must be torn down. This website shows a number of greenhouses abandoned and well on their way to being destroyed by the plants that were placed there.

    Abandoned Greenhouse. Site: Messy Nessy Chic

    Athroisis is the happy medium between order and disorder

    While I’ve been speaking of Nature as a complex entity with a hidden, fractal structure, we also look at it as a catabolic process that works against our artificial constructs. As such, it has a dynamic tension where, unless we interact to prevent it, nature will win. We also look negatively upon this process if it gets out of hand. But there is a sweet spot, a harmony where just the right balance is struck. We say, ”Yes, this is beautiful. Our gardens gracefully complement our building.” or, ”Those trees outside the window are just perfect for our house.”

    The following pictures show this blend of artificial and natural. Strong, geometric lines are balanced with the fractal, irregular and natural plants.

    Order and Disorder in a Neighborhood. Note the strong, Euclidean roofs interspersed among the fractal trees, mountains and bushes.

    Regularly-shaped roofs poking from irregularly-shaped trees.

    And finally, note the juxtaposition of lines from this university building.

    Strong, geometric lines play with fractal, irregularly-structured branches and leaves.

    We can take this balance and apply it to architecture. If we apply athroisis and self-similiarity of scale to the building while also maintaining a strong Euclidean regularity the combination will reflect the same result that we get from nature and building. This design will reflect a balance between anabolic and catabolic forces.