Ebook Chaos and Geometric Order in Architecture and Design
It is relatively easy to distinguish between geometric order and chaos in architectural compositions, but the definition of these concepts is difficult. The following definitions can be assumed: The geometric order is represented by ideal mathematical forms (in 2D: e.g. line, circle, quarter, or 3D: e.g. plane, sphere, cube) and ideal relationships (e.g. perpendicularly, parallelism, symmetry, rhythm/regularity). Chaos is the opposite of geometric order; it is represented by forms and relationships that are complex and difficult to describe with the language of classic mathematics.
From the point of view of spatial perception, other definitions can be assumed. In Fig. 1 two graphic compositions are presented, which consists of about 1600 points each. The average density of points is constant in the whole area of both compositions. In the first composition the circular area of regular points is visible on the background of random points. The other composition is inverse: the circular area of random points is visible on the background of regular points. Based on this example, we can indirectly define chaos as an interference of geometric order and geometric order – as an interference of chaos.
A new aspect in defining chaos and geometric order is the mathematical theory of chaos that has developed since the 60’s. According to this theory the order is a special coincidence of a wider chaotic arrangement and chaos is a deterministic and not scholastic phenomenon [1]. Very complex phenomenon (e.g. atmospheric phenomenon, turbulence, the number of natural population, exchange fluctuations) can be generated through simple formulas. An example of such a formula is one mathematical sequence:
x0,x1,x2,...xn, where xn+1 = k x2 n ? 1.
For k = 1,35 and x0 = 0,4 the generated sequence has a periodical recurrence. But for k = 2,0 the generated sequence is chaotic [7]. Based on the presented considerations, especially in the context of mathematical chaos theory, we can conclude that the geometric order and chaos are strongly connected together. Is this connection also visible in architecture and does it have an application in design?
From the point of view of spatial perception, other definitions can be assumed. In Fig. 1 two graphic compositions are presented, which consists of about 1600 points each. The average density of points is constant in the whole area of both compositions. In the first composition the circular area of regular points is visible on the background of random points. The other composition is inverse: the circular area of random points is visible on the background of regular points. Based on this example, we can indirectly define chaos as an interference of geometric order and geometric order – as an interference of chaos.
A new aspect in defining chaos and geometric order is the mathematical theory of chaos that has developed since the 60’s. According to this theory the order is a special coincidence of a wider chaotic arrangement and chaos is a deterministic and not scholastic phenomenon [1]. Very complex phenomenon (e.g. atmospheric phenomenon, turbulence, the number of natural population, exchange fluctuations) can be generated through simple formulas. An example of such a formula is one mathematical sequence:
x0,x1,x2,...xn, where xn+1 = k x2 n ? 1.
For k = 1,35 and x0 = 0,4 the generated sequence has a periodical recurrence. But for k = 2,0 the generated sequence is chaotic [7]. Based on the presented considerations, especially in the context of mathematical chaos theory, we can conclude that the geometric order and chaos are strongly connected together. Is this connection also visible in architecture and does it have an application in design?
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