**6. Discussion**

Theory of emergence, self-organization, evolution, and cosmogenesis rejected the concepts of determination, mechanism, reductivism, and materialism whose shift in thought had been reflected on engineers and architectures as well starting from Venturis' ideas for architects to fractal in architecture.

These views of complexity appear to be contradicting and rejecting modernism concepts in civil engineering, which is refused the plainer, clean, white architecture of modernism; instead, his ideas were directed to the indirect engineering meanings, forms, and compositions that satisfy the mind. Chaotic theory makes one think how things are put together; it takes time to be perceived and decoded. What chaotic theory was aiming for in civil engineers was actually found in the characteristics of fractal whose geometry plays an integral role between natures' complexity and civil engineering.

In civil engineering, starting from design views in 1960s through the postmodernism movement and till the digital age, engineers have started to design iconic cosmo-related works as it is called tending to be esthetically attractive.

The modernism perception of ornament is a crime was changed for the sake of nature. Where thoughts of ornaments as expensive decoration and it is a crime for the economy, waste of raw material and manpower. New thoughts were rejected and postmodernists returned to think about nature where they agreed that nature is the regulator morphology of the universe patterns and of the earth's surface occurrences. Nature is the source of patterns and the most which are complex ones.

In the new area with the use of computers, architects tend to create computergenerated natural occurrences and organizational patterns where the natural

designs became much more complex and in the shape of natural ornaments like river plume in sediment-laden rivers. Hydraulics engineers' interest was directed to create natural designs in river curvatures like growing elements of meanders in the plume. The postmodern engineers' goal became esthetic creating complexity by subdividing the elements into billions of smaller units. They thought to create cellular self-generating growing natural ornaments that generate the whole natural body whose work may ripple in river plumes and undulate like frozen vegetation, and it is often based on cellular forms that vary as nature's fractals.

As presented in the previous engineering examples, the use of fractal characteristics transformed from architectural morphology of masses to natural occurrence design where fractal characteristics of scaling are used, and this project was successful in showing it on various dimensions, in the articulation of masses and spaces. This idea of producing the form in different scales to be distributed on the earth's surface of complex phenomena and inside the project, enrich the idea of scaling and emphasize on it.

Since the 1990s, the use of fractal geometry has been presented more in geometrical designs and engineering skin as shown in river plumes of different geographical districts.

Civil engineers depended on fractal geometry esthetically, which can be perceived by users and public. The use of fractal geometry in architecture has neither appeared nor has been used in morphology, masses, and spaces. There is a risk of fractal geometry being narrowed to become a tool to create attractive geometrical patterns.

In river meander and plume, the fractal extruded river curvature of the meanders was designed as an environmental solution to cool the space. In nature, we find that the fractal design of river plume was designed functionally as well as esthetically. In natural phenomena, the curvature extension (the spiral), the spiral river design that is covered with fractile, was given as dune design to direct plumes' circulation and create the river boundary layer spaces. In these two examples, the forming of ripples and dunes in hydrodynamics plays a role in the hydraulics engineering where fractal geometry is still fixed on the river plume boundary layers. It works as an ornament, which decorates the bottom of plumes in artificial design, that can be replaced by whatever other motif depending on the engineers' choice in artificial design of boundary layers.

As presented in the examples, the use of fractal geometry in designing of river plume bottoms consists of subripples and dunes that contain elements that have the same shape. This prototyping makes it easy in realizing the natural occurrence of river plume's design.

Which overturns some researchers argument that new theory of chaotic behavior is waste of money, time, and manpower by the use of fractal geometry in civil engineering and skin design became more economically efficient method because of prototyping some new ideas from nature and space.

### **7. Results**

In contrast to river plume fractal dimensions, statistical fractals are self-affine fractals, or statistically self-similar; they are composed of statistically equivalent replicas of the whole object. Examples of strictly self-similar fractals are Sierpinski triangles, Koch flake, etc. as shown in **Figure 6**; the most fractal looking in nature do not display this precise from. The presence of self-similarity in the objects characterizes them as fractal.

**91**

**Author details**

Nisantasi University, Maslak, Turkey

provided the original work is properly cited.

\*Address all correspondence to: levent.yilmaz@nisantasi.edu.tr

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Levent Yilmaz

**Figure 6.**

*River Plume in Sediment-Laden Rivers*

*DOI: http://dx.doi.org/10.5772/intechopen.90089*

*Meander curvature in nature as defining the fractal dimensions [1].*

*River Plume in Sediment-Laden Rivers DOI: http://dx.doi.org/10.5772/intechopen.90089*

*Current Practice in Fluvial Geomorphology - Dynamics and Diversity*

designs became much more complex and in the shape of natural ornaments like river plume in sediment-laden rivers. Hydraulics engineers' interest was directed to create natural designs in river curvatures like growing elements of meanders in the plume. The postmodern engineers' goal became esthetic creating complexity by subdividing the elements into billions of smaller units. They thought to create cellular self-generating growing natural ornaments that generate the whole natural body whose work may ripple in river plumes and undulate like frozen vegetation, and it is often based on cellular forms that vary as nature's

As presented in the previous engineering examples, the use of fractal characteristics transformed from architectural morphology of masses to natural occurrence design where fractal characteristics of scaling are used, and this project was successful in showing it on various dimensions, in the articulation of masses and spaces. This idea of producing the form in different scales to be distributed on the earth's surface of complex phenomena and inside the project, enrich the idea of

Since the 1990s, the use of fractal geometry has been presented more in geometrical designs and engineering skin as shown in river plumes of different geo-

Civil engineers depended on fractal geometry esthetically, which can be perceived by users and public. The use of fractal geometry in architecture has neither appeared nor has been used in morphology, masses, and spaces. There is a risk of fractal geometry being narrowed to become a tool to create attractive geometrical

In river meander and plume, the fractal extruded river curvature of the meanders was designed as an environmental solution to cool the space. In nature, we find that the fractal design of river plume was designed functionally as well as esthetically. In natural phenomena, the curvature extension (the spiral), the spiral river design that is covered with fractile, was given as dune design to direct plumes' circulation and create the river boundary layer spaces. In these two examples, the forming of ripples and dunes in hydrodynamics plays a role in the hydraulics engineering where fractal geometry is still fixed on the river plume boundary layers. It works as an ornament, which decorates the bottom of plumes in artificial design, that can be replaced by whatever other motif depending on the engineers' choice in

As presented in the examples, the use of fractal geometry in designing of river plume bottoms consists of subripples and dunes that contain elements that have the same shape. This prototyping makes it easy in realizing the natural occurrence of

Which overturns some researchers argument that new theory of chaotic behavior is waste of money, time, and manpower by the use of fractal geometry in civil engineering and skin design became more economically efficient method because

In contrast to river plume fractal dimensions, statistical fractals are self-affine fractals, or statistically self-similar; they are composed of statistically equivalent replicas of the whole object. Examples of strictly self-similar fractals are Sierpinski triangles, Koch flake, etc. as shown in **Figure 6**; the most fractal looking in nature do not display this precise from. The presence of self-similarity in the objects

**90**

fractals.

scaling and emphasize on it.

artificial design of boundary layers.

of prototyping some new ideas from nature and space.

river plume's design.

characterizes them as fractal.

**7. Results**

graphical districts.

patterns.

**Figure 6.** *Meander curvature in nature as defining the fractal dimensions [1].*
