Fractal geometry in architecture and design pdf
Fractal - WikipediaIn mathematics , a fractal is a subset of a Euclidean space for which the Hausdorff dimension strictly exceeds the topological dimension. Fractals tend to appear nearly the same at different levels, as is illustrated here in the successively small magnifications of the Mandelbrot set ;     because of this, fractals are encountered ubiquitously in nature. Fractals exhibit similar patterns at increasingly small scales called self similarity ,  also known as expanding symmetry or unfolding symmetry ; if this replication is exactly the same at every scale, as in the Menger sponge ,  it is called affine self-similar. Fractal geometry lies within the mathematical branch of topology. One way that fractals are different from finite geometric figures is the way in which they scale. Doubling the edge lengths of a polygon multiplies its area by four, which is two the ratio of the new to the old side length raised to the power of two the dimension of the space the polygon resides in. Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is two the ratio of the new to the old radius to the power of three the dimension that the sphere resides in.
What is Fractal Geometry? - Junior Breakthrough Challenge Entry
Fractal geometry and architecture design: case study review
The increasing concerns on sustainability oriented buildings have added new challenges in building architectureral design and called for new design responses. Sustainable design integrates and balances the human geometries and the natural ones. As the language of nature, it is, therefore, natural to assume that fractal geometry could play a role in developing new forms of aesthetics and sustainable architectureral design. This paper gives a brief description of fractal geometry theory and presents its current status and recent developments through illustrative review of some fractal case studies in architecture design, which provides a bridge between fractal geometry and architecture design. Keywords: Fractal geometry, Architecture design, Sustainability. Introduction The idea of buildings in harmony with nature can be traced back to ancient Egyptians, China, Greeks and Romans. At the beginning of 21st century, the increasing concerns on sustainability oriented on buildings have added new challenges in building architecture design and called for new design responses.
Since the late twentieth century, fractal architecture has been one of the most important themes discussed in architecture and it is based on the chaos and complexity theories. By categorizing the practical examples of this architectural approach, they are analyzed in terms of their relationship with nature using the logical reasoning method to achieve a favorable architecture. Betsky A. Violated Perfection: Architecture and the Fragmentation of the Modern. Rizzoli New York.