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Publication# Fractal geometry and its applications in timber construction

Abstract

We have developed a geometric design method based on generalizations of IFS. We have shown that it is possible to extend the properties of fractal shapes to forms used in classical modeling (e.g Bézier or Splines). We have developed and studied a new formalism, which we named BCIFS (Boundary Controlled Iterated Function System), which could serve as basis for development of a computer aided design software called modeler. The resulting figures verify planarity constrains in order to facilitate their physical construction out of planar construction material. Finally, a series of tools has been worked out in order to convert the geometry data into a set of constructional elements, ready for integrated manufacturing.

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Related MOOCs (1)

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Advanced Timber Plate Structural Design

A trans-disciplinary approach in structural design and digital architecture of timber structures with advanced manufacturing workflow.

Fractal

In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is 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, the shape is called affine self-similar.

Fractal curve

A fractal curve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified, that is, its graph takes the form of a fractal. In general, fractal curves are nowhere rectifiable curves — that is, they do not have finite length — and every subarc longer than a single point has infinite length. A famous example is the boundary of the Mandelbrot set. Fractal curves and fractal patterns are widespread, in nature, found in such places as broccoli, snowflakes, feet of geckos, frost crystals, and lightning bolts.

Fractal dimension

In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension. The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.

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