A Generative Construction and Visualization of 3d Fractal Measures

Martyn, Tomasz

doi:10.1142/9789812774217_0009

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“…Oleschko, 2000, Khabbazi et al, 2015, is not a strict definition of fractals. One of the existing methods of defining fractals in the mathematical sense is the use of iterated function system (IFS) (Barnsley et al, 2005, Martyn, 2011. Fractals can be constructed using a system of iterated functions the form of the set { f 1, ..., f k }, where f i : X → X is a contraction for i = 1,..., k, while X -a closed subset of n-dimensional Euclidean space n .…”

Section: Introductionmentioning

confidence: 99%

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Set of Suffosion Holes Occurring After a Water Supply Failure as a Structure with Fractal Features

Iwanek¹

2022

J. Ecol. Eng.

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As a result of a buried water pipe unsealing, water often flows from the pipe to the soil surface, washing out the solid particles of soil and creating the so-called suffosion holes. It is a dangerous phenomenon, especially in urbanized areas, where it poses a threat to human safety and the stability of infrastructure. Uncontrolled outflows of water from water pipes belong to the main causes of suffosion in cities, occur in all water networks around the world and are difficult to predict. Therefore, it seems to be important to determine the size of the so-called the protection zone, which is the area around the potential leak where, in the event of a water pipe failure, it would be possible for water to flow in the soil. The analysis of the suffosion holes distribution around the place of leakage may be helpful in determining the size of the protection zone. Previous studies have shown that this distribution is random. Thus, the structure consisting of suffusion holes creates a certain geometric shape, which is difficult to describe using the classical concepts of Euclidean geometry. The study showed that this structure meets the conditions for probabilistic fractals, which means that elements of fractal geometry can be used to determine the size of the protection zone.

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Section: Introductionmentioning

confidence: 99%

“…The attractor described in this way is often a fractal, but it can also be an object without fractal features, called an IFS attractor (Barnsley et al, 2005, Gdawiec and Kotarski, 2008, Martyn, 2011. The fractals described as attractors are deterministic fractals, characterized by strict self-similarity.…”

Section: Introductionmentioning

confidence: 99%

Set of Suffosion Holes Occurring After a Water Supply Failure as a Structure with Fractal Features

Iwanek¹

2022

J. Ecol. Eng.

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A Generative Construction and Visualization of 3d Fractal Measures

Cited by 1 publication

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Set of Suffosion Holes Occurring After a Water Supply Failure as a Structure with Fractal Features

Set of Suffosion Holes Occurring After a Water Supply Failure as a Structure with Fractal Features

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