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Science & Tech.
Mahesh

11/12/23 12:47 PM IST

Use of fractals

In News 
  • Physicists use the fractal geometry approach to study quantum systems in dimensions like 1.55 or 1.58, or in fact anything between one and two dimensions.
Fractal Dimensions
  • Uncertainty is an inherent feature of all systems.
  • It is independent of the precision or the accuracy with which the system is measured.
  • It just is there, as an implicit element of the system’s existence. And it has forced physicists to find a practical approach to study quantum systems in ways that can circumvent the limitations it imposes.
  • One of the ways in which physicists have responded is via the so-called non-integer small dimensions, a.k.a. fractal dimensions. 
  • Fractality is ubiquitous in nature, if also sometimes hidden from plain sight.
  • A shape is fractal if it exhibits self-similarity, i.e. if parts of it at a smaller scale resemble parts at a larger scale. Such shapes can be easily produced by repeatedly modifying its edges using simple rules. 
  • The higher the ‘value’ of a fractal’s dimension, the greater is its ability to fill space as its shape evolves. For example, the Koch snowflake has a fractal dimension of around 1.26.
Appearance of Fractals 
  • On the macroscopic scale, fractals can be seen as irregular, complex patterns at all scales and in all views, near or far.
  • Some of the more remarkable examples of such patterns include the design of human fingerprints, the stumps of trees, in the shells of snails, the system of human veins, the network of rivers as seen from high up, the splitting of veins in a plant leaf, the edges of a snowflake, a bolt of lightning going branching off in different directions, the shapes of clouds, the mixing of liquids of different viscosity, the way tumours grow in the body, and so on.
  • Another example of fractal behaviour at the microscopic scale is available in graphene – a single-atom thick sheet of carbon atoms linked to each other.
Applications
  • The first attempt to apply fractal analysis in physics was for Brownian motion – the rapid, random, zigzagging motion of small particles suspended in a liquid medium, like pollen in water.
  • As such, the value of fractals is that they describe a new kind of order in systems that we may have otherwise overlooked.
  • They pave the way to potential new insights from otherwise familiar shapes like lines, planes, and points, in the unfamiliar milieu of a space with non-integer dimensions.
  • Researchers have also used the concept of fractality in data compression, such as to reduce the size of an image when storing it, and to design more compact antennae without compromising their performance.
  • Some have also used fractality to study patterns in galaxies and planets and, in cell biology, to make sense of some bacteria cultures. Fractal geometry has also found applications in chromatography and ion-exchange processes, among others.
  • Fractals are rooted in geometry but – like the fractal growth of branches on trees – they have far-reaching implications, more so as they interact with different natural processes in a variety of settings. There are self-similar structures around us that become increasingly complex with time.
Source- The Hindu 

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