It is beginning to look a lot like Christmas…but ever wondered about the science hidden in Christmas? Why waste an opportunity to learn? Let’s dive into it!
A thing as fragile and short-lived as a snowflake has something in common with the trees, rivers, human body and in fact the galaxies in the universe! A snowflake is an example of complex geometrical figure called “fractals”.
What exactly is a fractal?
A fractal is created by repeating simple geometrical shapes like a triangle over and over to form a complex figure such that each small part represents the whole i.e., if you keep zooming in a fractal you will find the same pattern repeating itself instead of finding new figures.
A Koch’s snowflake(refer to insert) is formed by expanding the middle third of each side of triangle. This can be repeated many n number of times. The whole snowflake can be fit into a circle, in other words the snowflake or a fractal
has a fixed area but infinite perimeter.[1]
Nature is made up of fractals, the trees and their branching, the rivers and their tributaries, even a simple vegetable like cauliflower. Human body is a fractal. The respiratory system, circulatory system has increased its surface area using the same principle.[2] The human chromosome prevents tangling and the brain processes information on the basis of fractals.[3] This idea is not just fascinating but has various applications in diverse fields.
Here are a few examples:
1]Telecommunication: The antennas used previously work for a particular set of frequencies corresponding to the multiples of length of antenna. This limited the range of frequencies which they can tune into. Cohen applied the principle of fractals to design an antenna which has more length but limited area similar to the concept of a Koch snowflake. This allowed to tune into a wider range of frequencies.[4] The application is finding its use in geospatial technologies, military aviation etc.[5]
2]Cancer research: Fractals knowledge has been under application for analysing tumor-normal tissue border and also angiogenesis. Traditionally tumors have been identified with their irregular dimensions and high rates of cell division, this is a qualitative approach. But by developing means to quantify the degree of irregularity of cancer tissue, staging can be done more precisely. This is achieved by calculating and comparing the fractal values(using a few mathematical equations) of normal and cancer tissue. The fractal value of normal blood vessels and tumor vasculature is different.
There are studies going on to use this application for mammograms and there by reduce the number of false positive reports. This will also help in making the treatment better for various cancers.[6]
3]Psychology: EEG studies have shown that our brain responds to fractals of certain kinds. These fractals help reduce stress levels to a major degree. Increasing urbanization has attributed to people being unexposed to the fractals which are generally present in nature. Artists and architects are now trying to develop novel fractal infused buildings[7]
Fractals have produced a positive effect on children with autism spectrum disorder and people with depression. [8]
Fractals have now found their way into art, technology, medicine and the number of applications might even increase in the near future. Whatever the field, fractals have stimulated us to view nature with chaos, roughness or irregularity and discover the beauty in it.
This was Sanjana Irukulla writing for Dialectic Doctors.
DISCLAIMER: This article is intended for educational purposes only.
References:
[1,3,4 ] https://youtu.be/WFtTdf3I6Ug
[2, 5] https://youtu.be/QNk0ECGFVVs
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