Prompt Cast
The Fascinating World of Fractals: From Geometry to Practical Applications
TLDR Fractals, discovered in 1975, are self-similar and recursive structures that describe complex objects in infinite detail. They have practical applications in various fields, from improving cell phone reception to predicting carbon capture in rainforests.
Timestamped Summary
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Fractals are a new branch of geometry that is non-Euclidean and were discovered in 1975.
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Fractals are a new field in geometry that describe complex objects in infinite detail and self-similarity.
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Fractals are self-similar and recursive structures that can be created through iteration, and examples include the Sierpinski gasket and the coastline.
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Fractals can have infinite perimeters but still contain a finite amount of space, creating a paradox, and artists like Da Vinci and Hokusai were creating fractals before they were even recognized as such.
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Fractals are created by plotting numbers on a plane, with different colors representing different numbers and black representing numbers that will eventually be zero, resulting in intricate patterns and shapes when zoomed in or out.
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Fractals were initially theoretical until the late 70s when mathematicians like Ben Wall Mandelbrot started feeding fractal formulas into computers, which led to practical applications such as CGI in movies.
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Fractals have practical applications in various fields, such as improving antenna reception for cell phones and predicting carbon capture in rainforests based on the self-similar system of a single tree.
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Fractals can be used to study the flow of blood in vessels, spot tumors, analyze heart rate for arrhythmia, understand natural systems, and explain the energy efficiency of larger animals compared to smaller ones.
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Fractal geometers have the ability to see fractals in natural systems and can describe them using math, making everything simpler to understand.
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Society & Culture
