Fractals can be difficult to define. From the natural harmonious shapes of trees, plants and flowers that seem to radiate elegance and perfection in their simplicity to some of those intricate and colorful geometric shapes that can often be found on New Age social media pages, fractals are some of the most enigmatic, strikingly simple and simply stunning geometric shapes in the universe. Following are a few of the facts about them that stand out the most.
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Slow Recognition
The term "fractal" has been around only in the past 30 years or so, but even before the famous mathematician Benoit Mandelbrot coined it, there were many other instances where the fascinating irregular shapes were used but never recognized. Lewis Fry came up with a similar concept when studying the English coastline and realized the infinite measurements required to accurately define its irregularity.
Fractals are complex, self-similar patterns found in nature, from the structure of galaxies to the veins in a leaf. They are created by repeating a simple process over and over, each time with a slightly different outcome. Fractals are used in a wide range of fields, from mathematics to finance. Here are seven more fascinating facts about fractals:
Fractals have applications in many areas of science, including physics, chemistry, biology, and computer science. For example, fractal antennas are used in cell phones, and fractal geometry is used to model the structure of proteins.
Fractals are also used in art and design, from wallpaper patterns to computer graphics.
Fractals are commonly used in mathematics to describe chaotic systems, such as the stock market or weather patterns.
Fractals are infinitely complex, meaning they can be magnified indefinitely without losing detail.
Fractal patterns are found in nature, such as the branching of trees, the shape of coastlines and mountains, and the patterns of snowflakes.
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The Beauty of Fractals
One of the most fascinating facts about fractal shapes is their captivating beauty. Able to depict stunning graphical imagery to its smallest possible detail, with recurring shapes, vibrant color combinations and an intricate, yet natural complexity, fractals represent the artistic and elegant side of mathematics, their depictions being commonly used in advanced 3D artwork and graphics.
Fractals are mathematical shapes that can be split into parts, each of which is a reduced-size copy of the whole. This phenomenon is called self-similarity and it is what makes fractals so fascinating. Fractals can be found in nature, such as in the branching of trees, the formation of clouds, the structure of snowflakes and the arrangement of leaves on a stem. They can also be used in computer-generated art, animation and video games. Fractals are also used in the fields of medicine, economics and engineering.
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Intelligent Design
Adepts of creationist and intelligent design theories often claim that nothing as beautiful or intricate as a butterfly's wing or a simple flower could have arisen without some form of “divine intervention.” However, the plotting of a simple combination of 2D array functions called Barnsley's Fern accurately depicts a leaf, and there are plenty of more complex fractals that faithfully mimic even some of the most intricate shapes in nature.
Fractals are a fascinating phenomenon of nature, and they have been used to explain a wide range of phenomena, from the structure of galaxies to the growth of plants. They are also used in computer graphics, art, and music.
Fractal geometry is an area of mathematics that looks at how patterns repeat themselves at different scales. This means that a pattern that appears on a large scale can also be seen on a much smaller scale. This phenomenon is known as self-similarity.
Barnsley’s Fern is a famous example of a fractal. It is a simple combination of 2D array functions that accurately depicts a leaf. Fractals can also be used to create intricate shapes in nature, such as the wings of a butterfly.
Fractals are also used in computer graphics to create realistic images. They are used to generate landscapes, trees, and other natural objects. Fractals can also be used to create realistic textures, such as wood, stone, and water.
Fractals are also used in music. Fractal music is a type of algorithmic composition that uses fractal algorithms to generate musical patterns.
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Apparent Simplicity
Despite their seeming complexity, one of the most remarkable facts about fractals is that they can be created from the simplest shapes. All versions of one of the most popular fractals, named Pythagoras' Tree, start from a simple line or square and reiterate to create a beautiful tree made from the same simple shapes scaled down according to a specific ratio.
Fractals are often used in computer graphics and animation to create realistic images and landscapes. They can also be used to create digital art and music. Fractals are also used in medical imaging to help physicians identify and diagnose diseases such as cancer and heart disease. Additionally, fractals are used in the field of chaos theory to study complex systems such as weather patterns, stock market trends, and population growth.
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Fractals and Video Games
An interesting fact about fractals is that they have become practically indispensable in video game graphics. Their beauty, simplicity and flexibility allows developers to use them for recreating the most complex sceneries with very little difficulty and a high level of detail – offering remarkable image quality and unprecedented rendering speeds.
Fractals have also been used in the creation of computer-generated art and animation. Fractal art is created by using algorithms to generate complex, often intricate patterns and shapes. Fractal animation is created by using fractals to create a sequence of frames that can be used to create motion. Fractal animation is often used in video games, television shows, and movies to create realistic backgrounds and landscapes.
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Those who cannot learn from history are doomed to repeat it.
Energy Healing and Sacred Geometry
Sacred geometry involves the use of geometric patterns and ratios that are seen by some to be the building blocks of life and that have gained significant popularity among New Age thinkers. Applied to certain fractals, such as spirals, trees and intricate triangle shapes, these ratios are believed to harmonize one's energy body and assist with some energy healing practices. One of the most popular sacred geometry ratios is the golden ratio (1.61803399), found in many places in the universe and throughout nature, including galaxies, sea shells and plants.
Sacred geometry has been used for centuries in various cultures to create artwork, architecture, and spiritual practices. It is believed that these patterns and ratios can help to create balance and harmony within the human body, as well as to increase spiritual awareness. Sacred geometry is often used in energy healing practices, such as Reiki, as a way to help restore balance and harmony in the body. Additionally, sacred geometry can be used to create powerful symbols, such as mandalas, which are used to aid in meditation and focus.
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Audio Fractals
Some musicians have even begun exploring the audible potential of fractals, attempting to leave the conventional fields of music and expressing wave forms through changes of air density over time. Melodious tunes, catchy beats and strange, psychedelic sounds can all be expressed and generated through obscure fractal vibes that have only just started being explored.
These are only some of the amazing facts about fractals that continue to mesmerize us to this day. What do you think about this list? Do you know about any other intriguing facts I've missed regarding fractals and their beauty or paradoxical simplicity?
Sources:
thenakedscientists.com
mathworld.wolfram.com
ecademy.agnesscott.edu
fractalenlightenment.com
prezi.com
sessionville.com
science.howstuffworks.com
