What is a Fractal?
Fractal patterns, like many other concepts of mathematics, are full of paradoxes. A source of creativity and beauty, a fractal structure can also be a powerful tool to analyze and communicate complex ideas.
In mathematics, this property of an object is called self-similarity. Shapes that exhibit self-similarity are known as fractals. Fractal patterns are deemed as the most beautiful and exquisite structures produced by nature and are present all around us.
We have an abundance of fractal geometry in nature like hurricanes, trees, mountains, rivers, seashells, coastlines, the edge of a snowflake, and many others.
These images could look very complex at first glance but if you take a closer look, both of these objects of nature follow a rather simple pattern.
Each individual part of the plant looks exactly similar to one another and to the entire plant, just smaller in size. The same pattern is repeated all over at smaller scales.
Some properties of fractals:
Self-similarity: A fractal is similar to itself on all scales. If you zoom in on a fractal, it will look similar or exactly like the original shape. Never-ending: Fractals are never-ending.
Irregular: Fractals are irregular.Simplicity: Fractals are simple. Dimensional: Fractals are dimensional. Fractals have finite area but infinite Circumference.
Practical uses of Fractals
Modeling natural structures - Fractals can be used to model geographical terrain, botanical plant structures, clouds, mountains, coastlines, blood vessels, and galaxies.
Computer graphics - Fractals can be used to produce realistic computer graphics, and in image compression.
Medical diagnostics - Fractals can be used to diagnose abnormal heart rhythms and tumors.
Engineering and architecture - Fractals can be used in the architecture of the internet, and in the design of fractal antennas.
Other uses - Fractals can be used in the study of chaotic phenomenon, convergence of iterative processes, and fractal art.
Some of the most common examples of Fractals in nature would include branches of trees, animal circulatory systems, snowflakes, lightning and electricity, plants and leaves, geographic terrain and river systems, clouds, crystals.