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What are Fractals?
A fractal is a neverending pattern. Fractals are infinitely complex patterns that are selfsimilar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.
For a simple description of fractals, please download our “One Pager” (380Kb).
For more detailed info, please download our 20 page “Educators’ Guide” (7.5Mb).
Explore the Mandelbrot fractal yourself, with the amazing realtime fractal zoomer, XaoS:
Fractals
Fractals, as with all of mathematics, can be full of paradoxes they can often be a source of creativity, beauty, and surprise while at the same time they can be a powerful tool for analyzing and communicating about complex ideas. Fractals often start with a simple geometrical object and a rule for changing the object that leads to objects that are so complex that their dimension is not an integer. According to Michael Frame, Benoit Mandelbrot (who first coined the word “fractal” and was the founding editor of this journal) considered himself above all a storyteller. In his wonderful TedX talk about fractals, Michael says “A fractal description of an object is a story about how it grows? Fractals remind us that science has a narrative component that we too often ignore. Fractals remind us that stories are important.” Here is the link to the talk: https://www.youtube.com/watch?v=bz8NJ7ZVXwQ
The applications of fractals range from economics to geography to medical imaging to art. This journal strives to show how fractals provide a beautiful language to describe nature and other systems. It is an honor for me to be part of the editorial team of the journal. I strongly echo Nathan Cohen’s statement: the editors have great respect and support for fractal research and education in all their aspects, as the fractals community continues to grow and prosper–through its many iterations.
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How Fractals Work
Fractals are a paradox. Amazingly simple, yet infinitely complex. New, but older than dirt. What are fractals? Where did they come from? Why should I care?

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Unconventional 20th century mathematician Benoit Mandelbrot created the term fractal from the Latin word fractus (meaning irregular or fragmented) in 1975. These irregular and fragmented shapes are all around us. At their most basic, fractals are a visual expression of a repeating pattern or formula that starts out simple and gets progressively more complex.
One of the earliest applications of fractals came about well before the term was even used. Lewis Fry Richardson was an English mathematician in the early 20th century studying the length of the English coastline. He reasoned that the length of a coastline depends on the length of the measurement tool. Measure with a yardstick, you get one number, but measure with a more detailed footlong ruler, which takes into account more of the coastline’s irregularity, and you get a larger number, and so on.
Carry this to its logical conclusion and you end up with an infinitely long coastline containing a finite space, the same paradox put forward by Helge von Koch in the Koch Snowflake. This fractal involves taking a triangle and turning the central third of each segment into a triangular bump in a way that makes the fractal symmetric. Each bump is, of course, longer than the original segment, yet still contains the finite space within. Weird, but rather than converging on a particular number, the perimeter moves towards infinity. Mandelbrot saw this and used this example to explore the concept of fractal dimension, along the way proving that measuring a coastline is an exercise in approximation [source: NOVA].
If fractals have really been around all this time, why have we only been hearing about them in the past 30 years or so?

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