Who Discovered the Fractals

Miller in Digital Art says that although understanding fractals requires complex math, the basic concept is simple. Ebola111 has uploaded an example of how simple mathematical fractals are created on YouTube. The clip is called Koch Snowflake. Helge von Koch a Swedish mathematician first described the creation of the Koch Snowflake in 1904. What he was describing was a simple fractal.

The relationship of fractals in math to fractals in the natural world, is one of the reasons artists have been so successful in re-creating natural scenes digitally

The Characteristics of Fractals

Fractals look the same at any scale. A close up detailed view of any fractal will look the same from any larger view of the same thing. Many of the clips on YouTube that present the beauty of fractals, zoom in and out so that the viewer can see the whole, and the parts that unify to create the whole.

According to Miller on page 24 of the book Digital Art Painting with Pixels, Fractals can be found throughout nature. He sites examples such as tree branches looking like the tree they came from, and rocks looking like the mountains they are found on. He also claims that the indentations of a coastline seen from space can look like the same coastline seen from only a few feet away; or even when seen under a magnifying glass.

The Discovery of the Fractal

When scientists and mathematicians first started exploring the idea of the fractal, they were only able to hypothesize about them. They plotted what they might look like with hand drawings. Miller says that in the late 60’s plotting the fractals on computer allowed the discovery of their amazing simplicity and beauty. It was then that artists began to realize the potential of the fractal. They started to use fractals to create special effects. They would later transfer them to paintings and other artworks. They fractal was valued for its own sake as a representation of natural beauty.

Fractal Based Software

Miller says that these days, one of the most important uses of fractals is to go straight to the core of natural forms. This means that software designers have been able to use the power of the fractal to describe natural forms such as clouds, trees, rocks and shorelines. Designers have been able to develop programs that can be used to create extraordinary realistic digital landscapes. Images created by programs such as Terragen™ can be life like. Sometimes they are impossible to tell apart from photographs of real landscapes, Miller claims.

Benoit Mandelbrot and Fractal Geometry

In the mid ‘70s Mandelbrot introduced Fractal Geometry using computer graphics. He set out to show that by using mathematical formulae, he could describe complex, irregular natural forms. He was able to describe clouds, the distribution of leaves and twigs on trees, as well as the shape of coastlines and the beauty of spiraling seashells.

The widespread use of these ideas within the realm of digital art did not really take off until the ‘80s. This was because computing itself had to become more cost effective. Printing needed to develop to a more sophisticated and cost effective stage of production. Once artists became involved in the use of this equipment, they were able to cause the generated fractals to become increasingly lifelike. They did this by introducing some randomness into the way the designs were created.

Artists don’t need to know anything about the extremely involved and complex mathematics of fractals to use them, Miller says. In the same way that none of really need to know how a computer works for us to turn it on and work with it. A large image may require trillions of calculations to produce what seems to viewers to be such a simple beauty.

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