Fractal Artist
In this history of fractal art, we examine some of the names mathematicians and artists have chosen to call their fractals and discover how these names came about and what they mean.
The human mind has a natural affinity with fractals. Our natural surroundings are filled with these intricate and beautiful patterns, and we have evolved with an instinctive ability to process visual information characterized by their forms.
Consider the patterns found in the branching of trees, the tributaries of a river, or the peaks and valleys of a mountain. These fractal shapes have always existed around us, and our understanding of their structure has helped us thrive in the natural world.
Fractals portray what is harmonious and beautiful in nature, and, not surprisingly, they have appeared in various art forms over the ages as artists have tried to express nature's intrinsic beauty.
Take, for example, the Japanese woodblock print "The Great Wave off Kanagawa" by Hokusai. In this artwork, he employed a fractal shape to portray a wave, where smaller waves nestle within the larger one, mirroring each other at different scales. This aligns closely with the principles of fractal geometry.
While Hokusai may not have consciously aimed to create a fractal, his keen observation of natural forms led him to depict the fractal shapes that waves exhibit.
Just as artists have recognized fractal patterns in nature, scientists have also recognized natural forms in the mathematical fractals they have created that remind them of familiar objects in the real world.
As mathematicians have developed various types of fractals, they have often named them after objects they may resemble for easier recognition and description.
One notable example is the Koch snowflake, a fractal shape introduced in 1904. It first appeared in a paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry," written by Swedish mathematician Helge von Koch.
With advancements in computer technology during the 1970s and 1980s, computer scientists began to generate highly detailed fractals. As they explored these shapes in depth, an increasingly sophisticated language developed to articulate and share their findings.
The term "fractal" itself was coined in 1975 by Benoit Mandelbrot, based on the Latin word "fractus," which means "broken" or "fractured." He used this term to draw parallels between fractals and real-world structures.
In his seminal book *The Fractal Geometry of Nature*, Mandelbrot also introduced the term "island" to describe features of the Mandelbrot set, conjuring up images of exotic archipelagos waiting to be explored.
Several geographic terms have entered common usage when describing fractals. The area at the center of the Mandelbrot set, often depicted in black, is frequently referred to as the "main continent."
Where this connects to smaller areas known as "bulbs," the narrow regions that protrude are often referred to as "valleys."
These valleys are often divided along lines of symmetry known as the eastern and western parts of the fractal.
As new shapes and structures emerged within the details, these sparked people's imaginations. Colorful names were given to individual valleys to help describe them. Names such as "seahorse valley" and "elephant valley" have become common parlance that is still used today.
At the peak of discovery in the 80s and 90s, a whole language grew in an attempt to classify the Mandelbrot set, and, in some ways, has come and gone now.
Like many languages that are no longer commonly spoken it is true that new words will emerge in the future to replace them; however, these familiar, often colloquial terms stand as a record of this time. They affect our ways of seeing and talking about fractals, and echoes of them are likely to persist long into the future.