By Morgan Nasholds

The concept of infinity is indeed a daunting abstraction in the world. Infinity itself is, simply put, impossible to fully comprehend. As with many concepts that are difficult to present, visual art provides one with the ability to witness the concept of infinity through the intriguing and fantastic world of fractals. Fractals are interminably repeating patterns that, for the most part, appear as beautiful and remarkable works of art. However, they are more than art—they are mathematical equations in an astonishing visual form.

The mathematician Gottfried Liebniz first conceptualized fractals in the 1700s. He simply put that “fractional equations” could repeat indefinitely, as fractions can be fractions of other fractions, and so on. For a long time, fractals were seen as monsters in the mathematical world; mathematicians did not appeal to the idea of infinity, thinking it was an anomaly and that everything had an end. Helge von Koch, in the early 1900s, brought change to the negative stigma surrounding fractals, and introduced one of the first fractals: the Koch Snowflake.

The Koch Snowflake was a triangle with smaller triangles added to the midpoints of the lines on the initial triangle. Repeating this pattern—putting smaller triangles on the bigger triangles—led to the first visual concept of a fractal.

Next, the mathematicians Pierre Fatou and Gaston Julia brought about other concepts of a fractal. Gaston Julia created the “Julia set” fractal, which generally appears as a variation of a vortex. Eventually, in the 1960s, Benoît Mandelbrot brought hundreds of years of fractal study and concepts into one book, called How Long Is The Coast of Britain? Statistical Self-Similarity and Fractional Dimension. This lengthy-titled book brought fractals and their ideas to the front line of the mathematical world, and it initially sparked a negative uproar. Many mathematicians simply did not want to bring fractals into the fray of the mathematical world; they were too “artistic” and were criticised for being “mathematic look-alikes.”

However, this criticism of the fractals faded quickly, as mathematicians began to realise that fractals appeared frequently around the world, in manifold ways. Nature was the most prominent user of fractals. Use a tree, for example: there is the trunk, which extends into smaller trunks, or branches, which in turn sprout their own little branches, which in turn either sprout smaller branches, or finally sprout their leaves. When imagination is put into good use, one can easily see how a tree could, technically, grow branches infinitely. Growing branches off of trunks, branches off of branches, and thusly ad infinitum growth of branches would result in a fractal tree. Soon enough, fractals became an accepted idea in the mathematical world, and were no longer seen as “monsters.”

Fractals are frequently used today in the visual arts field. They can be mathematical, yet they fit just as well into the artistic fields. Fractals have appeared on clothing, along with many other aesthetic articles. Their entrancing patterns have also been frequently associated with being high on drugs, as the hallucinatory effects apparently produce fractal-like patterns. It just goes to show that our brains can also produce fractals, so why would fractals ever be called “monsters”? They are beautiful concepts of infinity that will echo throughout the ages for as long as their own patterns repeat—which might I remind you, is infinite. Even when human civilisation is finished, and eternities after that event, fractals will still be in and around the universe.

Look at a galaxy, look at a galaxy cluster, just look at the universe as a whole! Technically speaking, the universe is a fractal, and off of the main branches of the universe sprouts the smaller branches. Humans are on one of those microscopic branches of the universal fractal, and we’ll go along with that fractal forever.