A fractal is defined as a never-ending geometric pattern that looks the same even at different scales which means that, if you zoom in on a part of it, it will look similar to the image if you zoomed out.

For many, fractals seem like a foreign concept. Especially when considering it in mathematical terms, it is beyond the scope of many (including myself). However, when looking at fractals as a concept, one find that it makes it home in many aspects of our lives. For example, consider the image below.

At first glance, it may not appear to have much in common with the example of a fractal above other than the fact that they’re the same color. However, let’s reexamine the definition of a fractal but in a more conceptual manner. Looking at the image above, if you block out the background, it seems as if the leaves spread out in a never ending pattern, and if you were to compare to another one next to it, they look almost identical. That is a fractal. In fact, the first image above isn’t some generated image from a fancy mathematical equation. It’s broccoli (Romanesco broccoli to be specific). Other examples include pine cones, snow and ice, succulents, tree branches, rivers and the veins of leaves.

Now that it is apparent that fractals are everywhere, what do you feel when you seem them? Is there a sense of fear, astonishment, intrigue, surprise, or all of the above? For me, I also felt a sense of doubt. It didn’t feel possible that something this “perfect” could have been made in nature but when I think about it more, it makes sense that something like this could have only been made in nature. It seems even more impossible for mankind to be able to make something unique aesthetic beauty of fractals. According to a study by J. C. Sprott’s study on the aesthetic appeal of fractals, 8 volunteers rated 750 computer generated fractals on a 5 point scale based on their aesthetic appeal. The results found that those with fractal dimension between 1.1 and 1.5 had the greatest appeal and that those with the highest ratings tended to be around 1.3. In a subsequent study, the findings supported their previous conclusion and expanded into the fact that the preferred value of 1.3 corresponded with the fractal dimension commonly found in nature (Mandelbrot, 1982). So, for most, they would correlate their feelings with a sense of beauty or satisfaction when viewing these fractals.

This begs the question: Why? Here is my take on it:

We as humans experience events in our lives that may make us feel unstable and out of control. Even though this is an integral part of our existence and especially our coexistence with other people and species, it is a feeling that has been biologically wired as a “bad thing”. So, we will naturally want to avoid it. The greatest example of this is when you try to do something and things do go your way or someone or something is acting in an unpredictable way. You feel uncomfortable. Now consider the fractal. It embodies the opposite of everything I just recalled: it is predictable, it will go in the way you expect it to, it is everything that we want it to be. Therefore, we find solace in its existence which overrides our inability to comprehend how the fractal was created or perpetuated. We find bliss in ignorance and comfort in predictability, drawing us deeper into the convincing sea of fractals in nature.

Citations:

Mandelbrot, B. B. 1982. The Fractal Geometry of Nature. W. H. Freeman, San Francisco. https://www.sciencedirect.com/science/article/abs/pii/S0097849303001547

Gunther S. 2022. 9 amazing fractals found in nature. Treehugger. [accessed 2025 Feb 20]. https://www.treehugger.com/amazing-fractals-found-in-nature-4868776