Introduction

For many years, I have been obsessed with fractals, the patterns they show and reveal, their connections to nature, and how math connects to nature in these beautiful designs.

If you don't know much about fractals, they are infinite patterns, share self-similarity in subunits, and are used for modeling things in nature, especially when some element of randomness is involved. You can learn more about fractals here.

I programmed the fractal tree below using JavaScript.

Fractal Tree

Meaning and Interpretation

Looking at this tree, I noticed some things with self-similarity and changing parameters. Trees are often good metaphors for life, and this fractal tree is no exception.

Regarding self-similarity, each piece of the fractal propagates itself outwards in the same pattern. In people, choices, decisions, and experiences can propagate themselves outward. Taking one path or decision causes other opportunities to present themselves. These opportunites differ based on past decisions. The tree as a whole represents the whole set of possibilities given the whole set of choices.

Just as every tree in a real forest is unique, every person's set of decisions and opportunities is unique. Changing the parameters in this fractal tree (angle and branch length) is like choosing a new set of life experiences, a different background, a different educational program, a different culture, or many other differences. These differences make the fractal tree appear very different, just as real trees appear different, and just as people appear very different on the outside. However, these fractal trees all start at the same point and have many similarities. The big differences may just be due to one small change in a parameter. The same thing applies to people, where we all have great similarities in being human and in the human experience, but some physical and personality traits differentiate us all. It is important to remember that we all are unique yet share so much as humans.

I find that the meaning hidden in fractals and nature allows me to connect more to other people. Fractals have shown me the diversity in people, but also how we are all similar in many ways. I can connect this to my life by appreciating the differences between people but also by understanding how we are fundamentally connected. By understanding that people's viewpoints vary based on their past experiences, I can attempt to place myself in their shoes and appreciate their viewpoints. This allows me to make connections with people on a deeper level.