Categories
Physics

Fractals

Fractals are complex patterns that are repeated over and over again at progressively smaller scales. They are found in physics, economics, physiology and nature.

Nerd Alert! 🤓 Benoit Mandelbrot was a brilliant mathematician that could SEE math. We can all see numbers, you say? Well yes, but Mandelbrot’s visualization of math immeasurably contributed to science on a deep level. You see, math tells a story. It explains the why, such as – if we had this, than that would happen. Or what if we had this, this and that? Then what would happen? Science is the product of the equation, or the end result. We all can SEE the science project, but math tells the hidden story of how to build it. Once we know the formula, we discover how to tell the story over and over again.

In a nutshell, Mandelbrot created the formula to create the geometric picture above – the Mandelbrot set. It is the result of connected points from his computations graphed in a complex plane. He plugged in a set of numbers, in a manner similar to a feedback loop which formed beautiful patterns within patterns, repeating themselves infinitely. These complex patterns appear the same on various scales which parallels a blueprint for nature.

Check out the mandelbrot set on Youtube to get the full backstory – it will not disappoint.

If mathematics is the science of patterns, then God used sophisticated algorithms to create the world.

Grit & Grace

fractals, nature + us

Let’s go down this rabbit hole….

My assignment was to write a paper on a fractal in nature. I thought, no problem. I’ll just write about a snowflake, broccoli, or a tree. I love trees, so I thought I would quickly write – ‘from a simple seed sprouting out of the ground appearing to look like small leaves on a vine, a tree grows and begins splitting off into branches. As each branch splits, again and again, this duplicative process repeats itself until the tiny sprout becomes a large tree. This large tree with many branches actually looks like smaller trees, masterfully assembled in a specific pattern.’ Boom! There is self-similarity represented by many branches that are actually small trees forming the large tree. Done. I am off to go for a run.

But not so fast. As I was researching for this assignment, I stumbled upon a video where a group of scientists cut down a tree to gather data. They were trying to determine how much carbon dioxide the rainforest could remove from the atmosphere. Their research determined that “the same fractal pattern found in the tree, is perpetuated throughout its home forest.” In other words, not only does one tree possess a fractal pattern, but this single tree’s fractal pattern was a blueprint of the entire rainforest!

Downward spiral…..

As I was thinking about the supreme intelligence behind this larger-scale fractal pattern of the rainforest, I also remembered how trees are designed to protect the air we breathe. For instance, in one year a mature tree will absorb more than 48 pounds of carbon dioxide from the atmosphere and release oxygen in exchange. The whole circle-of-life thing came full circle! I could see the similarity of the trees’ branches, our lungs, and how they both serve as respiration for life.

Rabbit stops here…..

I could have kept going deeper down the rabbit hole, but my assignment was only suppose to be a few paragraphs. I reluctantly stopped myself with this realization – God is a genius! All living things are designed so masterfully….and there is an algorithm to go along with it. We just haven’t even been able to build technology powerful enough catch up to the power of God. (Even Mandelbrot couldn’t have made his discoveries without the invention of the computer.) The self-similarity of fractals in nature mirror the self-similarity in us! How creative is that?! What a master plan!

Residual Thought: I have always had an admiration for trees. They make me feel safe. Maybe it is due to their strength, beauty, and resilience. They are vital to our ecosystem for animals as well as humans and provide natural resources. As a runner, I prefer trail races over road races due to the trees. In a race, the trees protect us from the heat of the sun, provide oxygen, and oddly enough emit a cooling effect when our body gets overheated. I thought I would become one with nature while out running among the trees because I was in the zone. But now I know it’s because of the connection that my body innately recognizes in nature. There is more to math and science than we were once taught in grade school. How exciting it is to open ourselves up to all the possibilities unfolding in fractals!

Fractals represent a state of self-similarity in all natural things.
Fun Fact!