Fractals in Nature

The term "fractals" derives from fractions and fractures, referring to the broken and fragmented forms we observe in nature. Take a look at river deltas; they exhibit stunning geometric structures.

While many associate geometry with shapes like triangles and circles, it fundamentally encompasses the mathematics of all forms. The interaction of land and sea produces patterns characterized by order—patterns that often elude those who don’t study them.

River deltas consist of convoluted channels that branch out and merge multiple times before reaching the ocean. This structure is mathematically recursive, where each segment mirrors the larger whole.

Consider the parallels between a river delta and a tree.

The resemblance is remarkable, prompting the question: why do these shapes appear so similar? This observation extends beyond water systems and trees; these fractal patterns are ubiquitous.

Take note of their geometry. Their likeness is striking, leading to a sense of wonder.

Moreover, the pattern of the human body reflects nature as well. Every cubic centimeter of our body is filled with blood vessels that follow similar patterns.

This connection doesn’t end there. The universe is woven with mathematical realities found in towering trees, fierce storms, flowers, broccoli heads, fern leaves, clouds, and more.

These forms exemplify "fractals." Once you start recognizing fractals, you'll see them everywhere, I assure you.

Like our other senses, our mathematical sense can be sharpened with practice. With time and proper guidance, you can learn to discern the mathematics surrounding you. Naturally, some individuals are born with a more acute sense than others.

Mathematical Patterns in Nature

We inhabit a cosmos rich in patterns, and we are wired to recognize these patterns. Humans excel at pattern recognition; our brains thrive on it. We learn and make decisions by identifying patterns in the information presented to us.

Neuroscientists affirm:

> "Humans constantly seek patterns in their environment, as it simplifies learning."

Those adept at creating patterns or using their creative faculties frequently hold titles such as artists, musicians, sculptors, painters, filmmakers, writers, and, of course, mathematicians—they are all creators of patterns.

You'll find captivating instances of mathematical patterns in Islamic art and design, where the aversion to depicting living beings resulted in a rich tradition of intricate tile designs and geometric forms.