Researchers have recently identified the initial fractal molecule found in the natural world

Fractals, which are self-repeating shapes that can be infinitely magnified without losing their intricate details, are remarkably prevalent in the natural world. Snowflakes, cauliflowers, coastlines, and even rabbits can be demonstrated to exhibit fractal patterns.

Undoubtedly, none of these instances can genuinely be considered fractal beyond the confines of the mathematics classroom, as the physical world operates in a fundamentally different manner. While mathematicians can easily approach infinity and its reciprocal by taking limits, the rest of us will inevitably encounter concepts such as “atoms” and the repercussions of attempting to go beyond that scale.

This prompts the inquiry: What is the minimum size that we can achieve? The solution is almost complete, according to recent findings by researchers at the Max Planck Institute in Marburg, Germany.

Living organisms are responsible for creating all the regular fractals found in nature, and these fractals can only be observed at the macroscopic level. Nevertheless, the team clarifies in their recent publication that no molecular-scale examples have been found in nature.

However, the situation has now completely changed. The paper states, “We have found a natural metabolic enzyme that can create Sierpiński triangles in a weak watery solution at normal room temperature.”

Put simply, they have found the very first instance of a naturally occurring fractal molecule.

“We discovered this structure serendipitously,” stated first author Franziska Sendker regarding the find. When we first used an electron microscope to capture images of it, we were astounded by what we saw.

“The protein forms intricate triangles,” she clarified, “and as the fractal expands, we observe progressively larger triangular gaps in their centers, which is completely distinct from any previous protein arrangement we have observed.”

What distinguishes this molecule from others? Utilizing electron microscopy, the team ultimately managed to unravel its structure, and the discoveries they made challenged conventional notions of protein assembly.

It is basically said that this molecule, citrate synthase from the cyanobacterium Synechococcus elongatus, does not have the selectivity that most proteins do. Instead of exhibiting symmetrical self-assembly, where each protein chain is arranged identically to its neighboring chains, S. elongatus underwent a slightly irregular assembly process. What is the outcome? A Sierpiński triangle structure remains intact even as the proteins increase in size.

“This was one of the more challenging yet also more captivating structures I have resolved in my professional trajectory,” expressed Jan Schuller, a researcher at Philipps University Marburg, whose team contributed to determining the structure.

“The challenge in determining the structure of a fractal arises from the complexity of the smaller triangles, which can serve as substructures within larger triangles,” he clarified. “The algorithm consistently focused on these smaller triangles instead of recognizing the larger structures to which they belonged.”

What is the most outstanding aspect? It appears that this distinctive molecular structure may have emerged purely through chance.

“The reasons behind past events are always uncertain,” stated Georg Hochberg, an evolutionary biologist and the senior author of the study. However, he clarified that this specific instance possesses all the characteristics of a seemingly intricate biological formation that spontaneously emerged without any discernible cause, solely due to its effortless evolution.

Undoubtedly, it is thrilling, to say the least. If molecular-scale Sierpiński triangles have been present in our surroundings, appearing sporadically due to their inherent capability, it raises the question of what other phenomena might exist, eagerly awaiting their revelation.

The research findings have been published in the esteemed scientific journal Nature.