Fractals in Nature

The chaos present in everything from a drop of water to the galaxies of our universe has long fascinated people in cultures around the world. The natural disorder present in tree branches, lightning bolts, and shorelines, to name a few examples, can appear completely chaotic, no matter how autonomous it may be. The similarity within these phenomena is much more organized than it seems. Repeated patterns in many natural objects and processes are known as

fractals

. Figures showing self-similarity at different levels. The study of

fractals

in both

nature

and pure mathematics has advanced numerous branches of science, such as computer science, telecommunications, fluid dynamics, biology, and medicine, and may offer innovative new perspectives on human science and technology.

Almost everything in the universe is constantly changing, and while fractals have been described as patterns of chaos, they can also be described as patterns of change in the context of

nature

. Fractals In many cases, fractal patterns are the most efficient way to deliver nutrients, collect sunlight, or form support structures for plants or animals, for example, the nautilus shell, a natural object that results from the growth of a nautilus, which is formed in a very precise logarithmic spiral, meaning that each shell compartment is larger than the previous compartment by the same factor, regardless of its position in the shell.

The veins of many leaves are also arranged in a fractal pattern, making it easier for nutrients to flow in and out of the leaf. Romanesque broccoli perhaps one of the best known fractal patterns in nature grows on branches or sprouts each large sprout has several smaller sprouts which in turn have smaller sprouts and so on, although these natural fractals are not infinite like their mathematical counterparts, their self-similarity is well modeled by fractals. many non-biological processes or objects also demonstrate repeated self-similar fractal features. Snowflakes have a fractal structure due to the organization of the water molecules within them, which is often reflected in the six branches of the snowflakes or in the frost seen on the windows.

Many metals have branched microstructures. features close in appearance to trees known as dendrites that result from specific crystallization parameters flowing water often spreads in fractal patterns such as the alluvial fans of rivers that end near mountains the flow of water, wind or other sources of erosion can form fractal patterns and Features such as coastlines and mountains, as driving forces of change, often act most strongly in areas that have already been acted upon in a larger-scale recursive loop. Solar systems in galaxies have been observed to organize themselves in self-similar patterns, something that challenges many. previous theories at the most basic level fractals occur in nature due to the repetition of a process or force acting on something such as the erosion of land by water or the growth of leaves on a fern plant, the persistent action of Water on a surface can introduce cracks that expand and open up more surface area for new cracks to form, thus creating self-similar features.

The force of evolution drives living beings to be as simple as possible and at the same time be able to survive. Shortening the genome of an organism can be beneficial as it would require fewer resources to reproduce. In this sense, fractals offer a wonderful method for simplifying living structures, since it is easier to genetically store the self-similar information of a fractal than the details of each small structure, as seen in the fractal patterns of fern leaves. For some natural fractals it is still unclear why they organize into self-similar patterns, although the driving principle is probably related.

Humans have noticed patterns in natural objects for thousands of years and many human creations have been inspired by fractal patterns, for example, the organizations of Historically, cities and towns have often followed fractal distributions. The logarithmic spiral is a predominant feature of much Renaissance art. Humans apparently unconsciously followed the self-similar patterns seen in nature, and modern research has shown that humans prefer artistic designs that display fractal geometry to those that did not investigate the patterns of natural structures such as ice crystals. nautilus shell or the veins of the human body? Human models of these patterns were simple, such as the logarithmic function or the repetition of geometric features, but they advanced several areas of mathematics, science, and technology.

Many scientists continued to investigate the mathematics of recursion and self-similarity, but the study of fractals was revitalized with the advent of computing in the late 20th century. In the late 1970s, Polish French mathematician Benoit Mandelbro began studying fractals, specifically the Julia sets created by French mathematician Gaston. Julia, six decades earlier, at the time Mandelbro was among the IBM research staff and used available computers to plot the Julia sets, specifically highlighting points in the set that did not go to infinity but remained between certain now-known limits like Mandelbro. was based on the work of George Cantor Gaston Julia Felix Hausdorff and Lewis Fry Richardson Benoit Mendelbro wrote many articles and books on a new field of study: fractals, a name he derived from the Latin word for fragmented mandelbro, demonstrated the application of fractals to natural phenomena such as coastlines, as well as unnatural phenomena such as the stock market, in addition to applications in mathematics, fractals have been used to model or design novel systems in fields such as medicine, computer science and electrical engineering, biology , chemistry, environmental sciences, cosmology and many more, different from the two known ones. and three-dimensional figures Fractals do not have integer topological dimensions and instead may have non-integer or Hausdorff dimensions that allow a closer approximation of natural features.

The simplicity and high surface area of ​​fractals make them ideal models for simplifying and improving existing or theoretical fractal designs. They have found ingenious applications in biology and medicine due to the multitude of natural systems that follow recursive patterns in at least one aspect. The growth of some bacteria has been well approximated by fractal models and these models can also help predict the location of bacterial colonies. The growth of blood. The vessels of the human body follow fractal division, a phenomenon that can be altered in cancerous tissue. Fractal analysis of blood vessel growth in tumor tissue may offer new insights into cancer.

The organization of neurons follows fractal patterns, a characteristic that can help understand how the human brain works. Fractal distributions have been used to determine the distribution of plants in managed forests, analyze the distributions of alveoli and lungs, and even investigate the genetic systems of cells. Fractal models have been successfully applied to physical processes such as turbulent flow and aggregation of molecules due to similarity. of the physical laws that govern how such things happen, fluid dynamics as chaotic and potentially recursive phenomena have been reproduced numerically using fractal approaches, helping to model things like the flow of fluids around airplanes and ships, the kinetics of mixing in industrial processes and many other engineering problems.

Some porous structures are fractal to some extent and fractal models have been used to model porous media for petroleum engineering. The randomness observed in fractals may be similar to the Brownian motion of molecules in liquid or gas and semifractal models have been used to approximate aggregation by diffusion and electrodeposition of molecules in materials engineering due to the high ratio between surface area and volume of fractal patterns. Designs incorporating fractals have been implemented to minimize mass or size for applications requiring high surface areas, such as antennas or cooling units, this approach has shown great promise in achieving equal or superior specifications with significantly less material usage. using the principles of self-similarity at any scale.

Fractal patterns have been used in a new image compression method that offers clear resolution at any scale. The natural world has a lot of chaotic elements. The processes that shape the world we live in and these processes often create the self-similar things we see around us. Learning from these natural fractals has given us the ability to advance our knowledge of the physical world and apply this knowledge to novel creations in the world. In the future, the study of fractals will lead to greater inventions and may help answer our lingering questions about the universe. Thanks for watching and as always, if you liked the video, please leave a like, watch more videos on the channel for other interesting topics or subscribe to the channel for more educational documentaries