Fractal is an geometry that shows similarity throughout the scale - that is, they all look the same regardless of whether they are large or small. In fact, they are everywhere in nature.
We will encounter many fractal examples in our daily life. The growth of pineapple follows fractal rules, and ice crystals are also formed in a similar fractal shape. Fractals allow plants to maximize exposure to the sun. They enable the cardiovascular system to effectively transport oxygen to various parts of the body.
Here we will explain 14 fascinating and beautiful fractal examples in nature.
Roman cauliflower
Roman cauliflower grows in a golden spiral shape, which is a pattern based on the golden ratio. The spiral widens the φ factor for every quarter of the rotation. This vegetable tends to accelerate germination, resulting in this spiral and conical shape. As cauliflower grows, the flower tips will get taller and taller.
Other golden spirals in nature include spiral galaxies and nautilus shells.
pine cones
pine cones are a woody, scaled fruit that hangs on evergreen trees and is the seed-bearing organ of the tree. You have no doubt noticed their satisfying spiral scales, which reflect the seeds they protect. They close tightly when wet or cold and then open when the seeds are best for spreading with the wind.
Likewise, fractal design is caused by accelerated growth. This is a natural example of a logarithmic or equiangular spiral.
succulent plants
In plant biology, fractal design is called spiral leaf-like arrangement, and the term "leaf-like arrangement" simply refers to the arrangement of plant leaves. There is a reason why the leaves of Spiral Aloe vera and some crescent lotus curl upwards: they help guide rainwater to the core of the plant, preventing the top leaves from obstructing the bottom leaves.
In the mid-21st century, a mathematician assumed that the reason for the spiral patterns of plants and fingerprints was the same, that is, relieve stress. He said forces acting in the opposite direction can cause the skin and plant tissue to bend inward during growth.
Ice and snow
No two snowflakes have the same design, but many branches of snowflakes produce their own side branches to represent fractals. If the snowflakes don't stop accumulating moisture and eventually melt, it may continue like this forever and become as big as the earth.
The most famous fractal snowflake pattern is called Koch snowflakes, which originates from an equilateral triangle forming another equilateral triangle and then forming another equilateral triangle. This is one of the earliest fractals described.
Tree branches
tree is one of the most typical fractals in nature. As they grow, branches will grow on the trunk, and each branch is like a smaller tree, growing its own branches. If you observe a complex tree, you will notice the repetition of the Y-shaped shape throughout.
This fractal design, like the spiral shape of succulents , helps trees optimize their exposure in the sun and prevents the top branches from obstructing lower branches.
Copper crystal
Fractal geometry is also common in chemistry. Copper crystals are well demonstrated by this phenomenon, they stretch in all directions like branches. Each "branch" is a new growth point - when it stretches out, it develops into solid metal copper . Due to its tree-like nature and unique reddish brown color, copper crystals are often used in art planting.
Rivers
Rivers forked into streams because water flows down from the main road, but why is it always meandering S-shaped? Although rivers can sometimes form a straight line, they quickly become curved because they adapt to the disturbances of wildlife nests. Just one disturbance can disrupt the flow of the river and make it bend throughout the river.
How wide are these streams are, it is also very formulaic. Experts found that these curves are always six times the width of the strait. This self-similarity is a characteristic of fractals and is why rivers around the world look similar.
Leaf Vein
In fact, trees are fractal from seeds to roots to leaves to crowns. If you look closely at the veins of leaves, you will find how self-similar they are. The smallest one looks like the main central vein (central vein), while the central vein looks like a trunk with branches.
This only works for reticular veins (reticular, not parallel veins).
foam
0 The foam on your morning latte is fractal. In nature, bubbles generated when waves break or raindrops fall will form a self-similar pattern where air pockets of varying sizes are separated from liquid films. Small bubbles are interspersed with large bubbles, smaller bubbles are interspersed with small bubbles, and so on.
Outside of nature, you will see these fractal patterns while you are in a soap bath or washing dishes in a sink.
