A new study shows that cutting-edge elements in nature grow in the same geometric pattern
No matter where you look at it, the thorns of roses, the horns of bulls, the paws of lions or the teeth of sharks have many sharp elements in nature. Although they are so common, it is still very difficult to explain how these structures grow so far.
The logarithmic spiral is one of the models proposed to understand the growth of the teeth, horns, claws or beaks of birds. This happens when one side of the structure grows faster than the other side at a constant rate.
In nature, you can find this spiral in the shell of a snail or the tail of a chameleon, as well as in the arms of tropical cyclones or in the shape of spiral galaxies. However, although this spiral describes the growth path of the structure, it cannot be used to generate these elements from scratch.
A group of researchers from Monash University in Melbourne, Australia found a The new universal rule of biological growth is called “the cascade of power” It explains the similarities between the shapes of sharp structures throughout the tree of life.
Puncture properties and logarithmic spiral
After the discovery of the logarithmic spiral, in 1659, anatomist, mathematician and physicist Christopher Wren He first proposed that the shell expands in a logarithmic spiral from its center like a cone.
About 300 years later, biologists and mathematicians Darcy Thompson concluded that teeth follow this conical growth pattern. Based on this idea, researchers at Monash University discovered that not only teeth follow this geometric shape.
Monash researchers explained the growth of the probe based on the power law. The power law is the relationship between two quantities, which means that a change in one quantity causes a change in another quantity. One quantity changes with changes in other quantities, regardless of its initial value.
Power laws can also be found in everything around us, such as the size of an earthquake, the size of a city, or the movement of the stock market. Monash researchers proposed a power law that lies between the radius of the structure, any line segment connecting the center to any point on it, and its length. In this way a shape called “power cone” is created.
For example, when the ivory of an elephant is elongated, cones are found in nature. The teeth expand at a very specific rate in which there is a linear relationship between the width and length of the teeth.
How does the puncture grow
Researchers used 3D scans of teeth such as Megatusaurus, Tyrannosaurus, or Mammoth. They also analyzed the claws, hooves, horns, and beaks of mammals and birds, as well as the fangs and shells of invertebrates.
All these elements follow the same natural pattern as they grow, and are followed by shapes such as rose bushes or lemon tree thorns, which has been verified.
In order to define the power cascade, a line was established to divide the sharp object in half in order to focus the measurement on the expansion rate of the tooth radius. In this way, it has been observed how shapes “cascade” in teeth following the power law.
When the radius increase is different from the longitudinal power increase, a power cone is created. That is to say, when it has not grown to a very long time.
The researchers said: “This new rule is the missing piece of the 350-year-old puzzle about how animals and their parts grow.” Knowing the cascade of forces can allow predicting when these natural structures might break through in the future. Model of evolution.