Natural geometrically regular patterns, or patterns, appear in the form of repeating forms, which can sometimes be described or represented by mathematical models.
Geometry in nature and life can be of various forms and types, for example, symmetry, spirals or waves.
History
For the first time, ancient Greek philosophers and scientists - Pythagoras, Empedocles and Plato - took up geometry in nature. By analyzing examples of predictable or ideal geometric shapes in plants and animals, they tried to demonstrate orderliness and symmetry in nature.
Modern attempts to study geometry in nature began back in the 19th century with the efforts of the Belgian physicist Joseph Plateau, who developed the concept of a minimal surface of a soap bubble. The first modern attempts at first focused on demonstrating ideal and predictable geometric shapes, and then went on to develop models that predict the appearance and manifestation of geometry in nature.
In the 20th century, mathematician Alan Turing worked on the mechanisms of morphogenesis, which explains the appearance in animals of various patterns, stripes, spots. A little later, the biologist Aristide Lindenmeier, together with the mathematician Benoit Mandelbrot, will complete work on mathematical fractals, which repeated the growth models of some plants, including trees.
The science
Modern sciences (mathematics, physics and chemistry) using technologies and models are trying not only to explain, but also to predict the geometric patterns that occur in nature.
The shape and color of many living organisms such as peacock, hummingbirds and sea shells are not only beautiful, but also geometrically correct, which attracts the curiosity of scientists. The beauty that we observe in nature can be determined naturally, mathematically.
The observed natural laws in mathematics are explained by the chaos theory, which works with spirals and fractals. Such regularities obey the laws of physics, in addition, physics and chemistry, using abstract mathematics, predict the shape of crystals, both natural and artificial.
Biology explains geometry in nature by natural selection, when such regular characteristics as stripes, spots, bright colors can be explained by the need to mask or send signals.
Types of patterns
In nature, there are many repeating patterns that manifest in various geometric forms. Types of the basic laws of geometry in nature, photos and their description can be found below.
Symmetry. This geometric shape is one of the most common in nature. In animals, mirror symmetry is most often found - butterflies, beetles, tigers, owls. It is also found in plants, such as maple leaves or orchid flowers. In addition, the symmetrical geometry in nature can be radial, five-beam or six-fold, as in snowflakes.
Fractals. In mathematics, these are self-similar constructions that are infinite. In nature, it is impossible to detect such an infinite self-repeating form, therefore, approximations of fractal patterns are called geometric fractals in nature. Such geometry in nature can be observed in fern leaves, broccoli, pineapple fruit.
Spirals. These forms are especially common among mollusks and snails. Scientists observe spiral forms in space, for example, spiral galaxies. The spiral is called the Fibonacci Golden Ratio.
Meanders. The randomness of dynamical systems in mathematics manifests itself in nature in such forms as meanders and flows. Natural geometry takes the form of a broken or rather curved line, for example, a river flow.
The waves. Caused by disturbances and movements of air, wind flows, spread both through air and through water. In nature, these are not only sea waves, but also desert dunes, which can form geometric shapes - lines, crescents and parabolas.
Mosaic. Created by repeating the same elements on the surface. Mosaic geometry in wildlife is found in bees: they build a beehive from honeycombs - repeating cells.
The formation of patterns
In biology, the formation of geometric color is due to the process of natural selection. Back in the mid-20th century, Alan Turing was able to describe the mechanism of the appearance of spots and stripes in the color of animals - he called it a reaction-diffuse model. Certain cells in the body contain genes that are controlled by chemical reactions. Morphogen leads to the formation of skin areas with dark pigment (spots and stripes). If the morphogen is present in all skin cells, the color of the panther is obtained; if it is unevenly present, a common spotted leopard.