• Mayur Pawar

Do you know: Nature also likes to stay in order

Updated: Dec 28, 2020

Nature- because of the enormous variety of its shapes and structure has always been the inspiring muse of a great number of writers, painters and poets. What is perhaps less known is that this great variety of shape and structure has well surprised, intrigued and excited a large number of mathematicians who have always tried to find regularities in the great diversity of natural patterns in order to decipher their mysteries. To evaluate if the tuning mechanism can actually be considered as a common underlying process promoting pattern formation in physics, chemistry and biology, a methodological shift in the usual way of employing mathematics is strongly required, the different role played by chemistry and biology as particularly enlightening.

1. Patterns found in leaves-

The living world is filled with strips and moulted patterns of contrasting colours with sculptural equivalents of those realized as surface crest and troughs; with the patterns of organization and behaviour even among individual organisms. People have long been tempted to find some obscure 'intelligence' behind all these biological patterns. Evan way back in the early 20th century the Belgian symbolist Maurice Maeterlicnk, pondering the efficient organization of the bee and termite colonies.

Leaf pattern refers to the pattern or method through which leaves attach themselves to twigs and stems. Botanists normally differentiate between three main leaf patterns: alternate, opposite, and whorled. The arrangement of veins in a leaf is called the venation pattern; monocots have parallel venation, while dicots have reticulate venation. ... In an opposite leaf arrangement, two leaves connect at a node. In a whorled arrangement, three or more leaves connect at a node.

The venation pattern of a leaf is classified as reticulated, parallel, or dichotomous. In reticulated venation, the veins are arranged in a net-like pattern, in that they are all interconnected like the strands of a net. In parallel venation, the veins are all smaller in size and parallel or nearly parallel to one another, although a series of smaller veins connect the large veins. Parallel venation occurs in the leaves of nearly all monocotyledonous Angiosperms, whose embryos have one cotyledon, as in flowering plants such as lilies and grasses.

2. Spiral pattern-

The Nautilus is another meticulous craftsman, who designs its shell in a shape called a logarithmic or equiangular spiral (explained ahead). This precise curve develops naturally as the shell increases in size but does not change its shape, ever growing but never changing its proportions. The process of self-similar growth yields a logarithmic spiral. We find the same spiral in the horns of mountain sheep and in the path traced by a moth drawn towards light. For the mathematically inclined, such a curve can be succinctly described by the formula ''R = C*(Ang), where R is the radius of the curve, C is a constant and (Ang) is the angle through which the curve has revolved. It can further confirm by Fibonacci series.

The Fibonacci sequence exhibits a certain numerical pattern which originated as the answer to an exercise in the first ever high school algebra text. This pattern turned out to have an interest and importance far beyond what its creator imagined. It can be used to model or describe an amazing variety of phenomena, in mathematics and science, art and nature. The mathematical ideas the Fibonacci sequence leads to, such as the golden ratio, spirals and self- similar curves, have long been appreciated for their charm and beauty, but no one can really explain why they are echoed so clearly in the world of art and nature.

Even more fascinating is the surprising appearance of Fibonacci numbers, and their relative ratios, in arenas far removed from the logical structure of mathematics: in Nature and in Art, in classical theories of beauty and proportion.

Consider an elementary example of geometric growth - asexual reproduction, like that of the amoeba. Each organism splits into two after an interval of maturation time characteristic of the species. This interval varies randomly but within a certain range according to external conditions, like temperature, availability of nutrients and so on. We can imagine a simplified model where, under perfect conditions, all amoebae split after the same time period of growth. We get a doubling sequence. Notice the recursive formula:  

An =2An

3. Pattern found in Zebra's strips-

Think of the striking regularity of alternating dark and light stripes on a zebra's coat, or the reticulations on the surface of fruiting body of a morel (a vareity of mushroom) mushroom. Zooming in for a close-up of a slime mold, you can observe the branching network patterns that emerge as the mold grows. On a still smaller scale, magnified several hundred times, similar patterns emerge on the surface of a pollen grain.

The zebra's coat alternates in contrasting areas of light and dark pigmentation. In technical jargon, the pigmentation reflects patterns of activation and inhibition - apt terms because of the dynamic process that generates the pattern. Cells in the skin called melanocytes produce melanin pigments, which are passed into the growing hairs of the zebra. Whether or not a melanocyte produces its pigment appears to be determined by the presence or absence of certain chemical activators in the skin during early embryonic development. Hence the patterns of the zebra's coat reflect the early interaction of those chemicals as they diffused through the embryonic skin. With a new set of rules, a two-dimensional cellular automaton can readily stimulate the pattern of the coat and so shed light on the mechanism of pattern formation in the zebra. Return to the square grid and randomly place a black cell or a white cell on each square. The grid will look something like the leftmost frame in figure 3. Assume that each black cell represents a certain minimum level of pigment activator. Such a random array of activator or its absence is thought to be the starting point of the early development of coat patterns.

4. Pattern found in Honeycomb-

Some patterns are molded with a strict regularity. At least superficially, the origin of regular patterns often seems easy to explain. Thousands of times over, the cells of a honeycomb repeat their hexagonal symmetry. The honeybee is a skilled and tireless artisan with an innate ability to measure the width and to gauge the thickness of the honeycomb it builds. Although the workings of an insect's mind may baffle biologists, the regularity of the honeycomb attests to the honey bee's remarkable architectural abilities.

The axes of honeycomb cells are always quasihorizontal, and the nonangled rows of honeycomb cells are always horizontally (not vertically) aligned. Thus, each cell has two vertically oriented walls, with the upper and lower parts of the cells composed of two angled walls. The open end of a cell is typically referred to as the top of the cell, while the opposite end is called the bottom. The cells slope slightly upwards, between 9 and 14°, towards the open ends.

5. Pattern found in molecules-

Crystals are likewise constructed with mathematical regularity. A chemist could readily explain how positively and negatively charged sodium and chloride ions arrange themselves neatly in a crystal lattice, resulting in salt crystals with a perfect cubic structure. And water molecules, high in the clouds with temperatures far below freezing, neatly coalesce to form crystalline snowflakes in the form of six-sided stars or hexagonal needles.

In an ice crystal, the water molecules are arranged in layers of hexagonal rings. These layers are called the basal planes of the crystal, and the normal to the basal plane is called the c-axis or the optical axis of the crystal. Ice is water frozen into a solid state. Depending on the presence of impurities such as particles of soil or bubbles of air, it can appear transparent or a more or less opaque bluish-white colour.

6. Pattern found in Seashell covers- Seashells, so often decorated with bold patterns of stripes and dots. Biologists seldom gave much thought to how these mollusks create the beautiful designs that decorate their calcified homes. Perhaps they simply assumed that the patterns were precisely specified in the genetic blueprint contained in the mollusk's DNA.

A special case of biological pattern formation is the emergence of the pigment patterns on the shells of mollusks. These patterns are of great diversity and frequently of great beauty. The shells consist of calcified material. The animals can increase the size of their shells only by accretion of new material along a marginal zone, the growing edge of the shell. In most species, the pigment becomes incorporated during growth at the edge. In this case, the pattern formation proceeds in a strictly linear manner. The second dimension is a protocol of what happens as a function of time along the growing edge. The shell pattern is, so to say, a space-time plot. The shells provide a unique situation in that the complete history of a highly dynamic process is preserved. This provides the opportunity to decode this process.

7. Pattern found in Embryonic brain- The embryonic brain develops, competing influences from the right and left eye determine the connections that are made at the back of the brain, the visual cortex. Clusters of neutrons from one eye or the other dominate portions of the cortex in a distinct pattern. The patterns are thought to develop because the neutrons from each eye compete with one another for space. Initially, the neuronal projections coming from the left or right eye are slightly different, a difference that presumably arises at random. The rules of the competition have the same general form as the rules of activation and inhibition of zebra coat pigment. Projections of the neutrons from one eye stimulate and encourage additional projections to the area in front of the eye. At the same time, those projections inhibit the projections to that area from the other eye. This local competition for real estate in the brain results in a pattern of stripes reminiscent of those of zebra.

8. Pattern found on desert sand- Self-organizing patterns extends to the non-living world as well. They appear in the mineral deposits between layers of sedimentary rocks, in the path of a lightening bolt as it crashes to the ground, in the undulating ripples of windblown sand on a desert dune. When the forces of wind, gravity, and friction act on the sand dunes, the innumerable grains of sand ricochet and tumble. As one grain lands, it affects the position of the other grains, blocking the wind or occupying a site where another grain might have landed. Depending on the speed of the wind and the sizes and shapes of the grains of the sand, this dynamic process creates a regular pattern of stripes or ripples.

9. Pattern found on Butterfly's wing-

In non-biological physical systems, self-organized patterns are epiphenomena that have no adaptive significance. There is no driving force that pushes cloud formations, mud cracks, irregularities in painted surfaces, or spiral waves in certain chemical reactions into developing the striking patterns they exhibit. In biological systems, however, natural selection can act to favor certain patterns. The particular chemicals within the skins of the developing zebra diffuse and react in such a way as to consistently produce stripes. If the properties of the zebra skin, or the composition of the chemical activators, were even slightly different from what they are, a pattern would not develop.

10. Pattern found in Spider's net-

Spider crates its sticky orb following a genetically determined recipe for laying out the various radii and spirals of the web. A caddisfly larva builds an intricate hideaway from grains of sand or other debris carefully fastened together with silk. Another very common example of invoked organization is the honeycomb made by bees (figure 5). In those cases the building of structures does involve indeed involve a little architect that oversees and imposes order and pattern. There are no 'subunits' that interact with one another to generate a pattern; instead, each of the animals acts like a stonemason, measuring, fitting, and moving pieces into place.

Here you can have a good understanding about patterns in nature-