Patterns in Nature PDF

Math in Nature Fibonnaci Sequence  Fibonnaci Sequence The Fibonacci sequence was discovered by the Italian mathematician Leonardo Pisano while calculating the growth of rabbit populations. He came up with a unique and important sequence that literally defined everything about natur...

Math in Nature Fibonnaci Sequence  Fibonnaci Sequence The Fibonacci sequence was discovered by the Italian mathematician Leonardo Pisano while calculating the growth of rabbit populations. He came up with a unique and important sequence that literally defined everything about nature and its processes. The sequence followed one simple rule: 𝐹𝑛 = 𝐹𝑛−1 + 𝐹𝑛−2 where 𝐹𝑛 is the nth term of the series.  Fibonnaci Sequence The remarkable thing about this series is that it can generate all the numbers that govern the laws of nature. Essentially, there exists no such group in nature which has a number of elements other than the ones generated by the Fibonacci sequence. For example, the number of seeds in sunflowers follows the same spiral pattern as generated by the Fibonacci sequence for different values of n. Many other plants follow the Fibonacci sequence during their growth. Fibonnaci Sequence Symmetry Butterflies are perfect examples of reflective symmetry found in nature.  Symmetry A symmetric structure is one which can be divided into two proportionate, equal halves. There are two main types of symmetry: reflective symmetry and rotational symmetry.  Symmetry Reflective symmetry occurs when one half of the object reflects the other half, i.e. it is a mirror image of the other half. A butterfly is the best natural example of this type of symmetry.  Symmetry Rotational symmetry occurs when an object appears the same after partially rotating on its axis. In mathematics, a circle is a geometric shape that is a common example of rotational symmetry. Many species of flowers are examples of rotational symmetry. Many microorganisms in the Protozoa kingdom (single-celled eukaryotes) also possess a wide range of symmetry. Symmetry  Fractals Ideal structure of a snowflake  Fractals Fractals are subsets of Euclidean figures where each part has the same statistical character as the main figure. In layman's terms, they can be explained as patterns that exist inside a solid geometrical figure or are a part of it and have patterns that re-occur at smaller scales.  Fractals Tree branches are another example of fractals, as they replicate themselves into similar structures. The leaves on these branches contain veins (the thin, small lines on the leaf) that originate from the midrib and form a network of veins replicating the parent vein, resulting in numerous such structures – yet another example of fractals. Rivers form deltas which are self-branched patterns that also resemble fractals. Fractals  Tessellations Tessellations are patterns formed by repeating tiles all over a flat surface. Tessellations