1. PATTERN. The repetitive or normal way in which something occurs or is done is
a pattern. In the universe, in human-made architecture, or in abstract theories, a
pattern is a periodicity. As such, in a repetitive fashion, the elements of a pattern
repeat.
EXAMPLE: Nature gives representations of many pattern forms, including fractally
dimensioned symmetries, trees and other structures, spirals, meanders, tides,
foams, tilings, cracks and stripes.
2. FIBBONACCI NUMBERS. A series called the Fibonacci sequence is generated by
Fibonacci numbers, commonly denoted Fn, so that each number is the sum of the
two preceding numbers, starting from 0 and 1. The numbers of Fibonacci are
closely connected to the golden ratio: the formula of Binet expresses the nth
Fibonacci number in terms of n and the golden ratio, and means that as n
increases, the ratio of two consecutive Fibonacci numbers tends to the golden
ratio.
EXAPMLE: The number of petals of flowers is given as a simple example in which
it is possible to locate the Fibonacci sequence in nature. Most of them include three
(like irises and lily), five (parnassia, rose hips) or eight (cosmea), 13 (some
daisies), 21 (chicory), 34, 55 or 89 (asteraceae). These numbers form part of the
famous series of Fibonacci mentioned in the preceding paragraph.
3. FIBONACCI SEQUENCE. The Fibonacci sequence is a series of numbers where
a number is the addition of the last two numbers, starting with 0, and 1. The
Fibonacci Sequence is a curious set of classical mathematics numbers that have
found applications in applied mathematics, nature, statistics, computer science,
and Agile Development.
EXAMPLE: It was Kepler who noticed that the leaves are aligned in a pattern that
contains two Fibonacci numbers on certain kinds of trees. Starting from each leaf,
there is often a leaf associated with the first one after one, two, three or five turns
of the spiral and, depending on the species, this would be the second, third, fifth,
eighth or thirteenth leaf.
4. FIBONACCI CIRCLE. In geometry, a golden circle or spiral is a logarithmic spiral
whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or
further from its origin) by a factor of φ for every quarter turn it makes.
EXAMPLES. Flower petals Seed head, pinecones, tree branches, shells, spiral
galaxies, hurricanes, faces, animal bodies and more.
5. RADIAL PATTERNS. Radial refers to the pattern you get from the middle of a circle
to a variety of points along the perimeter as straight lines are drawn.
EXAMPLES: See stuff from a central point branching out, and you've got a radial
pattern. It's everywhere: clock faces, wheel-round spokes, daisy-like trees, and so
on. Radial architecture has also attracted artists and creators because it provides
a simple focal point and simplifies organization.
6. BILATERAL PATTERNS. Bilateral symmetry applies to animals with body forms
that, along a midline called the sagittal plane, are mirror images. However, the
internal organs aren't always symmetrically arranged.
EXAMPLES: Bilateral symmetry is demonstrated by the vast majority of species;
this is also known as plane symmetry, a feature that extends to 99% of all animals,
in the majority of phyla: Chordata, Annelida, Arthropoda ETC.
7. FRACTALS. A fractal is a pattern which is never-ending. Fractals are infinitely
complex patterns that over various dimensions are self-similar. They are created
in an ongoing feedback loop by repeated a simple process over and over again.
EXAMPLES: Clouds, snowflakes, mountains, river networks, cauliflower or
broccoli, and blood vessel systems are examples. In fact, trees and ferns are
fractal and can be modelled using a recursive algorithm on a computer.
8. SPIRALS. Spiral, a plane curve that winds around a point in general, thus traveling
ever away from the point. In nature, the curves are observed, and human beings
have used them in machines and ornaments, especially architectural ones, such
as the whorl in an Ionian capital.
EXAMPLES: Spirals are snail shells, flower petals, pine cones, snakes, hurricanes,
DNA, curly hair, and even universes.