PatternPattern is an underlying structure that organizes surfaces or structures in a consistent, regular or predictable manner.

Pattern can be described as a repeating unit of shape or form (on the outside), but it can also be thought of as the "skeleton" that organizes the parts of a composition (inherent nature).

Elements of a pattern repeat in a predictable manner.

PatternIn art and architecture, decorations or visual themes may be combined and repeated to form patterns designed to have a chosen effects on the viewer.

PatternAny of the five senses may directly experience patterns.

But there exist abstract patterns in science, mathematics, or language which are observable only by analysis.

PatternVisual patterns in nature are often chaotic, never exactly repeating.

Natural patterns include spirals, meanders, waves, foams, tiling, cracks, stripes etc. and those created by symmetries of rotation and reflection.

All such patterns have an underlying mathematical structure; mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern.

Pattern > In NatureBranching, fractals

Branching is an evident form of patterning in the plant world. It can also be seen in geological formations such as river deltas and certain crystalline formations.

Fractals are infinitely self-similar, iterated mathematical constructs. Infinite iteration is not possible in nature so all 'fractal' patterns are only approximate.

Fractals in broccoli

Pattern > In NatureExamples - The leaves of ferns and umbellifers (Apiaceae) are self-similar (pinnate) to 2, 3 or 4 levels. Fern-like growth patterns occur in plants and in animals, and in non-living things, notably electrical discharges.

Pattern > In NatureLindenmayer system (L-system) fractals can model different patterns of tree growth by varying a small number of parametersincluding branching angle, distance between nodes or branch points, and number of branches per branch point.

An L-system is a parallel re-writing system, most famously used to model the growth processes of plant development, and the morphology of a variety of organisms.

An L-system consists of symbols that can be used to make strings, a collection of production rules which expand each symbol into some larger string of symbols, i.e.

An initial "axiom" string from which to begin construction

A mechanism for translating the generated strings into geometric structures.

Pattern > In Nature

If we count the length of each string, we obtain Fibonacci sequence of numbers (skipping the first 1, due to our choice of axiom):

1 2 3 5 8 13 21 34 55 89 ...

Pattern > In Nature

Pattern > In NatureFractal-like patterns occur widely in nature, in phenomena as diverse as clouds, river networks, geologic fault lines, mountains, coastlines, animal coloration, snow flakes, crystals, blood vessel branching, and ocean waves.

Pattern > In NatureApplications