Wallpaper Patterns

Wallpaper Patterns Biography
A pattern, from the French patron, is a type of theme of recurring events or objects, sometimes referred to as elements of a set of objects.
These elements repeat in a predictable manner. It can be a template or model which can be used to generate things or parts of a thing, especially if the things that are created have enough in common for the underlying pattern to be inferred, in which case the things are said to exhibit the unique pattern.
The most basic patterns, called Tessellations, are based on repetition and periodicity. A single template, tile, or cell, is combined with duplicates without change or modification. For example, simple harmonic oscillators produce repeated patterns of movement.
Other patterns, such as Penrose tiling and Pongal or Kolam patterns from India, use symmetry which is a form of finite repetition, instead of translation which can repeat to infinity. Fractal patterns also use magnification or scaling giving an effect known as self-similarity or scale invariance. Some plants, like Ferns, even generate a pattern using an affine transformation which combines translation, scaling, rotation and reflection.
Pattern matching is the act of checking for the presence of the constituents of a pattern, whereas the detecting for underlying patterns is referred to as pattern recognition. The question of how a pattern emerges is accomplished through the work of the scientific field of pattern formation.
Pattern recognition is more complex when templates are used to generate variants. For example, in English, sentences often follow the "N-VP" (noun - verb phrase) pattern, but some knowledge of the English language is required to detect the pattern. Computer science, ethology, and psychology are fields which study patterns.
"A pattern has an integrity independent of the medium by virtue of which you have received the information that it exists. Each of the chemical elements is a pattern integrity. Each individual is a pattern integrity. The pattern integrity of the human individual is evolutionary and not static."

Wallpaper Patterns

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P4g Wallpaper Pattern

Wallpaper Patterns

Wallpaper Patterns

Wallpaper Patterns Biography:


A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. There are 17 possible distinct groups.
Wallpaper groups are two-dimensional symmetry groups, intermediate in complexity between the simpler frieze groups and the three-dimensional crystallographic groups (also called space groups).
A symmetry of a pattern is, loosely speaking, a way of transforming the pattern so that the pattern looks exactly the same after the transformation. For example, translational symmetry is present when the pattern can be translated (shifted) some finite distance and appear unchanged. Think of shifting a set of vertical stripes horizontally by one stripe. The pattern is unchanged. Strictly speaking, a true symmetry only exists in patterns that repeat exactly and continue indefinitely. A set of only, say, five stripes does not have translational symmetry — when shifted, the stripe on one end "disappears" and a new stripe is "added" at the other end. In practice, however, classification is applied to finite patterns, and small imperfections may be ignored.
Sometimes two categorizations are meaningful, one based on shapes alone and one also including colors. When colors are ignored there may be more symmetry. In black and white there are also 17 wallpaper groups; e.g., a colored tiling is equivalent with one in black and white with the colors coded radially in a circularly symmetric "bar code" in the centre of mass of each tile.
The types of transformations that are relevant here are called Euclidean plane isometries. For example:
If we shift example B one unit to the right, so that each square covers the square that was originally adjacent to it, then the resulting pattern is exactly the same as the pattern we started with. This type of symmetry is called a translation. Examples A and C are similar, except that the smallest possible shifts are in diagonal directions.
If we turn example B clockwise by 90°, around the centre of one of the squares, again we obtain exactly the same pattern. This is called a rotation. Examples A and C also have 90° rotations, although it requires a little more ingenuity to find the correct centre of rotation for C.
We can also flip example B across a horizontal axis that runs across the middle of the image. This is called a reflection. Example B also has reflections across a vertical axis, and across two diagonal axes. The same can be said for A.
However, example C is different. It only has reflections in horizontal and vertical directions, not across diagonal axes. If we flip across a diagonal line, we do not get the same pattern back; what we do get is the original pattern shifted across by a certain distance. This is part of the reason that the wallpaper group of A and B is different from the wallpaper group of C.

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Tutorial : How To Make Custom Patterns / Wallpapers Designs