Patterns
<p >A <b>pattern</b>, from the <a href="http://en.wikipedia.org/wiki/French_language" title="French language" >French</a> <i>patron</i>, is a type of theme of recurring events or objects, sometimes referred to as elements of a <a href="http://en.wikipedia.org/wiki/Set_(mathematics)" title="Set (mathematics)" >set</a> of objects.</p>
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The elements of a pattern repeat in a predictable manner. Patterns can be based on a template or model which generates pattern elements, especially if the elements have enough in common for the underlying pattern to be inferred, in which case the things are said to <i>exhibit</i> the unique pattern.</p>
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The most basic patterns, called <a href="http://en.wikipedia.org/wiki/Tessellation" title="Tessellation" >Tessellations</a>, are based on <a href="http://en.wiktionary.org/wiki/repetition" class="extiw" title="wikt:repetition" >repetition</a> and <a href="http://en.wikipedia.org/wiki/Periodic_function" title="Periodic function" >periodicity</a>. In tessellation, a single template, <a href="http://en.wikipedia.org/wiki/Tile" title="Tile" >tile</a>, or cell is repeated without change or modification, usually in two dimensions to form a flat patterned surface.</p>
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Other patterns, such as <a href="http://en.wikipedia.org/wiki/Penrose_tiling" title="Penrose tiling" >Penrose tiling</a> and <a href="http://en.wikipedia.org/wiki/Pongal" title="Pongal" class="mw-redirect" >Pongal</a> or <a href="http://en.wikipedia.org/wiki/Kolam" title="Kolam" >Kolam</a> patterns from India, use <a href="http://en.wikipedia.org/wiki/Symmetry" title="Symmetry" >symmetry</a> which is a form of finite repetition, instead of <a href="http://en.wikipedia.org/wiki/Translation(geometry)" title="Translation (geometry)" >translation</a> which can repeat to infinity. <a href="http://en.wikipedia.org/wiki/Fractal" title="Fractal" >Fractal</a> patterns also use <a href="http://en.wikipedia.org/wiki/Magnification" title="Magnification" >magnification</a> or <a href="http://en.wikipedia.org/wiki/Scaling(geometry)" title="Scaling (geometry)" >scaling</a> giving an effect known as <a href="http://en.wikipedia.org/wiki/Self-similarity" title="Self-similarity" >self-similarity</a> or <a href="http://en.wikipedia.org/wiki/Scale_invariance" title="Scale invariance" >scale invariance</a>. Some plants, like <a href="http://en.wikipedia.org/wiki/Fern" title="Fern" >Ferns</a>, generate a pattern using an <a href="http://en.wikipedia.org/wiki/Affine_transformation" title="Affine transformation" >affine transformation</a> which combines<a href="http://en.wikipedia.org/wiki/Translation(geometry)" title="Translation (geometry)" >translation</a>, scaling, <a href="http://en.wikipedia.org/wiki/Rotation" title="Rotation" >rotation</a> and <a href="http://en.wikipedia.org/wiki/Reflection(physics)" title="Reflection (physics)" >reflection</a>.</p>
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A different kind of pattern generator is a <a href="http://en.wikipedia.org/wiki/Simple_harmonic_oscillator" title="Simple harmonic oscillator" class="mw-redirect" >simple harmonic oscillator</a>, which produces repeated movements in time.
<a href="http://en.wikipedia.org/wiki/Pattern_matching" title="Pattern matching" >Pattern matching</a> is the act of checking for the presence of the constituents of a pattern, whereas the detecting for underlying patterns is referred to as <a href="http://en.wikipedia.org/wiki/Pattern_recognition" title="Pattern recognition" >pattern recognition</a>. The question of how a pattern emerges is accomplished through the work of the scientific field of <a href="http://en.wikipedia.org/wiki/Pattern_formation" title="Pattern formation" >pattern formation</a>.</p>
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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 <a href="http://en.wikipedia.org/wiki/English_language" title="English language" >English language</a> is required to detect the pattern. <a href="http://en.wikipedia.org/wiki/Computer_science" title="Computer science" >Computer science</a>, <a href="http://en.wikipedia.org/wiki/Ethology" title="Ethology" >ethology</a>, and<a href="http://en.wikipedia.org/wiki/Psychology" title="Psychology" >psychology</a> are fields which study patterns.</p>