Pattern (structure)

Tiles that have a pattern and are used for decoration.

As a pattern is called visible surface or drawings - structures . In a broader sense, it can also be spatially or temporally sequential structures in signals .

Basics

Optical or acoustic signals without a recognizable pattern are called noise . All things significant for living beings have patterns whose perceptible properties are characterized by a minimum of repetitions ( periodicity ) and symmetries , both of which can be exact or approximate, i.e. stochastic .

Since patterns are inherent to repeated structures, they are easy to recognize. Brains are through the evolution of the pattern recognition adjusted. However, for natural organisms only patterns with a complexity between perfect symmetry and absolutely structureless noise are of essential importance: What is constantly repeated and does not immediately hurt or impair me, e.g. B. the ticking of a clock will be just as unimportant as the continued rushing of a stream . With medium entropy, patterns have the highest useful information for every living being.

The other pattern-oriented research direction is that of pattern formation (Engl. Pattern formation ). In particular, the branches of science of synergetics and chaos theory were able to prove that simple, recursive training rules are often sufficient to generate highly complex patterns, or how spontaneous (approximate) order can arise from apparent " chaos ".

Pattern formation and pattern recognition are complementary to one another, but are also mutually dependent, since on the one hand pattern recognition is generally an active process that not only analyzes but also creates regularities in signals (think of the perception of geometric "patterns" on noisy screens). In particular, human perception as an active mental achievement can be adjusted in such a way that one believes to recognize patterns even though none are present. This phenomenon is called pareidolia . On the other hand, proving the objective existence of some “patterns” is quite difficult without a subjective observer (think of the musical sensation that can give an experienced ear aesthetic enjoyment where the untrained listener only perceives “chaos”).

Examples of patterns

Geometry, math

• Fractals
• Tiling
• Pascal's triangle
• Figured number
  • Triangle Number , Tetrahedral Number , Centered Hexagonal Number

Computer science

• Generation pattern
• Structural pattern
• Behavior patterns (software)

nature

• Crystal lattice
• Chemical structure
• sand dunes
• Ripple marks on the beach
• Water waves
• Cloud formations
• Plant growth forms (especially the higher plants )
  • especially phyllotaxis
• Belousov-Zhabotinsky reaction (spatio-temporal)

art

• Knitting pattern , textile pattern
• Ornament (flat or three-dimensional)
• Music (temporal)
• kaleidoscope

literature

• Ernst Haeckel : Art Forms of Nature .
• Werner Ebeling, Jan Freund, Frank Schweitzer: Complex structures, entropy and information . Teubner, Stuttgart 1998, ISBN 3-8154-3032-1 .
• Dennis Pong: Experimental Approaches to Structure Formation . CD-ROM. Munster 2002; muenster.de (PDF)
• John H. Conway , Richard Guy: The Book of Numbers . 2nd ed. 1995, ISBN 0-387-97993-X

Web links

Commons : Patterns  - collection of images, videos and audio files

• didaktik.phy.uni-bayreuth.de
• am.uni-duesseldorf.de