What is a Pattern

The use of the word ‘pattern’ is ubiquitous in written and spoken discourse. Furthermore, most authors assume the intended reader knows what a pattern is, and hence do not define the term. We present an exploration of the variety of definitions of ‘pattern’ used in different domains of mathematics, the sciences, the arts, and the humanities, with the goal of searching for an overarching definition of pattern or at least a metapattern in the sea of definitions. Due to space limitations this paper is necessarily an incomplete survey of how the term pattern is used in different fields, but it provides a sample from which the interested reader may explore the topic further, and it points a direction in which to search for a practical computational approach to measure the amount of pattern contained in an entity.

[1]  George Nagy,et al.  The dimensions of shape and form , 1992 .

[2]  A. Kolmogorov.  Three approaches to the quantitative definition of information , 1968 .

[3]  J. Conway,et al.  The Symmetries of Things , 2008 .

[4]  U. Grenander.  Elements of Pattern Theory , 1996 .

[5]  K. Devlin.  Mathematics: The Science of Patterns , 1994 .

[6]  Michael I. Miller,et al.  Pattern Theory: From Representation to Inference , 2007 .

[7]  Brian Hanson,et al.  THE NATURE OF ORDER: AN ESSAY ON THE ART OF BUILDING AND THE NATURE OF THE UNIVERSE , 2005 .

[8]  Marina Schroder,et al.  Point And Line To Plane , 2016 .

[9]  Simon Bell,et al.  Landscape: Pattern, Perception and Process , 1999 .

[10]  Godfrey H. Hardy,et al.  A mathematician's apology , 1941 .

[11]  I Winckelgren.  How the brain 'sees' borders where there are none. , 1992, Science.

[12]  F. Papentin.  On order and complexity. I. General considerations , 1980 .

[13]  Godfried T. Toussaint,et al.  The Geometry of Musical Rhythm , 2013, JCDCG.

[14]  Frank Papentin,et al.  Binary sequences III. Complexity versus homogeneity and symmetry , 1983, Inf. Sci..

[15]  T. Volk.  Metapatterns across space, time, and mind , 1995 .

[16]  L. Steen.  The Science of Patterns , 1988, Science.

[17]  W. R. Garner.  Good patterns have few alternatives. , 1970, American scientist.

[18]  Liu Xun.  New Practical Chinese Reader:a Textbook for the New Millennium , 2003 .

[19]  Neil J. A. Sloane,et al.  The encyclopedia of integer sequences , 1995 .

[20]  Richard M. Proctor.  The principles of pattern for craftsmen and designers , 1969 .

[21]  J. Storer,et al.  On binary sequences , 1961 .

[22]  Gregory J. Chaitin,et al.  On the Simplicity and Speed of Programs for Computing Infinite Sets of Natural Numbers , 1969, J. ACM.

[23]  Tasneem Hameed,et al.  Change. , 2018, The Journal of the Oklahoma State Medical Association.

[24]  Michael Krüger.  Binary sequences II - Homogeneity and symmetry , 1983, Inf. Sci..

[25]  R. Gregory.  The intelligent eye , 1970 .

[26]  S. Kimmel.  Architecture , 2013, Arsham-isms.

[27]  Yang Liu,et al.  A Tessellation-Transformation Method for Categorizing and Generating Geometric Textile Design Patterns , 2008 .

[28]  Nikos A. Salingaros,et al.  Architecture, Patterns, and Mathematics , 1999 .

[29]  Hermann Haken,et al.  What are Patterns , 1991 .

[30]  Terry Knight,et al.  Infinite Patterns and their Symmetries , 2017 .

[31]  Godfried T. Toussaint,et al.  The use of context in pattern recognition , 1978, Pattern Recognit..

[32]  A. Mackay.  On complexity , 2001 .

[33]  Jeffrey W. Bloom,et al.  Toward a science of metapatterns: building upon Bateson's foundation , 2007, Kybernetes.

[34]  Keith Hagan.  The Complete Pattern Library , 2005 .

[35]  R. Feynman,et al.  The Pleasure of Finding Things Out: The Best Short Works of Richard Feynman , 1999 .

[36]  W. Marsden.  I and J , 2012 .

[37]  B. Ripley,et al.  Pattern Recognition , 1968, Nature.

[38]  G. Toussaint,et al.  The marble frieze patterns of the cathedral of Siena: geometric structure, multi-stable perception and types of repetition , 2011 .

[39]  Norbert Wiener,et al.  The human use of human beings - cybernetics and society , 1988 .

[40]  Ari Sihvola,et al.  Ubi Materia, Ibi Geometria , 2000 .

[41]  John Maddox.  Complicated measures of complexity , 1990, Nature.

[42]  Nikos A. Salingaros,et al.  A Pattern Measure , 2000, 1108.5508.

[43]  Razefsha Mohsen,et al.  MIND AND LANGUAGE , 2010 .

[44]  Petra Koenig.  Decorative Patterns Of The Ancient World , 2016 .

[45]  Wassily Kandinsky,et al.  Point and Line to Plane , 1979 .

[46]  D. Stephens.  Change, regularity, and value in the evolution of animal learning , 1991 .

[47]  W. Uttal.  The perception of dotted forms , 1987 .

[48]  Florian Cajori,et al.  A history of mathematical notations , 1928 .

[49]  D. Wade.  Symmetry : the ordering principle , 2006 .

[50]  J. Gibson.  What is a form? , 1951, Psychological review.

[51]  G. Toussaint,et al.  Subsymmetries Predict Auditory and Visual Pattern Complexity , 2013, Perception.