Browse Prior Art Database

Truchet-tile Characterization of Randomness

IP.com Disclosure Number: IPCOM000099407D
Original Publication Date: 1990-Jan-01
Included in the Prior Art Database: 2005-Mar-14
Document File: 3 page(s) / 117K

Publishing Venue

IBM

Related People

Pickover, C: AUTHOR

Abstract

Disclosed is a simple graphics technique which uses tiles to detect deviations from randomness in a data set. In particular, Truchet-like tiles are used for representing data.

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Truchet-tile Characterization of Randomness

       Disclosed is a simple graphics technique which uses tiles
to detect deviations from randomness in a data set.  In particular,
Truchet-like tiles are used for representing data.

      Note that the graphical detection and characterization of
subtle patterns within random data is an area of active interest in
science.  Since the Truchet approach is sensitive to certain small
deviations from randomness, it may have value in helping researchers
find patterns in complicated data.

      Interesting tiling patterns can be created using an orientable
square tile with curved lines that join to produce continuous
closures regardless of how the tiles are oriented.  A generating tile
can be represented as: To produce the figure, simply orient the
generating square randomly and place it within the corner of a large
square lattice.  Successive adjacent tiles are added to the lattice
for a particular row until it is filled, and a new row is started.
Continue this process until the lattice is filled. This is easily
achieved with a computer program using binary values {Bi, i =
1,2,3...,N}, with random values of 0 and 1 for Bi .  Simply map Bi to
two different orientations of the tiles.  For random orientations,
the circle fraction is approximately 0.054 (number of closed circles
in the pattern divided by the number of tiles).  The dumbbell
fraction is approximately 0.0125 (number of closed bilobed shapes
divided by the number of tiles).  Note that the eye perceives no
particular trends in the design.  This kind of pattern is reminiscent
of the tiles of Sebastien Truchet. Truchet's paper, written in 1704,
shows that numerous patterns can be generated by the assembly of a
single half-colored tiles in various orientations.

      The tiles in the figure can be used to represent different
kinds of noise distributions or...