Log24

Monday, December 10, 2012

Review of Leonardo Article

Filed under: General,Geometry — Tags: — m759 @ 12:00 pm

Review of an often-cited Leonardo  article that is
now available for purchase online

The Tiling Patterns of Sebastien Truchet 
and the Topology of Structural Hierarchy

Authors: Cyril Stanley Smith and Pauline Boucher

Source: Leonardo , Vol. 20, No. 4,
20th Anniversary Special Issue:
Art of the Future: The Future of Art (1987),
pp. 373-385

Published by: The MIT Press

Stable URL: http://www.jstor.org/stable/1578535 .

Smith and Boucher give a well-illustrated account of
the early history of Truchet tiles, but their further remarks
on the mathematics underlying patterns made with
these tiles (see the diamond theorem* of 1976) are
worthless.

For instance

Excerpt from pages 383-384—

"A detailed analysis of Truchet's
patterns touches upon the most fundamental
questions of the relation between
mathematical formalism and the structure
of the material world. Separations
between regions differing in density
require that nothing  be as important as
something  and that large and small cells of
both must coexist. The aggregation of
unitary choice of directional distinction
at interfaces lies at the root of all being
and becoming."

* This result is about Truchet-tile patterns, but the
    underlying mathematics was first discovered by
    investigating superimposed patterns of half-circles .
    See Half-Circle Patterns at finitegeometry.org.

No Comments

No comments yet.

RSS feed for comments on this post.

Sorry, the comment form is closed at this time.

Powered by WordPress