Dmitri Kozlov
Knots have been the subject of traditional art since ancient time.
Woven patterns and ornaments, stone and wood carving of knots were
popular throughout the world.
My approach is based on the idea that cyclic periodic knots made of
resilient filaments like steel wire or fiberglass behave as kinetic
structures of topological surfaces. Knots tied with such materials
must have a large number of physically contacting crossings that form
vertices of the surfaces. The crossings slide along the filaments
which twist around their central axes. The waves on the filaments move
and change their lengths to adapt to desired spatial disposition of
the contact crossings. The complicated knots of this type I designated
as NODUS-structures.
Torus and pretzel knots are the knots that can be tied on the
surfaces of tori and pretzels. The flower-like shapes of torus
knots and similar to them alternating Turk's Head knots are very
popular in different fields of math-art both traditional and
modern.
At the same time pretzel knots and corresponding to them
alternative knots are chosen by math artists quite rarely. Here I
present the linkage of two pretzel knots that form left and right
windings on a pretzel surface with two holes as an example of my
NODUS-structures.
I dedicate this my work to the recent discovery in physics, namely
detecting of gravitational waves. My woven pretzel surface may
serve as a mechanical model of spreading of g-waves through the
space-time tissue.