# Bridges 2010 Regular Paper

Brunnian Weavings

Douglas G. Burkholder

(Proceedings pages 263–270)

## Abstract

In this paper, we weave *Borromean Rings* to create interesting objects
with large crossing number while retaining the characteristic
property of the Borromean Rings. Borromean Rings are interesting
because they consist of three rings linked together and yet when
any single ring is removed the other two rings become unlinked. The
first weaving applies an iterative self-similar technique to produce
an artistically interesting weaving of three rings into a fractal
pattern. The second weaving uses an iterative *Peano Curve* technique
to produce a tight weaving over the surface of a sphere. The third
weaving produces a tight weaving of four rings over the surface of
a torus. All three weavings can produce links with an arbitrarily
large crossing number. The first two procedures produce Brunnian
Links which are links that retain the characteristic property of
the Borromean Rings. The third produces a link that retains some
of the characteristics Borromean Rings when perceived from the
surface of a torus.

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