Wednesday, October 4, 2017

Tighter synthetic weaving joins and marking by bend type

The tightest synthetic weaving join occurs when a double-bump bend (follow upper black wire) accommodates a single-bump bend (follow lower black wire.) (The edges shown have not yet been locked by the overlaying of third strands.)
Making the tightest possible join at a synthetic weave's 'crossings' adds a slight complexity since complementary portions (as opposed to congruent portions) must be brought into alignment. On the other hand, these two complementary types of bends can be exploited to indicate 'open' or 'close', without any other sort of marking needed on the scaffold strand.

The basket will still contain edges of both even and odd lengths (as measured in helical half wavelengths.)

A scaffold strand for a synthetic weave can be described by a four letter code (u, n, d, p). This is an 'undip' word as described earlier in this blog, only now the 'photon' edges have shrunk to zero length. Two sequential undip letters can be 'alike' or 'unlike' in two comparisons: up/down and open/closed.

Edges bounded by letters that compare as alike/alike or unlike/unlike will be even in length.

Edges bounded by letters that compare as alike/unlike or unlike/alike will be odd in length.

More concisely, call letter pairs {u, p} and {d, n} opposites. Then an edge has even length if it is bounded by identical letters or by opposite letters. Otherwise, it has odd length.

Same join as above after overlaying third strands.

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