Weaving is the interlacing of vertical (warp) and horizontal (weft) threads.
A loom holds warp threads in tension so that a weaver can lift and lower them in different combinations.
The temporary space created between raised and lowered warp threads is called a shed. You can just - whoosh - shuttle your weft thread through that shed, tighten it up against all your previously woven rows, and move along.
Most mechanical looms have four or eight or some other number of Harnesses (also called shafts) that can lift and lower groups of warp threads. Imagine we have two harnesses, and we alternate threading between them. One shaft lifts all the even numbered threads, and the other lifts the odds. As we add more harnesses, the possible shed combinations we have to choose from expands very quickly.
A weaving draft looks like this. The three matrices are called the Threading (top bar), the Tie-up (upper right corner), and the Treadling (right side column). The bottom left part of the image is called the Drawdown, and that’s a kind of preview of what your weaving will look like.
The threading matrix describes which warp threads should be threaded through each harness.
Each thread must pass through just one heddle on one harness, so each column of the tie-up needs to have a 1 in exactly one row, and all the other rows of that column are zeroes.
Floor looms have pedals that allow the weaver to lift and lower various combinations of harnesses (groups of warp threads.)
The tie-up matrix describes which harnesses should be lifted by each pedal.
It has a row for every harness and a column for every pedal.
Each pedal is tied to multiple harnesses, and multiple pedals can lift the same harness.
The treadling matrix describes the route each weft thread will take as it passes over and under warp threads. Put differently,