Woven Shibori creates a tie-dye effect by weaving in a strong pattern thread that can be used to gather and tie up the fabric (after it is removed from the loom) and create a resist when the fabric is dyed.
These scarves were all woven with white wool yarns, polyester kite twine for pattern threads, and overdyed with natural Indigo. Here you can see the white pattern threads (the polyester did not take up the dye). After they were dyed and untied, the texture created by pulling the threads tight still remained. This three dimensionality will always be there a little bit, but it can be lessened dramatically by gently steam pressing (wool setting used here).
The first two are a style called Taiten Shibori, in which the pattern threads are woven right in as if they were just part of the weave. In the top sample, the pattern thread is in the warp, which means the weaving is all just single shuttle plain weave!
The bottom sample has the pattern thread in the weft (so it's a two shuttle weave - one fabric yarn and one pattern yarn). My example used a kind of a random Fibonacci sequence in placing the shots of pattern thread.
Notice how the pattern ties are only a suggestion to the dye, and the dye sometimes goes in unexpected and exciting directions!
When the Taiten pattern threads are removed (after the fabric has been tied up and dyed), there will be a lace-like gap in the fabric.