The left scarf was done with blues and pinks to make the purples. The middle was done with browns, yellows, and oranges. The right scarf was done with pastels including some greens and oranges.I have tried various brands of permanent ink. Sharpies are the best by far, and they come in about a million colors. Blue and yellow are the best for saturation. I did try the bottled alcohol ink, and it was too saturated with alcohol already to do anything much. It was too expensive, also, for what I wanted to do.
You literally color (mark) the area to begin with the different colors you want to use. Mark heavy and mark so that individual marks don't necessarily show. Then saturate the colored area with alcohol either using a spray, an eye dropper, a dropper bottle, or a syringe. They make different patterns. The colors will blend. A syringe at the end will make the tie-dyed look.
In some cases where the Sharpie marks are still appearing, rub with your fingers, and just experiment. If you use enough alcohol, the color will go away, so then you can start again! The brightness you see when the fabric is wet will fade somewhat when dried.
This is a lot of fun and very creative.
I have used polyester and nylon tricot, and I have seen it done on silk. I want to try cotton and velvet, but right now I am finishing the galley proofs on my book, so it will be a couple of days.
Oh, be sure to let it dry between each coat or painting. Markers won't paint anyway when the fabric is wet with alcohol.
It takes about a day to do a scarf, working on and off and letting it dry.
Good luck and have fun!