From Ptil Tekhelet:
This method defines a chulyah as a group of three twists. It has 13 chulyot, and alternates white and Tekhelet between them, starting and ending with a chulyah of white. Those chulyot are distributed between five (double) knots with three chulyot between the top four knots and four chulyot between the fourth and last knot.
Sefer Hachinuch Mitzvah 386
How are the fringes made? (Mishneh Torah, Laws of Fringes 1:6) Four strings are passed through the corner of the garment, such that there are now eight ends hanging from the corner. This is not done precisely at the corner, but [a half-]thumb’s distance from the edge, as Rabbi Yaakov said that Rabbi Yochanan said in the Gemara (Menachot 42a), “It must be one large joint away.” One of the strings should be longer so that it can be used for winding [around] the others. Five double knots are tied (Tosafot on Menachot 39a, s.v. lo); and between each knot, he makes three rings (windings), and between the final knot, four rings, so that there are a total of thirteen rings. The strings are made long so that it be enough for two [thirds] of the length to be branching; meaning to say without the knots and rings, besides the knots and rings. This is the main [approach to the] ideal fulfillment of the commandment. But ex post facto, even one ring suffices, and so [too,] ex post fact, even if the strings of the fringes shorten, even if there is only enough to make a basic bow, it is fit (Menachot 38b). But if even one string is completely torn, it is disqualified.
‘ספר החינוך מצווה שפו
כיצד עושין הציצית, מעבירין ארבעה חוטין בכנף הבגד, שהן שמונה ראשי חוטין כשהן תלויין בכנף, ואין תולה אותן סמוך ממש לשפת הבגד ולא רחוק, אלא סמוך כשיעור גודל מראשו עד הפרק ראשון, כדאמר רבי יעקב אמר רבי יוחנן בגמרא [שם מ”ב ע”א], וצריך להרחיק כמלוא קשר גודל. ועושה אחד מהן גדול כדי שיכרוך בו האחרים, וקושרן בחמשה מקומות קשר כפול, ובין קשר וקשר עושה שלש חוליות ובאמצעות הקשר האחרון עושה ארבע חוליות, שנמצאו בין כולן י”ג חוליות.
Notes from Ptil Tekhelet:
- A “Single Knot” is made by taking the four strands from one side of the garment and the opposing four strands from the other side of the garment and tying a simple knot.
- A white “Chulya” is made by taking one white strand from the total of eight strands and wrapping it around the remaining seven strands three times. This “wrapping” strand is designated “Shamash” and is used for all subsequent white chulyot (though it is not halachically imperative that the same Shamash be used).
- A blue “Chulya” is made the same as a white one, but just using a blue strand.