From Ptil Tekhelet:
The Rambam understands the idea of Ptil as the string which winds around the others. Therefore, he requires all the twists to be of Tekhelet, except for the very first and very last. He defines a chulyah as a group of three twists. In this method, the chulyah is kept together by wrapping the string inside the chulyah. Though the Rambam doesn’t explicitly say so, generally a double knot is tied at the base where the strings touch the begged.
Note: Rambam 7 is exactly the same, but with 7 chulyot instead of 13.
Hilchot Tzitzit, Ch 1
7) One of the white threads is taken up and wound once about the other threads close to the garment. It is then dropped. The blue thread is then taken and wound twice about the other threads close to the winding with the white thread. The threads are then tied. These three windings are called a section. A small space is left; a second section is made, the windings being done with the blue thread only. A small space is left; a third section is made; and so till the last division where the blue thread is wound round the other threads twice and the third winding is done with a white thread, because, as the winding began with a white thread, it should also end with a white thread, on the principle that things sacred may be elevated to a higher degree but may not be degraded to a lower degree. The reason why the winding begins with a white thread is that the corner of the garment shall have adjacent to it threads of the same kind of material. This is the method followed with the four corners.
8) How many divisions are made in the fringes at each corner? Not less than seven and not more than thirteen. This is the choicest mode of carrying out the precept. But if one wound the threads, to form one division only, the fringe is regarded as correctly made. And if one wound the blue thread over the greater portion of the fringes, it is correctly made. The beauty of the blue thread is manifested if all the sections that are wound take up the first third of the pendent fringes, while the remaining two thirds are loose. The threads in this part need to be separated, so that they shall be like the fringes of hair on the head.
‘הלכות ציצית פרק א
ז) וְלוֹקֵחַ חוּט אֶחָד מִן הַלָּבָן וְכוֹרֵךְ בּוֹ כְּרִיכָה אַחַת עַל שְׁאָר הַחוּטִין בְּצַד הַבֶּגֶד וּמַנִּיחוֹ. וְלוֹקֵחַ חוּט הַתְּכֵלֶת וְכוֹרֵךְ בּוֹ שְׁתֵּי כְּרִיכוֹת בְּצַד כְּרִיכָה שֶׁל לָבָן וְקוֹשֵׁר. וְאֵלּוּ הַשָּׁלֹשׁ כְּרִיכוֹת הֵם הַנִּקְרָאִין חֻלְיָא. וּמַרְחִיק מְעַט וְעוֹשֶׂה חֻלְיָא שְׁנִיָּה בְּחוּט שֶׁל תְּכֵלֶת לְבַדּוֹ. וּמַרְחִיק מְעַט וְעוֹשֶׂה חֻלְיָא שְׁלִישִׁית וְכֵן עַד חֻלְיָא אַחֲרוֹנָה שֶׁהוּא כּוֹרֵךְ בָּהּ שְׁתֵּי כְּרִיכוֹת שֶׁל תְּכֵלֶת. וּכְרִיכָה אַחֲרוֹנָה שֶׁל לָבָן. מִפְּנֵי שֶׁהִתְחִיל בְּלָבָן מְסַיֵּם בּוֹ שֶׁמַּעֲלִין בַּקֹּדֶשׁ וְלֹא מוֹרִידִין. וְלָמָּה יַתְחִיל בְּלָבָן כְּדֵי שֶׁיְּהֵא סָמוּךְ לִכְנַף מִינָהּ. וְעַל דֶּרֶךְ זֶה הוּא עוֹשֶׂה בְּאַרְבַּע הַכְּנָפוֹת
ח) כַּמָּה חֻלְיוֹת הוּא עוֹשֶׂה בְּכָל כָּנָף. לֹא פָּחוֹת מִשֶּׁבַע וְלֹא יוֹתֵר מִשְּׁלֹשׁ עֶשְׂרֵה. וְזוֹ הִיא מִצְוָה מִן הַמֻּבְחָר. וְאִם לֹא כָּרַךְ עָלֶיהָ אֶלָּא חֻלְיָא אַחַת כְּשֵׁרָה. וְאִם כָּרַךְ הַתְּכֵלֶת עַל רֹב הַצִּיצִית כְּשֵׁרָה. וְנוֹי הַתְּכֵלֶת שֶׁיִּהְיוּ כָּל הַחֻלְיוֹת בִּשְׁלִישׁ הַחוּטִין הַמְשֻׁלְשָׁלִין וּשְׁנֵי שְׁלִישֵׁיהֶן עָנָף. וְצָרִיךְ לְפָרְדוֹ עַד שֶׁיִּהְיֶה כְּצִיצִית שְׂעַר הָרֹאשׁ
- The initial “Chulya” is made by wrapping one white strand and one blue strand and tucking in the ends to form a knot. The white is wrapped once first and then the blue twice.
- The 11 middle “Chulyot” are made by taking one blue strand from the total of eight strands and wrapping it around the remaining seven strands three times, and tucking the end into the wraps to form a knot. This “wrapping” strand is designated “Shamash” and is used for all subsequent chulyot (though it is not halachically imperative that the same Shamash be used).
- The final “Chulya” is made by wrapping one white strand and one blue strand and tucking in the ends to form a knot. The blue is wrapped twice first and then the white once.
2 Rambam setsH/T Dovid Aronin
Rambam with no Kesher ElyonRav Kapach holds Rambam tying should NOT have the double knot on top. It's in deference to the Ran that, bedieved the mitzvah is fulfilled by the first double knot. (R' David Ely Grundland).