The peculiar blue [תכלת, tekhelet] thread used in tzitzit [ritual fringes] (Numbers 15:37-41) also appears prominently in the construction of Tabernacle (Exodus 25ff). It is used in the inner curtains and the loops that connect them; it also appears throughout the priestly vestments.
Why this blue?
It has been taught: R. Meir used to say: Why is blue [תכלת] specified from all the varieties of colours? Because blue resembles [the colour of] the sea, and the sea resembles [the colour of] heaven, and heaven resembles [the colour of] the Throne of Glory, as it is said: And they saw the God of Israel and there was under His feet as it were a paved work of sapphire stone [לבנת הספיר], and as it were the very heaven for clearness (Exod. 24:10) and it is written: The likeness of a throne as the appearance of a sapphire stone [אֶבֶן-סַפִּיר] (Ezek 1:26).
— Sotah 17a (also: Menachot 43b and Chullin 89a)
Kedushat Levi links the above passage about blue, תכלת, to the stages of a creative act, beginning and ending with its purpose [תכלית]:
[A project from thought to completion] has undergone four distinct stages. 1) original mental image of the project; 2) clarification of the details, etc. 3) translating thought into deed. 4) carrying out the intention which originally prompted the project. [Punctuation follows translation.] When the original mental image of the project is seen reflected after its successful completion, the person inhabiting this building will experience a sense of satisfaction and joy.
— Kedushat Levi, p. 475 (see Source Materials for full citation)