Explore cluster algebras associated with Bott-Samelson braids in this hour-long lecture from the Western Hemisphere Virtual Symplectic Seminar. Delve into Legendrian links formed by rainbow closures of positive braids and discover how the coordinate ring of functions of an algebraic variety linked to these Legendrian links acts as a moduli of Lagrangian fillings. Learn about the construction of cluster algebras, including quivers and cluster variables, through the lens of symplectic topology. Examine the concept of weaves and their role in proving the main result, along with techniques for performing explicit computations. The lecture concludes with a discussion on the conditions for the "starfish lemma" in response to audience questions.