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We define a double affine $Q$-dependent braid group. This group isconstructed by appending to the braid group a set of operators $Q_i$, beforeextending it to an affine $Q$-dependent braid group. We show specifically thatthe elliptic braid group and the double affine Hecke algebra (DAHA) can beobtained as quotient groups. Complementing this we present a pictorialrepresentation of the double affine $Q$-dependent braid group based on ribbonsliving in a toroid. We show that in this pictorial representation we can fullydescribe any DAHA. Specifically, we graphically describe the parameter $q$ uponwhich this algebra is dependent and show that in this particular representation$q$ corresponds to a twist in the ribbon.

Graphical Calculus for the Double Affine Q-Dependent Braid Group