  We define a double affine $Q$-dependent braid group. This group is
constructed by appending to the braid group a set of operators $Q_i$, before
extending it to an affine $Q$-dependent braid group. We show specifically that
the elliptic braid group and the double affine Hecke algebra (DAHA) can be
obtained as quotient groups. Complementing this we present a pictorial
representation of the double affine $Q$-dependent braid group based on ribbons
living in a toroid. We show that in this pictorial representation we can fully
describe any DAHA. Specifically, we graphically describe the parameter $q$ upon
which this algebra is dependent and show that in this particular representation
$q$ corresponds to a twist in the ribbon.
