  We introduce a method of computing biquandle brackets of oriented knots and
links using a type of decorated trivalent spatial graphs we call trace
diagrams. We identify algebraic conditions on the biquandle bracket
coefficients for moving strands over and under traces and identify a new stop
condition for the recursive expansion. In the case of monochromatic crossings
we show that biquandle brackets satisfy a Homflypt-style skein relation and we
identify algebraic conditions on the biquandle bracket coefficients to allow
pass-through trace moves.
