Constructing examples of semigroups of valuations

We work with rational rank 1 valuations centered in regular local rings of dimension 3. Given a regular local ring R that has an algebraically closed coefficient field k and a zero-dimensional valuation ν, we provide an algorithm for constructing generating sequences for ν in R  . We then develop a method for determining a valuation on k(x,y,z)k(x,y,z) through the sequence of defining values. Using the above results we construct examples of valuations centered in k[x,y,z](x,y,z)k[x,y,z](x,y,z) and investigate their semigroups of values.