The flowsnake (also called a Gosper curve) is a space-filling curve, a surjection from . The flowsnake -function, a surjection , determines a complex value, , for points along the curve with preimages that belong to the restricted domain. All valid preimages can be written in the form . When is an integer and , the function values for the set of preimages determine a traditional flowsnake interpolation. These points can be computed using a simple Lindenmayer system or a so-called -function. Computation of other exact function values requires the -function, provided here.