Movement of pollen tube towards embryo sac is

Movement of pollen tube towards embryo sac is Chemotactic.
Chemotaxis is a fundamental biological process in which a cell migrates following the direction of a spatial cue. This spatial cue is provided in a form of a gradient of chemoattractants. Chemotactic movement causes the pollen grains to reach the embryo sac and results in fusion, which is also called syngamy.
The pollen tube arrives in the micropyle of the integument of the ovule, and enters the embryo sac. The synergids of the embryo sac literally put their energies together to burst the end of the pollen tube.