Sequences of harmonic maps in the 3-sphere

We define two transforms between non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between non-conformal harmonic maps into the 3-sphere, $H$-surfaces in Euclidean 3-space and almost complex surfaces in the nearly K\"ahler manifold $S^3\times S^3$. As a consequence we can construct sequences of $H$-surfaces and almost complex surfaces.