Recurrent iterated function systems in the three-dimensional space were introduced

from which

a class of recurrent fractal interpolation surfaces with multi-parameters were constructed.These surfaces

compared with self-affine fractal interpolation surfaces being constructed by the traditional iteration function system

can be more flexibly applied in simulating irregular object shape and image compression.It is proved that

under certain conditions

the class of recurrent iteration function system attractors are continuous curved surfaces passing through the given interpolation points.