1. A field programmable gate array device comprising a plurality of Variable Grain Blocks (VGB's) and a plural number, L of interconnect lines extending by the VGB's, wherein each VGB includes: (a) a signal acquisition layer having a first plurality of N input multiplexers where N is less than L, said N input multiplexers being configurable for acquiring, from a subset of said L interconnect lines that are adjacent to that VGB, a respective first plurality of N input term signals; (b) a function spawning layer having a second plurality of M lookup tables (LUT's), wherein each of the M LUT's is a function spawning LUT that can be configurably coupled to receive a respective subset of input term signals from the first plurality of N input term signals and to responsively produce a respective first level function signal, and further wherein the second plurality of M spawning LUT's have a total of at least N independent input terminals for consuming the acquired plurality of N input term signals; and (c) progressive function synthesizing layers including first and second function synthesizing layers, wherein: (c.1) said first function synthesizing layer is operatively coupled to the function spawning layer for combining the respective first level function signals of sets of two or more of the spawning LUTs to produce two or more second level function signals, each of said second level function signals being a function of more input term signals than is each of the correspondingly combined first level function signals used to produce that second level function signal, and (c.2) said second function synthesizing layer is operatively coupled to the first function synthesizing layer for combining sets of two or more of the respective second level function signals to produce two or more third level function signals, each of said third level function signals being a function of more input term signals than is each of the correspondingly combined second level function signals used to produce that third level function signal.