Each cell would have 4 input bits, 1 each from the neighbors, and 4 output bits, again, one to each neighbor. In the middle would be 64 bits of shift register from a long scan chain, the output of which goes to 4 16:1 multiplexers, and 4 bits of latch.
Through the magic of graph coloring, a checkerboard pattern would be used to clock all of the cells to allow data to flow in any direction without preference, and without race conditions. All of the inputs to any given cell would be stable.
This allows the flexibility of an FPGA, without the need to worry about timing issues or race conditions, glitches, etc. This also keeps all the lines short, so everything is local and fast/low power.
What it doesn't do is be efficient with gates, nor give the fastest path for logic. Every single operation happens effectively in parallel. All computation is pipelined.
I've had this idea since about 1982... I really wish someone would pick it up and run with it. I call it the BitGrid.