Earlier quoted context omitted.
What you're describing is a cellular automaton, in the same vein as of Conway's Game of Life. You can do lots of interesting things with those, but it's emphatically not where I'd start for a flexible computing platform. Why not go the extra mile, and make each tile a small CPU? There's a Zachtronics have called TIS-100 with this premise. https://store.steampowered.com/app/370360/TIS100/
Because each cell has it's own state, and 64 bits of "program" (16 bits in each of the 4 LUTs), it's unlike the game of life, where the rule is the same for each cell. I looked at a lot of choices for architecture, and wanted to allow data paths to cross without conflict, and the 4 in/4 out choice worked best without going too far. Someone did work out how you could run the game of life on a BitGrid, it's in the Esot…
Let's take the a Kintex Ultrascale+ from Xilinx as a fairly typical example of a modern FPGA. Relevant documentation is the UltraScale Architecture CLB User Guide [1] and the Xilinx Power Estimator spreadsheet [2].
Each "slice" contains two flip-flops and a lookup table with 6 input bits and 2 output bits. So two slices is enough to implement each cell with room to spare.
Let's say you have a 200 x 200 grid = 40k cells. That's 80k LUTs and 160k flip-flops. That's about 29% of the resources on a XCKU9P. If we assume a 100 MHz clock and 25% toggle rate (somewhat arbitrary), that's 4e12 state-changes per second. The spreadsheet indicates that circuit will consume 850 mW, or about 200 fJ per state-change.
That said, this is NOT an efficient way to do arithmetic. You'd need N cells to do a fixed-point addition with N-bit arguments, and O(N^2) (give or take) to do a fixed-point multiplication. Floating point requires orders of magnitude more. There's a reason modern FPGAs have dedicated paths for fast addition and hardwired multiplier macros.
[1] https://www.xilinx.com/content/dam/xilinx/support/documents/...
[2] https://www.xilinx.com/products/technology/power/xpe.html