Edit: Actually... what if you broke the grid up in to N by N blocks, and simulated 2N half time steps (each decreasing the side length by 2) of that block? You

Edit: Actually... what if you broke the grid up in to N by N blocks, and simulated 2N half time steps (each decreasing the side length by 2) of that block? You'd need to do a similar sort of chess grid over the blocks, and emit like "partial outputs" from each block, then run a pass going the reverse direction, consuming the partial outputs and initial inputs. This way, you can fit a block entirely within a cores L1 for N time steps, and naturally get parallelism by simulating multiple blocks at once. You should be able to simulate N time steps like this with just 2 loads of the data (program and state) instead of 2 * N.