Very interesting project. What I don't quite get is if you can calculate the state after 100 steps in one go what would make you select exactly100? Why not select 1007 or 10 million etc. ?
Thanks! That would be since the skippable timestep width is bounded by the size of the size of the patterns that you've memorized. Say we have a square pattern of size W. The outcome of this pattern within this region in 1 timestep is completely determined by its surrounding square region of size W+2c, with c as the speed of light (pixels per timestep), since patterns beyond that can never interfere with it unless its interference travels beyond the speed of light. For two timesteps the surrounding region would be of size W+4c, since more pixels can interfere with it within that amount of time. Therefore, If you memorize a pattern of size W+4c, you can predict the outcome of the inner square of size N after 2 timesteps, or the inner square of size W+2c after 1 timestep, etc. This sets an upper bound to the number of timesteps you can skip, depending on the sizes of the patterns that you have memorized. So if you've memorized a pattern of size W+200c, you can predict the outcome of the inner square of size c after 100 timesteps, but predicting the 101st timestep would require information of a region beyond the memorized pattern.