AlbertArmStain wrote: April 7th, 2022, 4:59 pm
To measure displacement, the displacement position will be relative to the original position.
This is still quite difficult to visualize -- the description is a little too vague. Would the following match your requirements?
-- Life pattern includes two sliding-block registers
-- a glider arriving on a certain lane from Direction 1 results in the entire pattern eventually moving (X1, Y1)
-- then a glider arriving on a certain lane from Direction 2 results in the entire pattern eventually moving (X2, Y2)...
-- but the contents of the two sliding-block registers change each time the pattern moves,
so first they contain (X1, Y1), and finally contain (X1+X2, Y1+Y2)
We can get away with just two sliding-block registers, if we either specify that X1, Y1, X2, Y2 are all positive numbers, or we do some annoyingly complicated stuff to store positive and negative numbers on one sliding-block register (0, 1, -1, 2, -2, 3, -3, ...)
We do theoretically know how to do this with a painfully huge stable pattern: a glider comes in to activate it, and the pattern builds a new copy of itself, copies its instruction tape to the new copy, copies the contents of the two registers, adjusts the registers by (Xn, Yn), and self-destructs.
It seems unlikely that this specific object will ever be built, unless there's some specific and interesting reason for these specific constraints: why "gliders from different directions"? are there constraints on what (X1, Y1) and (X2, Y2) should be? etc.