How does the Hestite Alg go on forever in Golly?

Question

In hash life, a field is usually regarded as a theoretically infinite grid with the pattern in question in the center near the origin. Quadtree is used to represent the field. Given a square of 22k cells, 2k on the side, at the kth level of the tree, the hash table stores the square of 2k-1-by-2k-1 cells in the center, 2k-2 generations in the future. For example, for a 4x4 square, the center of 2x4 is stored, 1 generation ahead; and for an 8x8 square, the center is 4x4, 2 generations ahead.

Thus, given the initial configuration of 8x8, we get 4x4 square 1 generation forward with an 8x8 center and 2x2 square 2 generations forward (1 generation forward with 4x4 square) with an 8x8 center. With each new generation, our understanding of the grid decreases, in turn, we get the following state of automata. We cannot go any further after we move forward to most of the internal 2x2 square 2k-2 generations

So how does the life of hashes in Golly go on forever? Also, his view of the field never decreases. It seems to show the status of all machines after 2k-2 generations. Moreover, given the initial configuration, which expands over time, the look of the algorithm seems to increase. Does the grid view shrink to show expanding automata?

Answer 1

There's a good article about Dr. Dobb that details how HashLife works. The main answer is that you are not just running the algorithm on existing nodes, but also using new shifted nodes to get the next generation.

Answer 2

To be clear (because your characters were missing), you ask:

Given a square of 2 ^ (2k) cells, 2 ^ k on the side, at the kth level, the hash table stores a square of 2 ^ (k-1) -by-2 ^ (k-1) cells in the center, 2 ^ (k-2) generations to come. [...]

, 8x8 [...] , . , 2x2 2 ^ k-2 .

, - Golly ? .

, 8x8, , , 8x8 . , 16x16, 8x8 4- . , 4x4 4- 8x8.

16x16, HashLife 8x8 , 4 .

? , 32x32, , 8x8 . 16x16, 8 .

, , , 16x16 8 ? - 64x64, , 16 , 8 .

, , ( Golly), , .

Answer 3

- . , .