Scaling Larger than Life Bugs: to range 25 and beyond

The Game of Life, also known as Life, is a cellular automaton discovered in the late 1960s by the British mathematician John Horton Conway. Each cell is in one of two states, live or dead, or on or off, and each cell interacts with its eight nearest neighbors. The state of a cell is calculated from the number of its neighboring cells that are dead and the number of the cells that are live. The "player" chooses how many and which cells are live at the beginning of the game and then observes the patterns formed by the cells as the game progresses. One of the things that makes Life interesting to study is its coherent structures, namely gliders, oscillators, and still lifes, which emerge "naturally" as the rule updates from random initial configurations. Even though Life has been extensively studied, its most stable states remain a mystery since its "simple" rule is nonlinear. In the early 1990's, David Griffeath wondered whether Life might be a clue to a critical phase point in the threshold-range scaling limit. To further examine this question, he proposed Larger than Life (LtL), a four-parameter family of two-dimensional cellular automata that generalizes Life to large neighborhoods and general birth and survival thresholds. Kellie Evans has extensively studied LtL with a focus on range 5. Evans' discoveries include finding more "Life-like" LtL rules that support generalizations of Life's gliders than initially imagined. In particular, these generalizations, called bugs, have intriguing geometries which are interesting in their own right. We extend some of Evans' range 5 results to ranges 25 and higher. In particular, we provide empirical evidence to support her conjectures that there are numerous sequences of bugs, each of which when scaled appropriately, converges to a Euclidean limit.