Problems
A still life is a non-empty pattern (it starts with at least one alive cell) that never changes. Show that a pattern consisting of a \(2\times 2\) square of alive cells is a still life.
An oscillator is a pattern that returns to its original state after some number of evolutions. Its period is the smallest number of generations it needs to return to its initial state, so for example, a still life has period \(1\) because after \(1\) generation, it looks just like before. Show that a \(3\times 1\) rectangle of alive cells is an oscillator, and find its period.
What is the smallest number of alive cells that a pattern needs to start with in order for the pattern to never die off?
A connected still life is a still life where you can get from any alive cell to any other alive cell by moving through neighbouring alive cells (remember that cells may touch at corners and still count as connected), Find a connected still life of exactly \(10\) alive cells.