Mathematica Problems on Recurrence Relations (RR) and Cellular Automata (CA)

3. Consider rule 110 (1D CA) and start with one black cell. Run it up to 1000 iterations so let your string be 1000 cells. Note it evolves to the left only. The moving structures you observe are called spaceships and your task is to look at one of them. Try first the periodic sequence 00010011011111. It consists of 14 cells and repeat it 20 times so the string length should now be a multiple of 14. It is called the background. Finally put 0001110111 sur-rounded by the periodic sequence above. This string has length 10 so start with 14n + 10 + 14n cells where n is an integer. What happens? Illustrate with a figure. You can read about it at the Wikipedia article about rule

110. Useful commands here are: ConstantArray, Flatten, Insert. If you use a For-loop, use AppendTo command.