Question

1. The Pentagonal Game of Life is a variant of the Game of Life played on a grid in which each cell has 5 neighbours. Live cells are shown in grey and dead cells are shown in white. The rules are as follows Two cells are considered to be neighbours if they share an edge. A dead cell comes to life it if has exactly 2 living neighbours. .A live cell remains alive if it has 2 or 3 living neighbours. A live cel dies if it has fewer than 2 or more than 3 living neighbours. (a) (6 marks) For the following initial population, compute enough generations to decide if the population will explode, go extinct, become periodic or migratory and state what you find. (b) (4 marks) Find an initial population that has the population from part (a) ation as the next gener- [10 marks] You may use the attached sheet of grids to show your answers if you wish.

Answer 1

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AS FOR GIVEN DATA...

grid in which each cell The Pentagonal Game of Life is a variant of the Game of Life played neighbours. Live cells are shown in grey and dead cells are shown in white. The rules are as on a has 5 S follows: . Two cells are considered to be neighbours if they share an edge A dead cell comes to life it if has exactly 2 living neighbours A live cell remains alive if it has 2 or 3 living neighbours A live cell dies if it has fewer than 2 or more than 3 living neighbours

EXPLANATION ::-

As the steps move following are the diagram which shows the growth of living and dead cells

white cells represent already living cells, black cells represent cells which become dead and the green cells represent cells which come to living, Here I have considered that the grid is infinite ant the corner and edge pentagons are connected with other pentagons which cant be shown in this picture.

(A) (6 marks) For the following initial population, compute enough generations to decide if the population will explode, go extinct, become periodic or migratory and state what you find.

SOL ::-

Final picture

So according to the computations the population will become stable and there will be a periodic patterning of these populations of dead cells growing.

B) Find an initial population that has the population from part (a) as the next gener- ation 10 marks You may use the attached sheet of grids to show your answers if you wish
Extra copies of Game of Life grids for Question 1 (a) Behaviour of the population (b)

SOL::

Behavior of the population is periodic as shown in figure 2 fourth cell.

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