With a Turing complete machine, you can theoretically perform any calculation. It was later proven that the game of life with John Conway found a set of simple rules with which it is possible to create structures within the simulation that can replicate, move, or interact with each other. A detailed description of the 'Game of Life' can be found in a separate article on this website. The simulation can create complex patterns using simple The new state of a cell only depends on the state of the neighboring cells in the previous time step. The simulation proceeds in discrete time steps. Cellular automata are discrete models that consist of a regular grid in which each cell has a defined state.

The 'Game of Life' developed by the English mathematician John Horton Conway is a cellular automaton. The proof of this result (see Berlekamp et al.) involves showing how various configurations of cells represent the components of a computer, including wires, storage, and the fundamental components of a CPU – the digital logic gates that perform and, or, and other logical and arithmetic operations.Other cellular automata can also be shown to be universal computing machines.John Conways Game of Life in Python - Introduction to cellular automata John Conways 'Game of Life' in Python A so-called 'spaceship pattern' in Game of Life The Game of Life That is, we can choose an initial configuration of live cells to represent any possible program and any set of input data, run the Game of Life, and the output data will appear in some region of the lattice. The Game of Life is an example of a universal computing machine.

Rewrite LifeApp so that it uses bit manipulation (see Section 14.6). (d) ∗ Do not do, but interesting to consider LifeApp has not been optimized for the Game of Life and is written so that other rules can be implemented easily. If p = 0.5, what is the steady-state density of live cells? Given that the density of live cells at time t is ρ(t), what is ρ(t + 1), the expected density at time t + 1? Do the simulation and plot ρ(t + 1) versus ρ(t). (c) Assume that each cell is initially alive with probability p. What types of patterns typically result after a long time? What happens for 20% live cells? What happens for 70% live cells? (b) Modify LifeApp so that each cell is initially alive with a 50% probability. Does it matter whether you use fixed or periodic boundary conditions? Use a 16 × 16 lattice. Some suggested initial configurations are shown in Figure 14.2b. Choose several initial configurations with a small number of live cells and determine the different types of patterns that emerge. (a) LifeApp allows the user to determine the initial configuration interactively by clicking on a cell to change its value before hitting the Start button. Also notice that we do not have any need for those diagonal reproductions in this assignment. Observe the central region is reproduced eight times.

Game of life computer version