Assignment for Dynamical systems theory

1)

a) Write down the rules of the game of life

b) list the name of an initial condition which is periodic

c) list as well the name of an initial condition which travels for ever.

d) Also write one sentence about the inventor of the game of life.

2) Take a calculator (on a phone, turn the phone to get an advanced version of a calculator).

a) Compute by hand the 100th iterate of x=5 under the map T(x)=Tan(x) and write down the result. Make sure you have "Rad" checked on the calculator and not "Deg". 

b) Now start with x=5 and push  alternating the button tan and 1/x, starting with 1/x so that every of the two buttons has been pushed 100 times. Write down the result. If you have time or access to a programming language, try to automate that and compare the result in both cases.