Math 5110/6830
Homework 11.1
1. For 1d Wolfram cellular automata:
a) iterate by hand automaton number 108. Its updating function has the
following set of numbers:
0 0 1 1 0 1 1 0.
Start with the following initial condition: 0 1 0 0 1 1 0 0 1 0 1 0 0
Formulate what pattern will an arbitrary set of zeros and ones evolve to.
b) (computing) Iterate on the computer and display an evolution of 100
cells starting with an arbitrary (non-trivial, not all 0’s or 1’s) initial condition
under updating function number 90 (from class), for 100 time steps. You should
obtain a fractal-like pattern
2. Game of Life.
a) iterate by hand sets of 3 connected cells
b) play with the applet (http://www.bitstorm.org/gameoflife/)
- study the behavior of tetrominoes (initial condition consisting of one of the
tetris pieces)
- observe and describe the behavior of a glider (it is one of he preprogrammed
initial conditions)
- make 2 gliders collide in several different ways. What happens?
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