Design and implement a Python program that will Check whether some numbers, stored in a file, represent a particular coding of a frieze, and - either...

Design and implement a Python program that will

Check whether some numbers, stored in a file, represent a particular coding of a frieze, and

- either display the period of the pattern of the frieze and the transformations that keep it

invariant, based on a result that classifies friezes into 7 groups of symmetries,

- or output some Latex code in a le, from which a pictorial representation of the frieze can be

produced.

The representation of a frieze is based on a coding with numbers in the range 0 . . . 15, each such number

n being associated with a particular point p such that

- if the rightmost digit of the representation of n in base 2 is equal to 1 then p is to be connected to

its northern neighbour: |

- if the second rightmost digit of the representation of n in base 2 is equal to 1 then p is to be

connected to its north-eastern neighbour: /

- if the third rightmost digit of the representation of n in base 2 is equal to 1 then p is to be connected

to its eastern neighbour: __

- if the fourth rightmost digit of the representation of n in base 2 is equal to 1 then p is to be

connected to its south-eastern neighbour: 

First example

The file frieze_1.txt has the following contents.

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0

0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0

0 0 0 0 4 4 1 5 4 4 4 4 8 0 0 0 0 0 0 4 4 1 5 4 4 4 4 8 0 0 0

0 0 0 2 0 0 5 1 0 0 0 0 0 8 0 0 0 0 2 0 0 5 1 0 0 0 0 0 8 0 0

0 0 2 0 0 0 0 0 0 0 0 0 0 0 8 0 0 2 0 0 0 0 0 0 0 0 0 0 0 8 0

0 6 4 4 4 4 4 4 4 4 4 4 4 4 4 0 6 4 4 4 4 4 4 4 4 4 4 4 4 4 0

1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1

1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1

1 1 0 0 0 0 0 0 4 4 4 12 4 4 4 1 1 0 0 0 0 0 0 4 4 4 12 4 4 4 1

1 1 0 4 4 0 0 0 1 2 0 0 8 1 0 1 1 0 4 4 0 0 0 1 2 0 0 8 1 0 1

1 1 0 5 5 1 0 0 3 0 0 0 0 1 0 1 1 0 5 5 1 0 0 3 0 0 0 0 1 0 1

1 1 0 5 5 1 0 0 5 4 4 4 4 1 0 1 1 0 5 5 1 0 0 5 4 4 4 4 1 0 1

1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1

1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1

1 5 4 5 4 5 4 4 4 4 4 4 4 4 4 1 5 4 5 4 5 4 4 4 4 4 4 4 4 4 1

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0

Here is a possible interaction:

$ python3

Python 3.6.4 (v3.6.4:d48ecebad5, Dec 18 2017, 21:07:28)

...

>>> from frieze import *

>>> frieze = Frieze('frieze_1.txt')

>>> frieze.analyse()

Pattern is a frieze of period 15 that is invariant under translation only.

>>> frieze.display()

The effect of executing frieze.display() is to produce a file named frieze_1.tex that can be given

as argument to pdflatex to produce a file named frieze_1.pdf that views as follows.