Sierpinski Triangle¶

🎯 Construct a Sierpinski Triangle with a Cellular Automaton.

Consider the following rules:

rules = {
    '   ': ' ',
    '  #': '#',
    ' # ': '#',
    ' ##': ' ',
    '#  ': '#',
    '# #': ' ',
    '## ': ' ',
    '###': ' ',
}

Now when you start with a string consisting of a single hash flanked by spaces:

The rules define how the next line looks like. For the new line you look up character triplets from the original string. The three triplets " #", " # ", "# " involving the original hash result in a new hash each. So the second line is:

###

If you propagate that line once again, the triplets with two hashes reult in a space:

#   #

If you propagate once again, the first four lines look like:

   #
  ###
 #   #
### ###

Write a program that propagates the following line 32 times:

line = " " * 32 + "#" + " " * 32

Add an empty space at the beginning and end of each new line so that the line length stays the same.

Hint

Experiment with the rule set defined by the dictionary by changing its values.

What you can practise in this coding challenge¶

loops
string operations
looking up things in dictionaries