First, neat picture! It's always cool to see the kind of emergent patterns that come out of simple rules like this.
Second, the few numbers you provided give *no* clue as to the pattern you're following. I had to puzzle thru your Python to figure it out instead. From what I can tell, the pattern is:
1. The 1st pattern, P₁, is the empty string.
2. If n is the mth prime, then Pₙ = "<" + Pₘ + ">". (So, since 2 is the 1st prime, P₂ = <>, which is P₁ wrapped in angle brackets. 3 is the 2nd prime, so it's <<>>, P₂ wrapped. 5 is P₃ wrapped, 7 is P₄ wrapped, 11 is P₅ wrapped, etc.)
3. If n is composite, it can be divided into its smallest prime factor j and the rest of the number k. Pₙ is then Pₖ+Pⱼ. (So P₄ is P₂+P₂ <><>, P₁₂ is P₄+P₃ <><><<>>, P₁₀₀ is P₅₀+P₂, etc.)
Third, your use of single-letter variables and some slightly unidiomatic Python made it a bit hard to follow. I've rewritten it here to help myself understand:
Code: Select all
patterns = [""] * limit
prime = 2
primeCount = 1
while prime < limit:
# If N is the Mth prime, generate its pattern from the Mth pattern.
patterns[prime] = "<" + patterns[primeCount] + ">"
# Generate patterns for every possible multiple of prime
# from the Prime'th pattern
# and the Multiplier'th pattern
for mult in xrange(2): # we won't use the whole range
if mult*prime >= limit:
patterns[multiplier*newPrime] = patterns[multiplier] + patterns[newPrime]
# Now find the next prime.
# Per Eratosthene's sieve, this is just the next unfilled value.
while prime < limit and patterns[prime]:
prime += 1
primeCount += 1
for pattern in patterns:
for command in pattern:
if command == ">":
I haven't run this, but I think it works? Is this code clear to you?