This is irrelevant to twin primes but it is interesting to observe another way in which the distribution of primes creates a fractal pattern.
The pattern of primes eg 1 x 5, 1 x 7, 1 x 11 etc is also fractally replicated in n-factor numbers. For 2-factor numbers a new pattern (congruent to the overall pattern of primes) starts at each prime eg 5 x 5, 5 x 7, 5 x 11… 7 x 5, 7 x 7, 7 x 11…. and so on. For 3-factor numbers we have a new repeat of the prime pattern starting from each 2-factor number and so on.
Each iteration of this pattern produces a set of numbers. A set of composite numbers with up to n factors where n is finite cannot define every possible composite number. So the pattern is replicated endlessly, in another fractal pattern, creating composites of n+1, n+2 etc factors.