The Density Plot of the Prime Gaps is a Fractal

As you look at the density plots of increasing numbers of prime gaps (the distance between subsequent primes), a fractal emerges.

Just get the gaps and graph the densities with this simple R code:

For increasing numbers of gaps (shown to 100_000_000), this results in the following graphs.  You can see the self-similar, fractal nature emerge:

gaps-simple-10gaps-simple-100gaps-simple-1_000gaps-simple-10_000gaps-simple-100_000gaps-simple-1_000_000gaps-simple-10_000_000gaps-simple-100_000_000

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