The density of primes is 1/log(n), so it does drop off, but not so fast that it would be obvious for small numbers.
I tried creating giant Ulam spirals one time, and I did correct for this, which made it look a lot more uniform.
I had initially hoped to find new patterns this way, but nothing turned up. While numerical experiments are fun, there are a huge number of potential avenues that could be explored. Finding the interesting ones is basically what mathematics is.
How did you correct for it? Did you just nonlinearly scale the final picture or did you scale the axis on the spiral itself and then sampled the result?
I was producing grey scale images where each pixel represented a block of numbers. The count in each block was divided by the density of primes (1/log(n)) at the center of the block.
However, this actually made the middle turn grey, because even though the mean value of each pixel was the same, the variance wasn't. So then I corrected for this by calculating a "z-score" instead.
But like I mentioned before, it didn't turn up any interesting patterns.
I guess it specifically didn't turn up interesting patterns because
a) you correct for density
b) the distribution of primes is "noisy" (which is why they're so puzzling) and by averaging out the noise you get a fairly flat distribution
I tried creating giant Ulam spirals one time, and I did correct for this, which made it look a lot more uniform.
I had initially hoped to find new patterns this way, but nothing turned up. While numerical experiments are fun, there are a huge number of potential avenues that could be explored. Finding the interesting ones is basically what mathematics is.