This is a visualization of numbers from 1 to 1,000,000, added in order in blocks of 1,000, located in the 2-D plane according to their prime factors:

The animation was created by John Williamson. The mathematical process begins by representing each integer as a vector of length 80,000: the first value is the number of times “2” is used in its prime factorization, the next for “3”, and so on through the primes. Then all of those vectors together represent one points in an 80,000-dimensional space, which is then reduced to two dimensions using a dimension-reducing algorithm. The interesting structure that results is partly an artifact of the algorithm, but also a results of the fractal nature of the primes on the number line.

That’s all from the blog for this week. Have a great weekend, and we’ll be back next week. See you then!

 





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