In a great win for new insight via visualization, Carlos Paris shares his amazing discovery of organized chaos in prime numbers through rendering stacked circles or sizes from 1 to 101.
Developing Figure 2 for the first few circles took me a few minutes, but that was more than enough. When I saw the pattern, it just exploded in my face. It is orderly chaos! That's when I felt something from beyond the screen staring back at me. The patterns and shapes generated above never repeat, they always look different depending on your location to the right of the origin. And most importantly, now you can visually tell how all circles fit into each other! I call the image a “Map of Factors” because it tells you all the factors for each number. Wherever you have only 2 circles intersecting the horizontal axis at their right quadrants, you have a prime number! The green vertical lines show the locations of the prime numbers.
The site shows the construction of several visualizations, and animates some of them which yields an odd 3d-like effect.