Description

This simulation is an application of the Ulam Spiral discovered by the Polish mathematician Stanislaw Ulam

There are currently three types of spiral, still the numbers are always drawn following the same pattern, in a counter-clockwise, right-angled spiral

• Prime numbers: the classic representation of the spiral as discovered by Ulam. Blacks dots are drawn for each prime number (2, 3, 5, 7, 11, 13, ...)
• Nb. of divisors: my favorite! A dot is drawn for each number, with its size and color depending on its number of prime divisors. The dot linked to the number 384, which has 8 prime divisors (2x3^7), will therefore be bigger than the one linked to the number 544, which has only 6 prime divisors (2x17^5)
• Prime web: segments are drawn between each increasing powers of prime numbers. The sequence will therefore be: 2 -> 3 -> 4 (2^2) -> 5 -> 7 -> 8 (2^3) -> 9 (3^2) -> 11, and so on...

For these 3 types of spiral, you'll just need to wait for a few seconds before seeing strange diagonal patterns. Mathematicians have yet to find an explanation to this bizarre distribution!

Controls

You'll just have to select a type of spiral in the drop-down list, and then click on the button "Launch Ulam Spiral!"

By moving your mouse over a dot, its number and prime divisors will be displayed