Number Portraits

I designed a set of number portraits for the integers from 1 to 36.

Each number is either a prime or a composite. If it is a prime number, then it has two divisors: 1 and itself. This is visualized as the gray-colored half circle, where the top represents 1 and the bottom represents the number itself. Composite numbers have other pairs of divisors, and these are visualized as the smaller, colored arcs.

The perfect squares (4, 9, 16, 25, and 36) each have a line segment located at the square root.

The numbers 6 and 8 each have one pair of divisors (besides 1 and themselves); they are (2,3) and (2,4), respectfully. Since the first number in each pair is 2, these arcs are colored green. Divisor pairs in which the first divisor is 3 are colored blue; divisor pairs in which the first divisor is 4 are colored red. And divisor pairs in which the first divisor is 5 are colored yellow. These colors visualize divisibility by these first 5 positive integers.

The highly-composite numbers 12, 24, and 36 are shown enlarged below.

The number 36 has the most divisors in this set. It’s divisor pairs are

(1, 36)  (2, 18) (3, 12) (4, 9) (6, 6).

These are in a similar spirit to the Divisor Plot images I created in 2010:

http://www.divisorplot.com/index.html