# Ulam Spiral Images

Ulam wrote the positive integers in a rectilinear spiral pattern and observed that
primes showed up on diagonals rather more than they might have been expected to.
Here are images illustrating the same kind of thing with other sequences of positive
integers. Since there seems to be no convention on this sort of thing, my spirals
start with 1, and then move upward to 2, then clockwise, like
this.

primes

twin primes (the lower twin)

squares

triangular numbers

pentagonal numbers

abundant numbers

abundant numbers (low res)

tau(n) divides n

tau(n) equals tau(n+1)

tau(n) equals tau(n+2)

tau(n), greyscale

happy numbers

### Modulo classes

modulo 2 (low res)

modulo 3 (low res)

modulo 4 (low res)

modulo 5 (low res)

modulo 8 (low res)

modulo 11 (low res)

modulo 13 (low res)

modulo 29

modulo 30

modulo 30, greyscale

modulo 31

Doctor Matt >> Mathematcs