In a spiral lattice,
the eye tends to connect nearest points into spirals. These
spirals are called parastichies.
There are two sets of parastichies winding in different directions.
In the figure to the right there are 8 parastichies illustrated
in red and 13 in grey. Spiral lattices are classified according
to the number of parastichies in each set. The lattice shown
here has parastichy numbers (8, 13).
Parastichy numbers are related to which
points are closest to a given point. The nearest
neighbor to point 0 is point 13. One of the grey parastichies
in the figure passes through the points labeled 0, 13, 26
etc. The difference between the numbers on two neighboring
points in this parastichy is always 13, which is the number
of grey parastichies. This is true for all of the grey parastichies.
Similar statements hold for the red parastichies.
The next nearest neighbor to point 0 is point 8. Points 0
and 8 lie on a red parastichy and 8 - 0 = 8. The next nearest
neighbor to point 7 is point 15. Points 7 and 15 lie on a
red parastichy and 15 - 7 = 8.