The Ulam Spiral

… and many other spirals¬†
inspired by it …

Findings (1) pt1-01

Fig. -1.

Spiral populated by
composite adjacents & prime adjacents.

In Fig -1:
A black square is shown
located between sector-lines -3 & -4.

In Fig. -2:
That square is shown again,
populated by only the numbers contained
on its borders & within these borders.

In Fig. -3:
The view per Fig. -2 is shown
populated only by composite adjacents.
The number-locations strongly suggest
a symmetry-group centered about
the shown symmetry-axis.

In Fig. -3a:
Only the numbers included in
the symmetry-group per Fig. -3
are shown.

In Fig. -3b:
Only the numbers excluded from
the symmetry-group per Fig. -3
are shown.

In Fig. -4:
The view per Fig. -2 is shown
populated only by prime adjacents.
The number-locations strongly suggest
a symmetry-group centered about
the shown symmetry-axis.

In Fig. -4a:
Only the numbers included in
the symmetry-group per Fig. -4
are shown.

In Fig. -4b:
Only the numbers excluded from
the symmetry-group per Fig. -4
are shown.

Findings (1) pt2-01
Findings (1) pt3.2-01