The Ulam Spiral

… and many other spirals 
inspired by it …

Det. -1.

Spiral populated by:
type – (1,1) 6-folds
type – (1,0) 6-folds
type – (0,1) 6-folds
type – (0,0) 6-folds

All the 6-folds

Tetrapolar-spiral-for-6-folds-Det1

All spirals this page: 
Spiral entries to be
multiplied by “6”

Det. -2.

Spiral populated by:
type – (1,1) 6-folds
type – (1,0) 6-folds
type – (0,1) 6-folds

All the 6-folds
having 1- or 2
prime adjacents. 

Tetrapolar-spiral-for-6-folds-Det2

Det. -3.

Spiral populated by:
type – (0,0) 6-folds

All the 6-folds
having no
prime adjacents. 

Tetrapolar-spiral-for-6-folds-Det3

Det. -4.

Spiral populated by:
type – (1,1) 6-folds
type – (1,0) 6-folds

All the 6-folds
having a lower
prime adjacent. 

Tetrapolar-spiral-for-6-folds-Det4

Det. -5.

Spiral populated by:
type – (1,0) 6-folds

All the 6-folds
having only a lower
prime adjacent. 

Tetrapolar-spiral-for-6-folds-Det5

Det. -6.

Spiral populated by:
type – (1,1) 6-folds
type – (0,1) 6-folds

All the 6-folds
having an upper
prime adjacent. 

Tetrapolar-spiral-for-6-folds-Det6

Det. -7.

Spiral populated by:
type – (0,1) 6-folds

All the 6-folds
having only an upper
prime adjacent. 

Tetrapolar-spiral-for-6-folds-Det7

Det. -8.

Spiral populated by:
type – (1,1) 6-folds

All the 6-folds
having a lower- & upper
prime adjacent. 

Tetrapolar-spiral-for-6-folds-Det8

Findings.

Det. -1:
This detail gives an efficient and immediate
overview of the interdistribution among each other of
the 4 types of 6-folds.

Det. -2:
In this detail a significant number of rows can be seen
but they come in 2 different kinds, as follows.
1):
Arcuate “on-track”-, unremarkable rows.
2):
Arcuate “across-track”-, remarkable rows
that become progressively more
straight and horizontal or vertical
further & further away from the center.

Due to the crowded population of the 6-folds
remarkable rows can emerge per chance, to some extent.
The determination of the situation -chance or not- might require a
computerized analysis of a more extensive spiral.

Det’s. -4, -5, -6, -7:
The situation in these details is much the same as it is with detail -2.

Det. -8:
The population in this detail might well be to sparse
-even in a more extensive spiral with computer analysis-
to present a meaningful display of rows of 6-folds.

Det. -3:
This detail presents the strongest appearance of
“across tracks” horizontal- & vertical rows of 6-folds
forming a display of interest and
it seems to be be a good candidate for
further computerized investigation of a more extensive spiral,
and maybe to find out what forms these rows.