Forrest, Figures 1–4

Hover the mouse over one of the boxes 1, 2, 3, 4 to view the corresponding figure.

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20 random dots on a map, and their alignments

Figure 1

20 random dots represent sites shown on a map. The alignments amongst these are noted, and the sites involved in alignments given numbers 1 to 16 inclusive. Four sites are thus not used.

Alignments are:

1,2,35,9,10
2,14,165,11,13
3,4,56,7,8
3,14,1510,11,12

i.e. 8 triads.

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The 20 random dots of figure 1, plus 10 sites not shown on the map

Figure 2

The 20 dots (blue) of fig. 1, with alignments, plus 10 circles (red) to represent sites which exist but which are not shown on the map. Where these circles fall in line with the numbered sites of fig. 1, they are noted and given letters (A, B, C).

Alignments are now:

1,2,35,11,13
2,14,16,C6,7,8
3,4,57,15,A
3,14,159,13,B
4,13,A10,11,12
5,9,10 

i.e. 10 triads and 1 tetrad.

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As figure 2, but with unnumbered dots and unlettered circles omitted

Figure 3

This is identical with fig. 2 except that all unnumbered dots or unlettered circles are omitted.

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As figure 3, with each site given a random nudge

Figure 4

The sites of fig. 3 are given a randomised nudge within their respective 1 km grid squares. C' is the nudged C, 13' is the nudged 13, etc.

This new set of 19 nudged sites are now inspected for alignments, these being:

1',6',7'3',5',14'
1',8',9'8',10',12'
1',14',C'9',12',13'

i.e. 6 triads in all.