A Family of New Designs (Page 2)
It became clear that, as o changed, the overall
look of the resulting figure changed, sometimes dramatically. As o
approaches 2s, for example, I got figures like this one:
Segments = 24, Offset = 46
If o exceeds 2s, however, one gets figures equivalent to
those with offsets less than 2s because points separated by k
segments moving counterclockwise are separated by 4s-k
segments moving clockwise. Because of symmetry going in one direction or
the other results in the same figure. Moreover, o = 2s
is a degenerate case, which yields figures with all lines meeting in the
middle of the square:
Segments = 24, Offset = 48
Offsets such as 1, –1, and 4s–1 are possible and lead to another
degenerate case. as shown below.
Segments = 24, Offset = 1 or –1
Offsets close to s/2 yield something close to a circle within the
square:
Segments = 24, Offset = 14
Then there are other figures that look somewhat different. (Continued on
next page)
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