A Family of New Designs (Page 2)
It took a little while to realize 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 4sk
segments moving clockwise, which is the same as the counterclockwise
distance if one starts from the second point. Moreover, o = 2s
is a degenerate case, which yields figures with all lines meeting in the
middle of the square:
Segments = 24, Offset = 48
It took me a little longer to realize that offsets between 1 and s1
were also possible. Offsets of 0 or 1 yield the same figure, another
degenerate case (negative offsets have positive offset equivalents, of
course):
Segments = 24, Offset = 0 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)
