A Family of New Designs (Page 3)
Here is a gallery of other designs, all for s = 24. For
small offsets, we get squares with little parabolas at the corners. For
example, o = 6, yields:
Segments = 24, Offset = 14
As the offset goes from s/2 to s, the central “circle”
develops vertices as the overlap between parabolas increases. When o = 20,
we get:
Segments = 24, Offset = 20
Around o = 3s/2, it is hard to see parabolas at all.
Instead, we get a kind of star pattern, with a central area approaching a
square and surrounded by something like octagon (o = 36):
Segments = 24, Offset = 36
This can be seen even better if we increase the number of segments in
the figure. Here is a figure with s = 36 and o =
54:
Segments = 36, Offset = 54
Of course, we could get another set of patterns by branching out from a
square. Any regular polygon—triangle, pentagon, hexagon, etc.—could
be the basis for similar designs. I did not build that generalization
into my program, however, so, for the moment, I’ll leave those designs
to others. Happy drawing!
— LED, 2/1/2003 |