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## A Family of New Designs (Page 3)

Here is a gallery of other designs, all for
= 24. For small offsets, we get squares with little parabolas at the corners. For example, = 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 = 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