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The Dragon Curve
© Copyright 2002, Jim Loy
On the left, we see eight orders (two through nine) of the dragon
curve (drawn using Fractint and
Paint Shop Pro). You may notice that the
third order curve (second picture) is made up of two second order curves. The
fourth order curve is made up of two third order curves. The fourth order curve
intersects (touches) itself at one point, but does not cross itself. This can
be drawn without the intersection, by making the corners round. This can also
be done for all of the higher order curves, too. But the simple procedure for
producing higher orders becomes complicated if the corner rounding idea is
thrown in, as each intersection is different.
Below, we see a thirteenth order dragon curve. It too is one space-filling
curve, which does not cross itself. The dragon curve bears some resemblance to
some Julia Sets.
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