This figure highlights six apparent features in the point plot of a vs. b,
where a and b are integer solutions to a*a + b*b = c*c for some integer c.
Three of the features are linear sequences of points passing through 0,0
with apparently regular spacing.  Two other features are slightly curved,
approximately horizontal, and start on the vertical axis.  The slope is
positive everywhere, but decreases as you move to the right.  The spacing
between points also increases as you move to the right.  The sixth feature
passes through a series of points starting at the top of the graph and
proceeding down and to the right until it passes out of the right side of
the graph.  I'm not sure how to describe it other than to give the
coordinates.  Starting at the top, the feature passes through 72,210 75,180
78,160 80,150 84,134 90,120 96,110 100,105 105,100 110,96 120,90 134,84
150,80 160,78 180,75 210,72 240,70 260,69 285,68.  These points are not
regularly spaced, but they do appear to form a smooth curve, with negative
slope everywhere, tending toward vertical as you move to the left or
horizontal as you move to the right.