Zeta Function Plotter
The applet below animates for real, where
is the Riemann Zeta
Function. See below for some tips on
using the applet controls.

For , is defined as
where the series converges absolutely and
uniformly, and is related to the prime numbers via the Euler
product formula
Although
fails to converge
for , can be
continued analytically to the entire complex plane except for
where the zeta function has a simple
pole. The famous Riemann Hypothesis is that all zeros of this
function lie on the line where
(called the critical
line). It is known that there are infinitely many zeros
located on the line. Zeros on this line occur where the little
square in the animation passes through the coordinate.
The applet uses the
RiemannSiegel formula for computing values of the zeta
function. Hopefully the applet controls are more or less
obvious; pass the mouse over the various buttons for a short
explanation in the ``messages'' area about their function. The
current and value
are shown in the upper left hand corner of the applet. Here a few
tips:
 You can adjust the starting value
to anything greater than or equal to 20,
but once you get up around 1,000,000,000 or so I would be
suspicious about the accuracy. The tracing is buggy for
up in the tens of millions (it leaves
gaps occasionally); not quite sure what the problem is
there.
 Adjusting will
change the difference between sample points, which in effect
speeds up or slows down the animation. As increases so does the frequency of zeros, so you may
want to set to 0.05 or something
smaller.
 The trace button ``T'' will produce a nice
trace of the path followed by the plot as increases. Click it again to clear the current
trace.
 The magnifying glasses are for changing
the axis scales. The largest scale shows a window from
(20,20) to (20,20), while the smallest scale shows a viewing
window from (1,1) to (1,1).
If you spot any booboos or have any comments,
please send me some mail.