Use pointplot to plot a few points, and display to combine several plots.

Use pointplot to plot a few points, and display to combine several plots.

I expect igcd to be more efficient, but does gcd not produce the same result as igcd when applied to natural numbers?  In fact, using trace it appears that gcd ends up calling igcd. 

I expect igcd to be more efficient, but does gcd not produce the same result as igcd when applied to natural numbers?  In fact, using trace it appears that gcd ends up calling igcd. 

> plottools[rotate](%, Pi/2, [0,0]);

> plottools[rotate](%, Pi/2, [0,0]);

That's what the red and green curves are.  If point [r,x] is on the curve, x is an equilibrium point for that value of r.

That's what the red and green curves are.  If point [r,x] is on the curve, x is an equilibrium point for that value of r.

Yes, it was pretty much arbitrary. You might note that nothing very interesting happens from the point of view of bifurcation outside the interval -1 <= r <= 1.

Yes, it was pretty much arbitrary. You might note that nothing very interesting happens from the point of view of bifurcation outside the interval -1 <= r <= 1.

This is not the Miller-Rabin test.  See the description of Miller-Rabin in en.wikipedia.org/wiki/Miller-Rabin_test .  You're just testing whether a^k == (+/-) 1 mod n, where k is the largest odd factor of n-1.

This is not the Miller-Rabin test.  See the description of Miller-Rabin in en.wikipedia.org/wiki/Miller-Rabin_test .  You're just testing whether a^k == (+/-) 1 mod n, where k is the largest odd factor of n-1.

As I said, stability depends on the derivative wrt x:  diff(f(r,x), x) = r - cos(x).

As I said, stability depends on the derivative wrt x:  diff(f(r,x), x) = r - cos(x).

Because implicitplot allows the range for the second variable to depend on the first, but not vice versa.