I've never had to do this before, but this is what I came up with.
% just some similarly-shaped curves
x = linspace(0.1,1,10);
a = x.^0.2;
b = x.^0.3;
plot(x,a); hold on
plot(x,b,'k:');
xs = x(1);
ys = a(1);
n = 1;
while ~isnan(xs(n)) && n<100
xs(n+1) = interp1(b,x,ys(n));
ys(n+1) = interp1(x,b,xs(n+1));
ys(n+2) = interp1(x,a,xs(n+1));
xs(n+2) = interp1(a,x,ys(n+2));
n = n+2;
end
% if loop walks off the end of a non-converging dataset
xs = xs(~isnan(xs));
ys = ys(~isnan(ys));
% if the curves don't converge, bring the line to the x-limit
if xs(end) < x(end)
xs = [xs x(end)];
ys = [ys ys(end)];
end
plot(xs,ys,'b')
If the curves always converge, then some of this could be removed. Note the use of interp1 makes sure the plots touch even if the resolution is low. If the goal here is to count the number of steps or something, you'll have to figure that out. I just picked some arbitrary limit of 100.
