That's really impressive that you were able to write a C++ program to solve the Lorenz equations and use Maple to graph the results! It's always great to see students taking on challenging projects and using their skills to solve complex problems.
As for your question about finding initial conditions for a metachaotic result, I can offer a few suggestions. First, you can try varying the initial conditions for each of the three equations (x, y, and z) and see how that affects the overall behavior of the system. This way, you can get a sense of which initial conditions lead to a chaotic result and which lead to a more stable result.
Another approach is to use a bifurcation diagram, which shows how the behavior of the system changes as a parameter (in this case, r) is varied. By plotting the values of r against the resulting behavior, you can see where the system transitions from chaotic to stable. From there, you can choose initial conditions that correspond to the desired behavior.
I would also recommend looking into techniques such as sensitivity analysis and parameter estimation, which can help you identify the most influential parameters and initial conditions in your system. This can save you time in trying out different combinations and provide more insight into the dynamics of the system.
Overall, it's great that you're exploring the metachaotic behavior of the Lorenz equations and I'm sure with some further experimentation and analysis, you'll be able to find the right initial conditions for your desired result. Best of luck with your project!