Empirically determine μ and κ for the bi-∞ M{content}M Cookie system

Determine the empirical values of μ and κ, where μ is the mass fraction of an M{content}M Cookie contributed by M{content}M mix-ins and κ is the mass fraction of a Crunchy Cookie M{content}M contributed by cookie mix-ins, in order to numerically evaluate the limiting compositions given by Theorem 4 (bi-∞ M{content}M Cookie).

Background

The coupled recursion for the M{content}M Cookie and the Crunchy Cookie M{content}M yields closed-form limits a* and b* that depend only on two empirical parameters: μ (the M{content}M mix-in fraction in the cookie) and κ (the cookie mix-in fraction in the candy).

While the formulas are exact, the paper does not report measured values for μ and κ, so the numerical evaluation of the limits remains incomplete.