The ∞-Oreo Abstract: >What happens when a food product…
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The ∞-Oreo
Abstract:
>What happens when a food product contains a version of itself? The Oreo Loaded—a cookie whose filling contains real Oreo cookie crumbs—can be viewed as the result of mixing a Mega Stuf Oreo into a Mega Stuf Oreo. Iterating this process yields a sequence of increasingly self-referential cookies; taking the limit gives the ∞-Oreo. We model the iteration as an affine recurrence on the creme fraction of the filling, prove convergence, and compute the limit exactly: the stuf of the ∞-Oreo is approximately 95.8%\~creme and 4.2%\~wafer. We then extend the framework to pairs of foods that reference each other, deriving a coupled recursion whose fixed point defines a *bi-∞ food*, and illustrate the construction with M&M Cookies and Crunchy Cookie M&M's. Finally, we classify ∞-foods by the number of foods in the recursion and introduce *homological foods*, whose recursive structure is governed by cycles in a directed graph of commercially available products. We close with a conjecture. All products used in this paper can be purchased at a supermarket.
Direct link to PDF: https://arxiv.org/pdf/2604.00435
#science
Abstract:
>What happens when a food product contains a version of itself? The Oreo Loaded—a cookie whose filling contains real Oreo cookie crumbs—can be viewed as the result of mixing a Mega Stuf Oreo into a Mega Stuf Oreo. Iterating this process yields a sequence of increasingly self-referential cookies; taking the limit gives the ∞-Oreo. We model the iteration as an affine recurrence on the creme fraction of the filling, prove convergence, and compute the limit exactly: the stuf of the ∞-Oreo is approximately 95.8%\~creme and 4.2%\~wafer. We then extend the framework to pairs of foods that reference each other, deriving a coupled recursion whose fixed point defines a *bi-∞ food*, and illustrate the construction with M&M Cookies and Crunchy Cookie M&M's. Finally, we classify ∞-foods by the number of foods in the recursion and introduce *homological foods*, whose recursive structure is governed by cycles in a directed graph of commercially available products. We close with a conjecture. All products used in this paper can be purchased at a supermarket.
Direct link to PDF: https://arxiv.org/pdf/2604.00435
#science
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