The $\infty$-Oreo$^{^\circledR}$
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908930137915392 |
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| author | Bosca, Vicente |
| author_facet | Bosca, Vicente |
| contents | 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 $\infty$-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 $\infty$-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 \emph{bi-$\infty$ food}, and illustrate the construction with M\&M Cookies and Crunchy Cookie M\&M's. Finally, we classify $\infty$-foods by the number of foods in the recursion and introduce \emph{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00435 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The $\infty$-Oreo$^{^\circledR}$ Bosca, Vicente History and Overview Combinatorics Dynamical Systems 00A08 (Primary) 39A06, 37C25, 05C20 (Secondary) 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 $\infty$-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 $\infty$-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 \emph{bi-$\infty$ food}, and illustrate the construction with M\&M Cookies and Crunchy Cookie M\&M's. Finally, we classify $\infty$-foods by the number of foods in the recursion and introduce \emph{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. |
| title | The $\infty$-Oreo$^{^\circledR}$ |
| topic | History and Overview Combinatorics Dynamical Systems 00A08 (Primary) 39A06, 37C25, 05C20 (Secondary) |
| url | https://arxiv.org/abs/2604.00435 |