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This paper brings these tools together via a deterministic spatial PD model that distributes cooperators at the prime-numbered locations of Ulam\u2019s spiral. The model focuses on a narrow boundary game variant of the PD for ease of comparison with early studies of the spatial PD. Despite constituting an initially small portion of the population, cooperators arranged in Ulam\u2019s spiral always grow to dominance when (i) the payoff to free-riding is less than or equal to 8\/6 (\u22481.33) times the payoff to mutual cooperation and (ii) grid size equals or exceeds 23\u2009\u00d7\u200923. As in any spatial PD model, particular formations of cooperators spur this growth and here these formations draw attention to rare configurations in Ulam\u2019s spiral.<\/jats:p>","DOI":"10.1155\/2023\/1649440","type":"journal-article","created":{"date-parts":[[2023,4,25]],"date-time":"2023-04-25T22:50:09Z","timestamp":1682463009000},"page":"1-10","source":"Crossref","is-referenced-by-count":0,"title":["Seeding the Spatial Prisoner\u2019s Dilemma with Ulam\u2019s Spiral"],"prefix":"10.1155","volume":"2023","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3014-9722","authenticated-orcid":true,"given":"Tim","family":"Johnson","sequence":"first","affiliation":[{"name":"Atkinson Graduate School of Management, Willamette University, Salem 97301, OR, USA"},{"name":"Center for Governance and Public Policy Research, Willamette University, Salem 97301, OR, USA"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1002\/cplx.1040"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.csfx.2022.100081"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.csfx.2022.100079"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1038\/s41562-020-01024-1"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/8\/2\/022"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1209\/epl\/i2006-10217-3"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1109\/access.2019.2922200"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2020.126391"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2021.126149"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2016.08.014"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.77.011904"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.78.051120"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.80.021901"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2022.128274"},{"key":"15","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1146\/annurev.es.03.110172.001205","article-title":"Altruism and related phenomena, mainly in the social insects","volume":"3","author":"W. 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