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We prove that such a cluster exists in the planar case $ d = 2 $, for any choice of the areas $ a_k $ with $ \\sum \\sqrt a_k &amp;lt; \\infty $. We also show the existence of a bounded minimizer with the property $ P({\\bf{E}}) = \\mathcal H^1({\\tilde\\partial} {\\bf{E}}) $, where $ {\\tilde\\partial} {\\bf{E}} $ denotes the measure theoretic boundary of the cluster. Finally, we provide several examples of infinite isoperimetric clusters for anisotropic and fractional perimeters.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2023053","type":"journal-article","created":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T11:36:05Z","timestamp":1682076965000},"page":"1226-1235","source":"Crossref","is-referenced-by-count":6,"title":["Isoperimetric planar clusters with infinitely many regions"],"prefix":"10.3934","volume":"18","author":[{"given":"Matteo","family":"Novaga","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy"}]},{"given":"Emanuele","family":"Paolini","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy"}]},{"given":"Eugene","family":"Stepanov","sequence":"additional","affiliation":[{"name":"Scuola Normale Superiore, Piazza dei Cavalieri 6, Pisa, Italy"},{"name":"St. Petersburg Branch of the Steklov Mathematical Institute of the Russian Academy of Sciences, St. Petersburg, Russia"},{"name":"Faculty of Mathematics, Higher School of Economics, Moscow, Russia"}]},{"given":"Vincenzo Maria","family":"Tortorelli","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2023053-1","unstructured":"L. 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