{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T02:51:59Z","timestamp":1777517519540,"version":"3.51.4"},"reference-count":43,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2021,10,18]],"date-time":"2021-10-18T00:00:00Z","timestamp":1634515200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Computability"],"published-print":{"date-parts":[[2022,5,13]]},"abstract":"<jats:p>This paper investigates the algorithmic dimension spectra of lines in the Euclidean plane. Given any line L with slope a and vertical intercept b, the dimension spectrum [Formula: see text] is the set of all effective Hausdorff dimensions of individual points on L. We draw on Kolmogorov complexity and geometrical arguments to show that if the effective Hausdorff dimension [Formula: see text] is equal to the effective packing dimension [Formula: see text], then [Formula: see text] contains a unit interval. We also show that, if the dimension [Formula: see text] is at least one, then [Formula: see text] is infinite. Together with previous work, this implies that the dimension spectrum of any line is infinite.<\/jats:p>","DOI":"10.3233\/com-190292","type":"journal-article","created":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T18:28:18Z","timestamp":1634668098000},"page":"85-112","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Dimension spectra of lines"],"prefix":"10.1177","volume":"11","author":[{"given":"Neil","family":"Lutz","sequence":"first","affiliation":[{"name":"Computer Science Department, Swarthmore College, Swarthmore, PA 19081, USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.M.","family":"Stull","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Northwestern University, Evanston, IL 60208, USA."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2021,10,18]]},"reference":[{"key":"ref001","unstructured":"47th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2006), 21\u201324 October 2006, Berkeley, California, USA, Proceedings, in:\n                      FOCS\n                      , IEEE Computer Society, 2006. 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