{"id":51214,"date":"2021-10-29T15:32:29","date_gmt":"2021-10-29T14:32:29","guid":{"rendered":"https:\/\/blogs.bmj.com\/bmj\/?p=51214"},"modified":"2021-11-05T10:05:58","modified_gmt":"2021-11-05T09:05:58","slug":"jeffrey-aronson-when-i-use-a-word-medical-cellular-automata","status":"publish","type":"post","link":"https:\/\/blogs.bmj.com\/bmj\/2021\/10\/29\/jeffrey-aronson-when-i-use-a-word-medical-cellular-automata\/","title":{"rendered":"Jeffrey Aronson: When I Use a Word . . . Medical cellular automata"},"content":{"rendered":"<p><span style=\"font-weight: 400\">As I wrote <\/span><a href=\"https:\/\/blogs.bmj.com\/bmj\/2021\/10\/22\/jeffrey-aronson-when-i-use-a-word-cellular-automata\"><span style=\"font-weight: 400\">last week<\/span><\/a><span style=\"font-weight: 400\">, a cellular automaton is a computational system with two components: an ordered array of cells and a set of rules that determines the state of each cell at any time, depending on its relation to other cells in its immediate locality.<\/span><\/p>\n<p><span style=\"font-weight: 400\">A cell in such a system is generally represented by a square in the grid. The simplest state of such a cell is that it is either occupied (e.g. black) or unoccupied (e.g. white), on or off. An example of a simple rule is that a cell can be switched on if it is adjacent to a cell that it is already switched on. From such simple systems highly complex patterns can arise. Here\u2019s an example.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Imagine a row of beds in a Nightingale-style ward, each represented by a cell in a one-dimensional array. A consultant visits one of his patients, represented by the black cell<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-51215 alignnone\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct.jpg\" alt=\"\" width=\"611\" height=\"75\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct.jpg 611w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct-300x37.jpg 300w\" sizes=\"auto, (max-width: 611px) 100vw, 611px\" \/><\/p>\n<p><span style=\"font-weight: 400\">Each time he comes to the ward thereafter he visits his other patients in an order that is determined by a simple rule: he will visit only those patients who have just one immediate neighbor who has already been visited. Anyone with no such neighbours or two such neighbours does not get visited. Here\u2019s how the pattern of consultations builds up on successive visits:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-51216 alignnone\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_2.jpg\" alt=\"\" width=\"623\" height=\"209\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_2.jpg 623w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_2-300x101.jpg 300w\" sizes=\"auto, (max-width: 623px) 100vw, 623px\" \/><\/p>\n<p><span style=\"font-weight: 400\">Eventually all the patients get a visit, some lucky (or unlucky) ones more than once. In the following diagram each row represents a single visit to the ward, imagining the number of beds to be infinite:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-51217 alignnone\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_3.jpg\" alt=\"\" width=\"652\" height=\"320\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_3.jpg 652w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_3-300x147.jpg 300w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_3-640x314.jpg 640w\" sizes=\"auto, (max-width: 652px) 100vw, 652px\" \/><\/p>\n<p><span style=\"font-weight: 400\">We have seen this pattern <\/span><a href=\"https:\/\/blogs.bmj.com\/bmj\/2021\/03\/29\/jeffrey-aronson-when-i-use-a-word-self-experimentation\"><span style=\"font-weight: 400\">before<\/span><\/a><span style=\"font-weight: 400\">; it is the Sierpi\u0144ski triangle, a fractal pattern generated by recurrently removing inverted equilateral triangles from within larger upright equilateral triangles, or by shading in the odd numbers in Pascal\u2019s triangle. The simplest of rules has generated an exceptionally complex pattern. And it is impossible to predict from any rule and any starting position what patterns will emerge.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Cellular automata are playing increasing roles in medical science. In illustration of this, Figure 1 shows the numbers of publications containing the term \u201ccellular automat*\u201d in a PubMed search up to 2020 (n =1596). With isolated exceptions from 1966 and 1981, papers started appearing in 1985 and have been steadily increasing in number ever since, particularly in the last few years. Recent papers have described, for example, studies of the <\/span><a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/34530391\/\"><span style=\"font-weight: 400\">effect<\/span><\/a><span style=\"font-weight: 400\"> of lockdown, migration, and vaccination on the dynamics of covid-19 and <\/span><a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/34352565\/\"><span style=\"font-weight: 400\">modelling<\/span><\/a><span style=\"font-weight: 400\"> its spread in Brazil.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-51218 alignnone\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_4.jpg\" alt=\"\" width=\"676\" height=\"366\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_4.jpg 676w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_4-300x162.jpg 300w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_4-640x347.jpg 640w\" sizes=\"auto, (max-width: 676px) 100vw, 676px\" \/><\/p>\n<p><b>Figure 1. <\/b><span style=\"font-weight: 400\">The numbers of publications year on year containing the term \u201ccellular automat*\u201d; blue: all publications; orange: titles (source PubMed)<\/span><\/p>\n<p><span style=\"font-weight: 400\">Increasingly often our biological cells are being studied using computerized ones.<\/span><\/p>\n<p><em><strong>Jeffrey Aronson<\/strong>\u00a0is a clinical pharmacologist, working in the Centre for Evidence Based Medicine in Oxford\u2019s Nuffield Department of Primary Care Health Sciences. He is also president emeritus of the British Pharmacological Society.<\/em><\/p>\n<p><strong>Competing interests:<\/strong>\u00a0none declared.<\/p>\n<p><a href=\"https:\/\/oeis.org\/wiki\/Welcome\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-51228 size-full\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_integer_again.png\" alt=\"\" width=\"650\" height=\"3162\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_integer_again.png 650w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_integer_again-316x1536.png 316w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_integer_again-421x2048.png 421w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/10\/aronson_29_oct_integer_again-640x3113.png 640w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>As I wrote last week, a cellular automaton is a computational system with two components: an ordered array of cells and a set of rules that determines the state of [&#8230;]<\/p>\n<p><a class=\"btn btn-secondary understrap-read-more-link\" href=\"https:\/\/blogs.bmj.com\/bmj\/2021\/10\/29\/jeffrey-aronson-when-i-use-a-word-medical-cellular-automata\/\">More&#8230;<\/a><\/p>\n","protected":false},"author":419,"featured_media":38359,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5762],"tags":[14784],"class_list":["post-51214","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-jeff-aronsons-words","tag-fp_columnist"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Jeffrey Aronson: When I Use a Word . . . 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