{"id":3110,"date":"2014-08-08T00:49:31","date_gmt":"2014-08-08T07:49:31","guid":{"rendered":"http:\/\/punyamishra.com\/?p=3110"},"modified":"2022-07-25T13:45:23","modified_gmt":"2022-07-25T20:45:23","slug":"self-similarity-in-math-ambigrams-article-3-in-series","status":"publish","type":"post","link":"https:\/\/punyamishra.com\/2014\/08\/08\/self-similarity-in-math-ambigrams-article-3-in-series\/","title":{"rendered":"Self-similarity in math & ambigrams 3\/3"},"content":{"rendered":"

Self-similarity\u00a0in geometry is the idea of repeating a similar shape (often at a different scale) over and over again.\u00a0<\/span>In other words, a self-similar image contains copies of itself at smaller and smaller scales, such as the image below of the word “zoom.”<\/p>\n

\"zoom-scaling\"<\/p>\n

Self-similarity is a rich mathematical idea and connects to other powerful concepts such as\u00a0infinity, iteration, fractals, recursion and so on.\u00a0<\/span>As it turns out self-similarity is also a rich\u00a0source of ambigrams. This is why the third article in the series Of Art &\u00a0Math<\/em>\u00a0is devoted to Self-Similarity.<\/strong>\u00a0This series written\u00a0with my friend\u00a0<\/span>Gaurav Bhatnagar<\/a>\u00a0is published by\u00a0At Right Angles<\/a>\u00a0(a mathematics education magazine).\u00a0<\/span><\/p>\n

\"screenshot\"<\/p>\n

I think this is easily the best article of the three we have written so far. It has some of the best original designs I have created. Gaurav\u00a0pushed me hard mathematically, and I dare say, I met the challenge (at least part of the way). I don’t want to reveal too many of the designs in\u00a0the article (links to download the article are given below) but here are a couple. Below\u00a0are two different designs for the word “Infinity.”<\/p>\n

\"infinity-circle-and-symbol\"<\/p>\n

These\u00a0two different ambigram designs for \u201cinfinity\u201d are subtly different from each other. In both cases the word can be read even when you rotate the design around – both at the top of the circle and the bottom! Notice how in the first design the chain is created by \u201cin\u201d mapping to itself and \u201cfinity\u201d mapping to itself. In contrast the second design breaks the word up differently, mapping \u201city\u201d to \u201cin\u201d and \u201cfin\u201d to itself. In addition the first design wraps around a circle – for ever and ever and the second says infinity both in words and in symbol!<\/p>\n

The idea of infinity is captured somewhat differently in the next two images.<\/p>\n

\"infinity-2<\/p>\n

The first focuses on mapping the design onto a sphere while the second is a self-similar shape that circles inwards forever. In either case the design can be interpreted in two different ways. Either being made of an infinite repetition of the word \u201cfinite\u201d or the infinite repetition of the word \u201cinfinite\u201d (where the shape that reads as the last \u201ce\u201d in the word \u201cfinite\u201d can be read as \u201cin\u201d in the word \u201cinfinite\u201d when rotated by 90 degrees).<\/p>\n

There are lot more designs in the actual article.\u00a0If you love math or ambigrams are just interested in exploring some cool\u00a0ideas, go ahead click the links at the end of this post.<\/p>\n

All in all this series\u00a0seeks to reveal the hidden beauty of mathematics – and thus it is only fitting that it ends with this design for “hidden beauty.”<\/p>\n

\"hiddenbeauty\"<\/p>\n

You can download\u00a0each of the articles in the series\u00a0Of Art & Math<\/em>\u00a0by following the links below<\/p>\n

    \n
  1. Introducing Ambigrams<\/strong>: Blog post<\/a> |\u00a0Direct link to PDF<\/a><\/li>\n
  2. Symmetry<\/strong>: Blog post<\/a>\u00a0|\u00a0direct link to PDF<\/a><\/li>\n
  3. Self-Similarity<\/strong>:\u00a0Direct link to PDF<\/a><\/li>\n<\/ol>\n

    Alternatively you can download all three articles<\/strong>\u00a0in one large(-ish) PDF\u00a0by clicking here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Self-similarity\u00a0in geometry is the idea of repeating a similar shape (often at a different scale) over and over again.\u00a0In other words, a self-similar image contains copies of itself at smaller and smaller scales, such as the image below of the word “zoom.” Self-similarity is a rich mathematical idea and connects to other powerful concepts such […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[21,30,10,11,5,25,28,9,15,42,29,49],"tags":[],"_links":{"self":[{"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/posts\/3110"}],"collection":[{"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/comments?post=3110"}],"version-history":[{"count":3,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/posts\/3110\/revisions"}],"predecessor-version":[{"id":9315,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/posts\/3110\/revisions\/9315"}],"wp:attachment":[{"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/media?parent=3110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/categories?post=3110"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/punyamishra.com\/wp-json\/wp\/v2\/tags?post=3110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}