{"id":2646,"date":"2017-03-09T03:00:05","date_gmt":"2017-03-09T09:00:05","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=2646"},"modified":"2017-03-08T17:30:48","modified_gmt":"2017-03-08T23:30:48","slug":"a-thrice-a-day-complex-analysis-infusion","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2017\/03\/09\/a-thrice-a-day-complex-analysis-infusion\/","title":{"rendered":"A Thrice-a-Day Complex Analysis Infusion"},"content":{"rendered":"

Sometimes I like to sit back and take i<\/span><\/a>n math via pictures only. The newest addition to my math picture blog stable is kettenreihen.wordpress.com<\/span><\/a> where three times a day, a beautiful picture appears.<\/span><\/p>\n

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Credit: Thomas Baruchel<\/p><\/div>\n

These are graphs of complex-valued functions based on continued fractions. White points\u00a0are where the function takes on real values, black are imaginary, and the other points are colored according to angle.\u00a0On the blog’s “about<\/a>” page, Baruchel explains the notation, which is not the most common continued fraction notation.\u00a0<\/span><\/p>\n

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It’s fun to look at a graph and try to figure out why it looks the way it does: why are there purely real or imaginary values in particular places, why a graph has horizontal or vertical symmetry, and so on. These are not straightforward functions, so I must admit I don’t always get anywhere, but it’s fun to think about anyway. If I were teaching complex analysis, I would probably try to work this blog into my class somehow, if only to gawk at pretty things with my students.<\/p>\n

I’ve been trying to decide which kinds of graphs are prettiest.\u00a0“Flowers” are nice.<\/p>\n

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Credit: Thomas Baruchel<\/p><\/div>\n

But so are hearts.<\/p>\n

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Credit: Thomas Baruchel<\/p><\/div>\n

Graphs that evoke mathematical symbols are always on trend.<\/p>\n

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Credit: Thomas Baruchel<\/p><\/div>\n

Simple ones are nice.<\/p>\n

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Credit: Thomas Baruchel<\/p><\/div>\n

And so are the wild, busy ones.<\/p>\n

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Credit: Thomas Baruchel<\/p><\/div>\n

Luckily you don’t have to choose. Just add the blog to your feed, put your feet up, and relax with some gorgeous mathematical illustrations.<\/p>\n

<\/div>","protected":false},"excerpt":{"rendered":"

Sometimes I like to sit back and take in math via pictures only. The newest addition to my math picture blog stable is kettenreihen.wordpress.com where three times a day, a beautiful picture appears. These are graphs of complex-valued functions based … Continue reading →<\/span><\/a><\/p>\n

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