smoketrail lacunaries

 

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Erik Nelson noted that the plumes of exponents kind of look like smoke trails, so I’m going to appropriate that as terminology. These are smoketrail lacunaries. What’s interesting here is that we’re not looking at an escape time or Newton’s method fractal per se, but there are features of these smoketrail lacunaries that are on the way to being Cantor Bouquets. For a good introduction to Cantor Bouquets, read Bob Devaney’s http://www.ams.org/notices/200401/fea-devaney.pdf Cantor and Sierpinski, Julia and Fatou: Complex Topology Meets Complex Dynamics, Notices of the AMS)

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