> I've been completely silent on the J forums for the past few years You were silent for too long Ewart ;) Welcome back!
> I am partially confused by Ewart's definition of the "critical line" Brian, the "critical line" is used in the context of the Riemann hypothesis; see [0]. One way to get some insight into the behavior of complex functions is via domain coloring; see [1] and the first couple of graphs on the page [2]. One can produce this kind of graphs using J thanks to Andrew Nikitin; see [3]; for example, try, viewrgb 8 ccEnhPh (zetahat"0) 20 * sq 256 (where zetahat is from Ewart's script and the rest from Andrew's script) and compare to the two graphs mentioned above; see [2]. References [0] Zeros, the critical line, and the Riemann hypothesis https://en.wikipedia.org/wiki/Riemann_zeta_function#Zeros,_the_critical_line,_and_the_Riemann_hypothesis [1] Domain Coloring https://en.wikipedia.org/wiki/Domain_coloring [2] Riemann zeta function https://en.wikipedia.org/wiki/Riemann_zeta_function [3] Andrew_Nikitin/Phase_portraits http://code.jsoftware.com/wiki/User:Andrew_Nikitin/Phase_portraits On Sat, May 5, 2018 at 6:55 AM, Ewart Shaw <[email protected]> wrote: > I've been completely silent on the J forums for the past few years > (pressure of work), but have been keeping up with developments, and > really appreciate the work by Henry Rich and others. > > The good news is that I'm retiring (slightly) early, and starting a BA > in fine art in September. My main aim, after a lifetime staring at > computer screens, is to get my hands dirty and my clothes covered with > paint, but I hope to have more time for J as a full-time art student > than as a full-time statistics lecturer. > > The immediate J connection is that, after blithely agreeing at an Open > Day that I could use my maths and computing skills to produce artwork, > I realised I'd better prove it, so cobbled together the (draft) > document at > http://www.ewartshaw.com/temp/dirlink.pdf > > Enjoy! > -- > Ewart Shaw [J.E.H.Shaw] http://www.ewartshaw.com [Work in Progress] > [email protected] http://www.facebook.com/ewart.shaw > 3 ((4&({*.(=+/))++/=3:)@([:,/0&,^:(i.3)@|:"2^:2))&.>@]^:(i.@[) <#:3 6 2 > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
