Here are some images created by Sciwise's Lambert W Fractint formula. His post and formula are below along with some of the parameter sets that created my images. Full-sized views are the most accurate. Essentially all these images are composed of the same figures arranged in slightly varying patterns. I kept zooming out until Fractint (Richard's Fractint for Windows beta 5) wouldn't zoom out any more and called that image the parent: (Anti-aliased, with vivid color map, to try and show any structure in the fractal.) http://www.emarketingiseasy.com/Sciwise/S170128Z.jpg Zooming in towards the right end reveals similar features: (Anti-aliased) http://www.emarketingiseasy.com/Sciwise/S170128A.jpg Another further zoom in, with the color map shown: http://www.emarketingiseasy.com/Sciwise/S170128B.jpg Further zooming in gives: http://www.emarketingiseasy.com/Sciwise/S170128C.gif The left end of the figure in C: http://www.emarketingiseasy.com/Sciwise/S170128D.gif Center right figure in D: http://www.emarketingiseasy.com/Sciwise/S170128E.gif Further zooming into E: http://www.emarketingiseasy.com/Sciwise/S170128F.gif http://www.emarketingiseasy.com/Sciwise/S170128G.gif The figure at the "knee" of G: http://www.emarketingiseasy.com/Sciwise/S170128H.gif A zoom showing the area around the center dark triangle of H. The smooth edges are starting to get ragged from loss of precision, as mentioned by Sciwise: http://www.emarketingiseasy.com/Sciwise/S170128J.gif Fractint refuses to zoom in any farther due to the extreme precision loss: http://www.emarketingiseasy.com/Sciwise/S170128L.gif My PAR file is pasted below and is also on my server: http://www.emarketingiseasy.com/Sciwise/170128.PAR - Hal Lane ######################## # hallane@earthlink.net ######################## ----- Begin PAR file: ----- comment { Date: Sat 1/28/2017 9:40 AM Subj: [Fractint] Lambert W From: Fractint <fractint-bounces@mailman.xmission.com>; on behalf of; sciwise@ihug.co.nz This is a late night , early morning , endeavour ; therefore not as well investigated as usual. There are fractals for the power tower however there didn't appear to be anything for the basic Lambert W function. _______________________________________________ Fractint mailing list Fractint@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint } LamW-test1 { ; 256 enntry color map w contrasting colors ; Set Periodicity=3 ; Fractal area set for Evolver compatibility. ; Richard's Fractint For Windows beta 5 w 0.75 ; image aspect ratio correction applied! reset=2099 type=formula formulafile=170125Nm.PAR formulaname=LamW passes=1 center-mag=0/0/0.08707267/0.75 params=0/0.09375 float=y maxiter=2048 inside=0 periodicity=1 sound=off colors=000z00<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<\ 3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K0\ 00z<3>00Kz0z<3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAA\ A000z00<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKz\ z0<3>KK0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K000z<3>\ 00Kz0z<3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z0\ 0<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKzz0<3>K\ K0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K000z<3>00Kz0z\ <3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z00<3>K0\ 00z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKzz0pp0 } frm:LamW(XAXIS) {; Edward Montague (c) 2017 ; ; Checked for complex values with Maxima ; ; Lambert's W function via Halley's root finding ; algorithm , with addition imaginary constant . ; ; ; c = z = Pixel w=0.1 : wold=w w=w - (w*exp(w) - z)/((exp(w)*(w+1)-(w+2)*(w*exp(w)-z)/(2*w+2))+(0,0.000001)) .000001 < |w-wold| ; && |w| } LamW-test2 { ; 256 enntry color map w contrasting colors ; Set Periodicity=0 = NO Periodicity! ; Can't zoom out any farther! ; Richard's Fractint For Windows beta 5 w 0.75 ; Fractint Version 2099 Patchlevel 8 reset=2099 type=formula formulafile=170128.PAR formulaname=lamw passes=1 center-mag=-9620/0/7.7e-005/0.75 float=y maxiter=2048 inside=0 periodicity=0 sound=off colors=000z00<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<\ 3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K0\ 00z<3>00Kz0z<3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAA\ A000z00<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKz\ z0<3>KK0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K000z<3>\ 00Kz0z<3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z0\ 0<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKzz0<3>K\ K0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K000z<3>00Kz0z\ <3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z00<3>K0\ 00z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKzz0pp0 } LamW-image-A { ; 256 enntry color map w contrasting colors ; Set Periodicity=0 = NO Periodicity! ; ; Richard's Fractint For Windows beta 5 w 0.75 ; Fractint Version 2099 Patchlevel 8 reset=2099 type=formula formulafile=170128.PAR formulaname=lamw passes=1 center-mag=19.5617/6.65068e-012/0.011538/0.75 float=y maxiter=2048 inside=0 periodicity=0 sound=off colors=000z00<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<\ 3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K0\ 00z<3>00Kz0z<3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAA\ A000z00<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKz\ z0<3>KK0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K000z<3>\ 00Kz0z<3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z0\ 0<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKzz0<3>K\ K0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K000z<3>00Kz0z\ <3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z00<3>K0\ 00z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKzz0pp0 } LamW-image-B { ; 256 enntry color map w contrasting colors ; Set Periodicity=0 = NO Periodicity! ; ; Richard's Fractint For Windows beta 5 w 0.75 ; Fractint Version 2099 Patchlevel 8 reset=2099 type=formula formulafile=170128.PAR formulaname=lamw passes=1 center-mag=-0.846865/0/2.7264/0.75 float=y maxiter=2048 inside=0 periodicity=0 sound=off colors=000z00<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<\ 3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K0\ 00z<3>00Kz0z<3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAA\ A000z00<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKz\ z0<3>KK0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K000z<3>\ 00Kz0z<3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z0\ 0<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKzz0<3>K\ K0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K000z<3>00Kz0z\ <3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z00<3>K0\ 00z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKzz0pp0 } LamW-image-C { ; 256 enntry color map w contrasting colors ; Set Periodicity=0 = NO Periodicity! ; ; Richard's Fractint For Windows beta 5 w 0.75 ; Fractint Version 2099 Patchlevel 8 reset=2099 type=formula formulafile=170128.PAR formulaname=lamw passes=1 center-mag=-0.40557902602007789/+0.000000000000000\ 00/1108653/0.75 float=y maxiter=2048 inside=0 periodicity=0 sound=off colors=000z00<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<\ 3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K0\ 00z<3>00Kz0z<3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAA\ A000z00<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKz\ z0<3>KK0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K000z<3>\ 00Kz0z<3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z0\ 0<3>K000z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKzz0<3>K\ K0AA0zzz<3>KKKAAA000z00<3>K000z0<3>0K000z<3>00Kz0z\ <3>K0K0zz<3>0KKzz0<3>KK0AA0zzz<3>KKKAAA000z00<3>K0\ 00z0<3>0K000z<3>00Kz0z<3>K0K0zz<3>0KKzz0pp0 } ----- End PAR file -------- --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus