Sciwise suggested modifying P1 values passed into the Newman1 formula he posted to see if that could shed some light on the fractal. So, I used Fractint's Evolver (<ctrl><e>) to specify P1 values. I set the Evolver to: - vary real(P1) across the grid of fractal thumbnails in X, and to - vary imag(P1) up and down the grid of fractal thumbnails in Y to see what might appear. I also filled all 256 values of the color map with contrasting colors to try and not miss seeing any features of the fractal: http://www.emarketingiseasy.com/Sciwise/170125color-map.jpg I didn't see a way to have Fractint write out a file containing the Evolvers' "Evolution Mode" Options, so I screen captured my settings: http://www.emarketingiseasy.com/Sciwise/170125evolv-F.jpg For those not familiar with Fractint's Evolver -- briefly, it can draw a grid of thumbnail-sized fractals with some parameter(s) in the fractal varied across X and Y to show the fractal's sensitivity to those parameters. Each thumbnail has the identical corner locations in the complex plane -- only the automatically calculated parameters are different between the thumbnails. You'll need the Fractint docs to get more detailed info on the Evolver. The Fractint docs don't clearly say that the <b> command exits Evolver mode and draws the central thumbnail at the full size of Fractint's window. I used the Evolver to vary the real and imaginary components of P1 across and up and down the grid of thumbnail fractals. This is the grid of thumbnail images the Evolver produced: http://www.emarketingiseasy.com/Sciwise/S170125H.gif Note: Richard's Fractint for Windows beta 5 has an aspect ratio anomaly that I usually remember to correct by setting the: X Magnification Factor to 0.75 on the Image Coordinates screen: <z>, <F6> If you create these same images, the aspect ratio may not match that of mine... Here are enlargements of the three Evolver thumbnails just above the central P1=(0,0) red thumbnail: http://www.emarketingiseasy.com/Sciwise/S170125J.gif http://www.emarketingiseasy.com/Sciwise/S170125K.gif http://www.emarketingiseasy.com/Sciwise/S170125L.gif The images to the left and right of the P1=(0,0) thumbnail: http://www.emarketingiseasy.com/Sciwise/S170125M.gif http://www.emarketingiseasy.com/Sciwise/S170125N.gif And the three thumbnails just below the P1=(0,0) thumbnail: http://www.emarketingiseasy.com/Sciwise/S170125P.gif http://www.emarketingiseasy.com/Sciwise/S170125Q.gif http://www.emarketingiseasy.com/Sciwise/S170125R.gif And a zoom into S170125K above gives: http://www.emarketingiseasy.com/Sciwise/S170125S.gif Misc Settings in Above Images: ----------------------------------------- Passes=1 Maxiter=2048 Outside=iter Periodicity=3 My parameter set with Sciwise's original post and email-mauled, repaired formula are below. But, to avoid any possible email tampering with the formula's equations, you can also get it from my server: http://www.emarketingiseasy.com/Sciwise/170125Nm.PAR - Hal Lane ######################## # hallane@earthlink.net ######################## ------- Start parameter file: ------------- comment { Date: Wed 1/25/2017 8:06 AM From: Fractint <fractint-bounces@mailman.xmission.com>; on behalf of; sciwise@ihug.co.nz Subj: [Fractint] Newman1 This formula was constructed after reading a pdf from Yu and Ben-Israel. Doesn't appear to generate what I expected , maybe I need to delve into this a bit more , any comments from the list might be useful. If you comment out the line p1=1 then the parameter p1 is selectable from the parameter box. _______________________________________________ Fractint mailing list Fractint@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint } test2-RGBcmyEvolvr { ; 256 enntry color map w contrasting colors ; Set Periodicity=3 ; Fractal area set for Evolver compatibility. ; Fractint Version 2099 Patchlevel 8 reset=2099 type=formula formulafile=170125Nm.PAR formulaname=newman1 passes=1 center-mag=-2.36228/7.10543e-015/0.08707267/0.75 params=0/0.09375 float=y maxiter=2048 inside=0 periodicity=3 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:Newman1(XAXIS) {; Edward Montague(c) 2017 ; ; Supposedly equivalent to the Mandelbrot Set. ; ; Ref , The Newton and Halley Methods for Complex Roots ; Lily . Yau and Adi Ben-Israel ; ; c = z = Pixel ; p1=1 per Sciwise instructions. : ed=exp(-(2*atan((2*z-1)/sqrt(4*c-1)))/sqrt(4*c-1)-(2*atan(1/sqrt(4*c-1)))/sq rt(4*c-1)) edp=-exp(-(2*atan((2*z-1)/sqrt(4*c-1)))/sqrt(4*c-1)-(2*atan(1/sqrt(4*c-1)))/ sqrt(4*c-1))/(z^2-z+c) zold=z z=z - p1*ed/edp .0001 < |z-zold|; && |z| } ------- End parameter file --------------- --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus