------------- Edward Montague posted: ------------------
Over at Fractal Forums, which I can't reach at present...
When I went to <https://www.fractalforums.com/> just now (Aug 20, 2023 ~1:20 am EST [USA]) I did get a page to load, which said: ####################################################### END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG it was a great time but no longer maintainable by c.Kleinhuis Contact him for any data retrieval, thanks and see you perhaps in 10 years again /// this forum will stay online for reference /// The All New FractalForums https://fractalforums.org/ is now in Public Beta Testing! Visit FractalForums.org and check it out! ####################################################### The New FractalForums currenntly has a very modest number of posts. I haven't had a chance to try the formulas you posted (thanks!) yet, but I hope to soon. - Hal Lane ######################## # hallane@earthlink.net ######################## -----Original Message----- From: Edward Montague <sciwiseg@gmail.com> Sent: Saturday, August 19, 2023 3:55 AM To: fractint@mailman.xmission.com Subject: [Fractint] Mandel deriv inte Over at Fractal Forums, which I can't reach at present, there's an attempt to integrate the Mandelbrot series via the Euler method or similar. It occurs to me that one way to check the validity of this approach is to apply the integration method to the derivative of the Mandelbrot series. This is my initial attempt, feel free to make your own formulas from this. Try p2 between 0.01 and 1 For d--mand, p1 should be large For ed-mand , p1 0.1, p2 0.01 , or similar , this is examining the region where integral of the derivative is mostly the same as the iterated function. d--mand.frm ; Euler integration method, y[n+1] = y[n] + h*f(tn,y[n]) ; For Mandelbrot set, f(tn,y[n]) = y[n]^2 + c ; y[n+1]=y[n] + h*(y[n]^2 + c) e---mand {; Ed Mont, (c) 2023 z = c = pixel, u = p2*z : z = z^2 + c; u = u + p2*z |u|<p1 } ; First derivative of the Mandelbrot series . ; z[n+1]' = ( 2*z[n]'*z[n] ) + 1 d---mand {; Ed Mont, (c) 2023 z = c = pixel, u=1: u = (2*u*z) + 1 z = z^2 + c; |u|<p1 } ; First derivative of the Mandelbrot series . ; z[n+1]' = ( 2*z[n]'*z[n] ) + 1 ; Then Eulers method . ed---mand {; Ed Mont, (c) 2023 z = c = pixel, u=1, w = p2*u,v=c: z=v u = (2*u*z) + 1 w = w + p2*u v = z^2 + c |w-z| < p1 } _______________________________________________ Fractint mailing list -- fractint@mailman.xmission.com To unsubscribe send an email to fractint-leave@mailman.xmission.com