Sciwise got me interested in trying his formula for Volterra-Lotka fractals. First I made his 'x' and 'y' initialization constants into parameters and then had Fractint's Evolver vary them from (0,0) to (1,1) in a quick & dirty Solid Guessing mode: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtka7.gif I then zoomed into the parameter space nearer to the (0.0) [lower left corner.]: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtka9.gif and found some variation as a function of the two parameters. I then: - selected a thumbnail image in the Evolver, - exited the Evolver, - set Single Pass, and - raised maxiter from 512 to 2048 (I think it was), and got this image: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk11.gif Be sure to not let your browser resample the image -- just click on it once. Sciwise's use of the Volterra-Lotka equations gives quite a different image from Fractint's built in Volterra-Lotka fractal. I used Richard's Fractint for Windows beta 5 (now called Iterated Dynamics) http://tinyurl.com/FractInt-for-Win-beta5 or: https://legalizeadulthood.wordpress.com/2007/04/13/fractint-for-windows-beta -5/ running on Windows 8.1(!) for the first time to create these images. Sorry to not have the PAR file, but I overflowed a buffer in the code and crashed the program while trying to save the PAR file -- likely due to my having too long a directory name. - Hal Lane ######################## # hallane@earthlink.net ######################## -----------Original Message------------- Author: sciwise Date: 2015-11-07 23:49 -500 To: fractint Subject: [Fractint] Volterra Lotka PH This is the second part of the Volterra Lotka formulas , in this instance we are selecting an initial condition and varying the parameters p & h across the plane. There's now another FreeBASIC file to obtain the sequences from the map generated by V-HeunPH.frm . The coordinates I used were : Top left corner: -2.0 1.5 Bottom right corner: 2 -1.5 ---------------------------------------------------------------------------- ------- comment{ Volterra Lotka , p , h variable . V-HeunPH.frm initial condition [ x = 0.8 , y=0.8 ], this initial condition might be determined from the V-Heun map . [ p , h ] varied over plane . x' = x - x*y y' = -y + x*y } V-HeunPH { x=0.8 y=0.8 p=real(pixel) h=imag(pixel): u=x-x*y w=-y+x*y a=x+p*u b=y+p*w c=x+h*(u+(a-a*b)) d=y+h*(w+(-b+a*b)) x=c y=d z=x+flip(y) |z| } --- --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus