Okay , this is a very basic example , doesn't look particularly interesting . It's as if integrals smooth away the fractal structure . The group might be able to do someting with this . f1Mandelbrot(XAXIS) {;sciwiseg , Edward Montague ; ; | x' - fn1(Pixel) | < 0.1 ; ; Integral via derivative of Mset . x = Pixel u = fn1(x) y = 1 : y= 2*x*y+1 z = u - y x = x*x + Pixel |z| < 0.1 } On Sun, Nov 12, 2017 at 9:34 PM, Tony Hanmer <a.hanmer@gmail.com> wrote:
Sounds intriguing! Could we have some examples, please?
Tony Hanmer
On 12 November 2017 at 07:29, Edward Montague <sciwiseg@gmail.com> wrote:
Lets examine a very basic differential equation :
y' - fn1(x) = 0
this is a test condition that we're interested in , we might even relax this to :
| y' - fn1(x) | < epi , where epi is a small tolerance .
We're quite familiar with this in fractint .
Now suppose that we're able to generate y' and y , as iterated functions . Then when the aforementioned condition is satisfied we have a value for the integral of fn1(x) at x = Pixel ; this being y .
As available , via an earlier post of mine , a general formula for finding the derivative of an iterated function .
Initially this might just be examined as a fractal .
At this stage I really don't know what this might produce ; maybe some interesting fractals . _______________________________________________ Fractint mailing list Fractint@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint
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