The group might be able to do something with this . I changed the bailout value to 4 and was able to see a few more iterations than when it was 0.1 . I'm in the process of trying different functions and color maps.
I set p1 and the function in the z screen. With p1=0 (making the bailout be 4), the function exp() get iterations up into the 30's. - Hal Lane ######################## # hallane@earthlink.net ######################## -------- Start of PAR file: ---------------- IntgrDerivOfMset { ; hhlane Colors from Jim Muth reset=2004 type=formula formulafile=basicer.frm formulaname=f1Mandelbrot passes=1 center-mag=-0.465582/0.0/1.0/1/ float=y maxiter=1000 inside=0 logmap= periodicity=6 colors=00054L65K76K87K98K99MAAOABQ9CS9EU9GW9IY8K_8\ La8Mc8NeAPcBQaDS`ETZGVYHWWIYVKZTL`SNaQOcPQdNRfMSgK\ UiJVjHXlGYmE_oD`pBaqA`oC`nD_mE_lFZkGZjIYiJYhKXgLXf\ MXeNWcPWbQVaRV`SU_TUZVTYWTXXSWYSVZSVZSV_SV_KWVCZQ4\ `L6aO7aQ9bTAbVBcXDc_EdaGddHefIehKfkMfmOfnQfnSfoU_o\ UZoVYoVXoWWpWVmXUjXTgYSdYQaZOZZPW_MT_JR`GQ`DM_BJYA\ F_6AY6BX6CW6CV7DT7ES8ER9FQAGPBGNBHMCILDIKEJJFKHFKG\ GLFHMEIMDJNBJOAKO9LP8MQ3PR5NQ7MQ9LQBJQDIQFHQGGQIEQ\ KDQMCQOAQQ9QS8QT7QU9PVAPWBPXCPYDPZFP_GP`HPaIPbJPcL\ PdMPeNPfOPgPPfSJgRMhQPiPSjOVkNYlM`mMcnLfoKipJlqIor\ HrsGusGwrIurJsrLqrMprOnrPlrQkrSiqTgqVeqWdqXbqZ`q__\ qaYqbWpdUpeTpfRphPpiOpkMplKpmJolInkHmjGmjGliFkhEjh\ EjgDifChfCgeBgdAfdAdc9ba8a_8_Y7YW6ZV3ZV5ZV6_W8_Y9`\ _B`aC`cE_eF_gHZhIZiKYjLYjMYjMWkLWkKWkKVkJVlJUlIUlI\ UlHUmHUmGUmGVmFWmEYnE_oDapDdrCgsCitBkuBmvAowAqx8ty\ 7wz6zz5zz3zz2zz1zz0zzTzzU } frm:f1Mandelbrot(XAXIS) {;sciwiseg , Edward Montague ; ; | x' - fn1(Pixel) | < 0.1 ; ; Integral via derivative of Mset . x = Pixel test = (4 + p1) u = fn1(x) y = 1 : y= 2*x*y+1 z = u - y x = x*x + Pixel |z| < test } -------- End of PAR file ------------------ -----Original Message----- From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Edward Montague Sent: Monday, November 13, 2017 12:22 AM To: Fractint and General Fractals Discussion <fractint@mailman.xmission.com> Subject: Re: [Fractint] Integration under differentiation . 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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