Re: [Fractint] Roots of Mandelbrot Set
Edward,
Using my established method for finding the derivative of the Mandelbrot series and Newton's formula for finding the roots of a function I produced this formula .
In theory there a convergence towards the roots is expected , meaning that the condition for bailout happens when |x| approaches a small value . This isn't obvious with this formula , any improvements are welcome .
Your formula does produce an interesting image. Periodicity needs to be set to 0. This can be done like this: R1Mandel(XAXIS)[periodicity=0] {;sciwiseg , Edward Montague ... Jonathan
R1Mandel(XAXIS) {;sciwiseg , Edward Montague ; ; Roots of Mset via derivative of Mset . ; ; y , derivative ; x , Mset . ; ; x = Pixel y = 1 :
y= 2*x*y+1 x = x*x + Pixel
x = x - (x/y)
x| < 4
}
Let's see a hi-res image please! Thanks. On 10 December 2017 at 16:51, Jonathan Osuch <osuchj@mediacombb.net> wrote:
Edward,
Using my established method for finding the derivative of the Mandelbrot series and Newton's formula for finding the roots of a function I produced this formula .
In theory there a convergence towards the roots is expected , meaning that the condition for bailout happens when |x| approaches a small value . This isn't obvious with this formula , any improvements are welcome .
Your formula does produce an interesting image. Periodicity needs to be set to 0. This can be done like this:
R1Mandel(XAXIS)[periodicity=0] {;sciwiseg , Edward Montague ...
Jonathan
R1Mandel(XAXIS) {;sciwiseg , Edward Montague ; ; Roots of Mset via derivative of Mset . ; ; y , derivative ; x , Mset . ; ; x = Pixel y = 1 :
y= 2*x*y+1 x = x*x + Pixel
x = x - (x/y)
x| < 4
}
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Thanks for the code correction . The second to last line of code should have a |x| < , perhaps the copy and paste was in error . Prior to someone producing a high resolution image I shall attempt to adjust the bailout conditions . On Mon, Dec 11, 2017 at 3:06 AM, Tony Hanmer <a.hanmer@gmail.com> wrote:
Let's see a hi-res image please! Thanks.
On 10 December 2017 at 16:51, Jonathan Osuch <osuchj@mediacombb.net> wrote:
Edward,
Using my established method for finding the derivative of the Mandelbrot series and Newton's formula for finding the roots of a function I produced this formula .
In theory there a convergence towards the roots is expected , meaning that the condition for bailout happens when |x| approaches a small value . This isn't obvious with this formula , any improvements are welcome .
Your formula does produce an interesting image. Periodicity needs to be set to 0. This can be done like this:
R1Mandel(XAXIS)[periodicity=0] {;sciwiseg , Edward Montague ...
Jonathan
R1Mandel(XAXIS) {;sciwiseg , Edward Montague ; ; Roots of Mset via derivative of Mset . ; ; y , derivative ; x , Mset . ; ; x = Pixel y = 1 :
y= 2*x*y+1 x = x*x + Pixel
x = x - (x/y)
x| < 4
}
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I'm continuing to sort out the root finding formula for the Mset , there are plenty of similar formulas for finding the roots of a polynomial and various function . The Mset however is bit unique . So along the way I've produced this formula . R2Mandel(XAXIS) {;sciwiseg , Edward Montague ; ; Roots of Mset via derivative of Mset . ; ; y , derivative ; z2 , Mset . ; ; x = Pixel z2=1 y = 1 : y= 2*x*y+1 z2 = x*x + Pixel x = x - (z2/y) .0001 < |z2| } On Mon, Dec 11, 2017 at 7:11 AM, Edward Montague <sciwiseg@gmail.com> wrote:
Thanks for the code correction .
The second to last line of code should have a |x| < , perhaps the copy and paste was in error .
Prior to someone producing a high resolution image I shall attempt to adjust the bailout conditions .
On Mon, Dec 11, 2017 at 3:06 AM, Tony Hanmer <a.hanmer@gmail.com> wrote:
Let's see a hi-res image please! Thanks.
On 10 December 2017 at 16:51, Jonathan Osuch <osuchj@mediacombb.net> wrote:
Edward,
Using my established method for finding the derivative of the Mandelbrot series and Newton's formula for finding the roots of a function I produced this formula .
In theory there a convergence towards the roots is expected , meaning that the condition for bailout happens when |x| approaches a small value . This isn't obvious with this formula , any improvements are welcome .
Your formula does produce an interesting image. Periodicity needs to be set to 0. This can be done like this:
R1Mandel(XAXIS)[periodicity=0] {;sciwiseg , Edward Montague ...
Jonathan
R1Mandel(XAXIS) {;sciwiseg , Edward Montague ; ; Roots of Mset via derivative of Mset . ; ; y , derivative ; x , Mset . ; ; x = Pixel y = 1 :
y= 2*x*y+1 x = x*x + Pixel
x = x - (x/y)
x| < 4
}
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A further bit of code was required in the declaration of the formula . R2Mandel(XAXIS) [periodicity=0] {;sciwiseg , Edward Montague ; ; Roots of Mset via derivative of Mset . ; ; y , derivative ; z2 , Mset . ; ; x = Pixel z2=1 y = 1 : y= 2*x*y+1 z2 = x*x + Pixel x = x - (z2/y) .0001 < |z2| } On Mon, Dec 11, 2017 at 9:57 AM, Edward Montague <sciwiseg@gmail.com> wrote:
I'm continuing to sort out the root finding formula for the Mset , there are plenty of similar formulas for finding the roots of a polynomial and various function .
The Mset however is bit unique .
So along the way I've produced this formula .
R2Mandel(XAXIS) {;sciwiseg , Edward Montague ; ; Roots of Mset via derivative of Mset . ; ; y , derivative ; z2 , Mset . ; ; x = Pixel z2=1 y = 1 :
y= 2*x*y+1 z2 = x*x + Pixel
x = x - (z2/y)
.0001 < |z2| }
On Mon, Dec 11, 2017 at 7:11 AM, Edward Montague <sciwiseg@gmail.com> wrote:
Thanks for the code correction .
The second to last line of code should have a |x| < , perhaps the copy and paste was in error .
Prior to someone producing a high resolution image I shall attempt to adjust the bailout conditions .
On Mon, Dec 11, 2017 at 3:06 AM, Tony Hanmer <a.hanmer@gmail.com> wrote:
Let's see a hi-res image please! Thanks.
On 10 December 2017 at 16:51, Jonathan Osuch <osuchj@mediacombb.net> wrote:
Edward,
Using my established method for finding the derivative of the Mandelbrot series and Newton's formula for finding the roots of a function I produced this formula .
In theory there a convergence towards the roots is expected , meaning that the condition for bailout happens when |x| approaches a small value . This isn't obvious with this formula , any improvements are welcome .
Your formula does produce an interesting image. Periodicity needs to be set to 0. This can be done like this:
R1Mandel(XAXIS)[periodicity=0] {;sciwiseg , Edward Montague ...
Jonathan
R1Mandel(XAXIS) {;sciwiseg , Edward Montague ; ; Roots of Mset via derivative of Mset . ; ; y , derivative ; x , Mset . ; ; x = Pixel y = 1 :
y= 2*x*y+1 x = x*x + Pixel
x = x - (x/y)
x| < 4
}
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participants (3)
-
Edward Montague -
Jonathan Osuch -
Tony Hanmer