October 2016 - Fractint - mailman.xmission.com

A Differential Equation
by sciwise＠ihug.co.nz 14 Nov '16

14 Nov '16

Continuing from previous posts on the topic of the derivative[s] of the Mandelbrot Series. I now attempt to examine the regions of stability for this D.E. y'' + y' + y'*y' + y - exp(y*y') = 0 Where I set y equal to the Mandelbrot series , with initial conditions determined by the value of Pixel. I remain uncertain at this stage as to how to interpret the results. I'm assuming that the regions with the fewest iterations are what we require. Another approach to solving second order differential equations is to use the Euler - Heun method ; this however provides less information as it's usually implemented as a purely numerical approach. Non linear differential equations have been difficult to solve as the elementary functions don't provide the scope required. Anyway here's the code . de2bmand(XAXIS){; Edward Montague ; 2nd order non linear differential equation = z. ; y'' + y' + y'*y' + y - exp(y*y') = 0 ; 2nd derivative of mandelbrot series = w. ; 1st derivative of mandelbrot series = u. ; Mandelbrot series = v v = Pixel u = 1 w = 0 z = 0: w = 2*u*u +2*w*v u = 2*v*u + 1 z = w +u + u*u + v - exp(v*u) v = v*v+Pixel |z| < 1 }

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Re: [Fractint] We're still alive and well at Fractal Central
by David Jones 29 Oct '16

29 Oct '16

Everyone has their own personal PTSD reaction to the 9/11/01 WTC attacks. I guess Jim's choice to turn to the "irrational" side of the Force is his. ;) David W. Jones gnome(a)hawaii.rr.com authenticity, honesty, community http://dancingtreefrog.comOn Oct 27, 2016 15:07, John Wilson <1stdiscus(a)gmail.com> wrote: > > Really? > "I find it easier to believe than something unknown is creating the more > intricate of these formations other than a couple guys with boards or > groups who show that at least the more simple circles could be done by > humans in one night." > > How about--- http://www.mymodernmet.com/profiles/blogs/simon-beck-snow-art > > One guy only! He hasn't enlisted any unknowns either. > > John W. > > On 27 October 2016 at 11:49, Jim Muth <jimmuth(a)earthlink.net> wrote: > > > > > Fractal fans of years past: > > > > We're still alive and kicking here at Fractal Central, > > but things have not been going too well in the past > > couple months. To start, we found a one week old > > abandoned kitten in the fractal yard on July 31, which > > we bottle fed until it was old enough to take care of > > itself. Then the oldest fractal cat, Nicholas, passed > > away on September 27, and we decided to keep the > > orphan kitten, which is a little girl we named Riley. > > The new girl is now 14 weeks old and learning how to > > get along with the established cats, Jasmine and Lida. > > But being raised by humans, she does not yet know how > > to properly interact with other cats, and some > > occasional hissing and growling still occurs. > > > > As for the fractals, I am still very interested in > > them, but I am also becoming quite interested in > > things that are not totally rational, such as alien > > abductions, crop circles, bigfoots, hauntings and > > other things widely considered paranormal. I have > > never seen a convincing image of an alien, ghost or > > bigfoot on a TV show, but crop circles definitely > > have existed. The photos are plentiful, and despite > > the claims that they are all hoaxes, which appears to > > satisfy skeptics, I find it easier to believe that > > something unknown is creating the more intricate of > > these formations other than a couple guys with boards > > or groups who show that at least the more simple > > circles could be done by humans in one night. > > > > Perhaps the most intriguing thing of all I have gotten > > into is the furor between materialists and idealists > > over the meaning of the quantum discoveries of the > > past almost 100 years as they apply to the everyday > > world. I see materialists defending their position > > that the material world is real, while idealists are > > claiming that material is an illusion created by the > > mind, a belief that supports the mystical claims of > > eastern religions. Since no one really understands > > the quantum, both sides can spin the quantum > > discoveries and results of experiments to make it > > appear as their own theory of reality is true, but to > > me at least, it appears that the materialist side is > > doing the greater amount of spinning. I also notice > > that materialists are quicker to slip into anger and > > launch ad hominem attacks when they have no real > > rebuttal of idealist claims. To me this is how people > > react when they begin to doubt their own beliefs. > > > > Then again, maybe it's all a tempest in a teapot . . . > > > > Jim M. > > > > _______________________________________________ > > Fractint mailing list > > Fractint(a)mailman.xmission.com > > https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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We're still alive and well at Fractal Central
by Jim Muth 28 Oct '16

28 Oct '16

Fractal fans of years past: We're still alive and kicking here at Fractal Central, but things have not been going too well in the past couple months. To start, we found a one week old abandoned kitten in the fractal yard on July 31, which we bottle fed until it was old enough to take care of itself. Then the oldest fractal cat, Nicholas, passed away on September 27, and we decided to keep the orphan kitten, which is a little girl we named Riley. The new girl is now 14 weeks old and learning how to get along with the established cats, Jasmine and Lida. But being raised by humans, she does not yet know how to properly interact with other cats, and some occasional hissing and growling still occurs. As for the fractals, I am still very interested in them, but I am also becoming quite interested in things that are not totally rational, such as alien abductions, crop circles, bigfoots, hauntings and other things widely considered paranormal. I have never seen a convincing image of an alien, ghost or bigfoot on a TV show, but crop circles definitely have existed. The photos are plentiful, and despite the claims that they are all hoaxes, which appears to satisfy skeptics, I find it easier to believe that something unknown is creating the more intricate of these formations other than a couple guys with boards or groups who show that at least the more simple circles could be done by humans in one night. Perhaps the most intriguing thing of all I have gotten into is the furor between materialists and idealists over the meaning of the quantum discoveries of the past almost 100 years as they apply to the everyday world. I see materialists defending their position that the material world is real, while idealists are claiming that material is an illusion created by the mind, a belief that supports the mystical claims of eastern religions. Since no one really understands the quantum, both sides can spin the quantum discoveries and results of experiments to make it appear as their own theory of reality is true, but to me at least, it appears that the materialist side is doing the greater amount of spinning. I also notice that materialists are quicker to slip into anger and launch ad hominem attacks when they have no real rebuttal of idealist claims. To me this is how people react when they begin to doubt their own beliefs. Then again, maybe it's all a tempest in a teapot . . . Jim M.

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Condolence
by John Wilson 28 Oct '16

28 Oct '16

BTW, Jim. So sorry about Nicholas--- I think he was a friend of all of those who followed your works. John W.

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Re: [Fractint] We're still alive and well at Fractal Central
by David Jones 27 Oct '16

27 Oct '16

On Oct 27, 2016 09:37, Bill Jemison wrote: > > On Thu, Oct 27, 2016 at 12:49 PM, Jim Muth wrote: > > > maybe it's all a tempest in a teapot . . . > > > > or maybe it's all a tempest in a teapot in a tempest in a teapot in a > tempest etc... > > Bill > audiofractals <https://sites.google.com/site/audiofractals/home> Reality is a figment of your imagination. Reality is what kills you. David W. Jones gnome(a)hawaii.rr.com authenticity, honesty, community http://dancingtreefrog.com

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Looking the other way
by sciwise＠ihug.co.nz 15 Oct '16

15 Oct '16

If you look at the fractal generated by my differential equation , for |z| > 10000 ; then the traditional Mandelbrot set appears plus embellishments. I shall examine a more well known differential equation at some other stage. There are various to choose from. Sciwise

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