November 2016 - Fractint - mailman.xmission.com

Another series derivative
by sciwise＠ihug.co.nz 25 Nov '16

25 Nov '16

This is the first derivative of the iteration z= sin(z) + c . I'm standardizing the variables , z for series , u for first derivative, v for second derivative. d1cos(XAXIS){; Edward Montague ; (c) Copyright 2016 ; ; z = sin(z) + c ; 1st derivative of z series = u. ; c = Pixel z = c u = 1 u0 = u: u = cos(z)*u + u0 z = sin(z)+c |u| < 10000 }

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Re: [Fractint] I live in New Zealand , where there are major fault lines around the country.
by Harold Lane 22 Nov '16

22 Nov '16

> I live in New Zealand , where there are major fault lines around the > country. Were you affected by the current earthquake and aftershocks? Are you OK? - Hal Lane ######################## # hallane(a)earthlink.net ######################## ---------------Original Message----------------------------------- From: Fractint [mailto:fractint-bounces+hallane=earthlink.net@mailman.xmission.com] On Behalf Of sciwise(a)ihug.co.nz Sent: Saturday, October 29, 2016 9:48 AM To: fractint(a)mailman.xmission.com Subject: Re: [Fractint] We're still alive and well at Fractal Central Hi I live in New Zealand , where there are major fault lines around the country. The Christchurch earthquake that made the news a few years ago was quite devastating ; problems with liquefaction , in the suburbs persist through to the present. The inner city was built upon basaltic rock , nevertheless there was widespread damage to new and old buildings alike. Prior to the earthquake various oil companies were using horizontal drilling in an attempt to find oil and gas deposits. Of course earthquake fissures assume a fractal pattern. If you've ever read about Nikola . Tesla then you might appreciate how he was dealing with fractal objects ; like the electrical discharges that he was so well known for. Sciwise On 28/10/2016 ---------------------------------16:48, Kathleen Roth wrote: --------------- > "I was told that the truth of the matter > is that these days a skyscraper can be built on a swamp, and that the force > distributing buildings large and small over the island was the aggregate of > many financial decisions by developers over the centuries." > > Interesting to see this discussion here. In fact, very much in the news in > the San Francisco Bay Area is the Millennium tower that was completed > in 2009. It does not have a foundation that goes to bedrock. It has 58 stories and a foundation that goes ~80 feet into > bay-fill that can liquefy in an earthquake. It has been sinking at > a much faster rate than predicted and is now tilting. > They are claiming that it is still safe in an earthquake. > My medium-sized wood frame house near the Hayward fault has concrete piers that > go 14-24' into the ground, into bedrock. > > http://www.sfchronicle.com/bayarea/article/As-charges-fly-in-SF-tests-begin- on-sinking-9289898.php [12] > > http://sf.curbed.com/2016/9/16/12945600/why-millennium-tower-sinking [13] > > Kathy Roth > > ----- Original Message ----- > From: "Timothy Wegner" > To: "Fractint and General Fractals Discussion" > Sent: Thursday, October 27, 2016 7:37:23 PM > Subject: Re: [Fractint] We're still alive and well at Fractal Central > > David wrote: > >> Everyone has their own personal PTSD reaction to the 9/11/01 WTC attacks > > I just returned from a visit to NYC for the first time in 35 years. The > visit to the 911 memorial was certainly an intense experience. While not > exactly a fractal, a giant twisted beam in the basement had assumed a shape > I found strange indeed. The rectangle-based structure of the beam built > originally straight from Plato's world of forms had morphed into multiple > twists and loops under forces beyond imagination. The result was a > sculpture that looked more from nature than human imagination. > > Manhatten itself can be seen, from one perspective, as a fractal. I asked > about the distribution of the buildings and skyscrapers. While possibly > true once, the oft-repeated claim that the sturdy New York bedrock is what > permitted the over-scale buildings, I was told that the truth of the matter > is that these days a skyscraper can be built on a swamp, and that the force > distributing buildings large and small over the island was the aggregate of > many financial decisions by developers over the centuries. > > My condolences also to Jim concerning the fractal cat. > > Tim > > On Thu, Oct 27, 2016 at 8:54 PM, David Jones wrote: > >> 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 [7] authenticity, honesty, community http://dancingtreefrog.comOn [8] Oct 27, 2016 15:07, John Wilson < 1stdiscus(a)gmail.com [9]> 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- [1] >> snow-art >> >>> One guy only! He hasn't enlisted any unknowns either. John W. On 27 October 2016 at 11:49, Jim Muth 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 [2] https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [3] >>> _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com [5] https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [6] >> _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com [10] https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [11] > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com [17] > https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [18] > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com [19] > https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [20] Links: ------ [1] http://www.mymodernmet.com/profiles/blogs/simon-beck- [2] mailto:Fractint@mailman.xmission.com [3] https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [4] mailto:jimmuth@earthlink.net [5] mailto:Fractint@mailman.xmission.com [6] https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [7] mailto:gnome@hawaii.rr.com [8] http://dancingtreefrog.comOn [9] mailto:1stdiscus@gmail.com [10] mailto:Fractint@mailman.xmission.com [11] https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [12] http://www.sfchronicle.com/bayarea/article/As-charges-fly-in-SF-tests-begin- on-sinking-9289898.php [13] http://sf.curbed.com/2016/9/16/12945600/why-millennium-tower-sinking [14] mailto:tim@tswegner.net [15] mailto:fractint@mailman.xmission.com [16] mailto:gnome@hawaii.rr.com [17] mailto:Fractint@mailman.xmission.com [18] https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [19] mailto:Fractint@mailman.xmission.com [20] 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 --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus

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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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