January 2016 - Fractint - mailman.xmission.com

Re: [Fractint] David's post re "kinda fun" fractal
by Harold Lane 26 Jan '16

26 Jan '16

John, David, Do you have any idea what the thresholding is doing? http://homepages.slingshot.co.nz/~alpersj/mandelbrot/ When I was holding down the threshold "S" key, at one point the fractal does a kind of "inside out" transformation and then eventually becomes an M-set. This sudden transformation is very intriguing to me. The "inside out" transformation the fractal did reminded me of the Fractint feature: "Inversion" that I've read about. The concept is very simple, but the docs warn of such "bizarre effects" that you can need "something to hang on to." I put a copy of the Fractint docs for inversion below. I just Factory Restored my computer and can't try it on a fractal myself yet. Would someone try some inversion values (<Y> options screen) on an M-set and let me know if this is what David's post's web site is doing? I had the idea that when the inversion circle radius passed through the value of one, that this is where the fractal might be doing its inside-out flip/transformation... "Inverting through a circle not centered on the origin..." might be a fun thing to try the Fractint Evolver on! Thanks, - Hal Lane ######################## # hallane(a)earthlink.net ######################## Fractint Version 20.04 Page 92 3.5 Inversion Many years ago there was a brief craze for "anamorphic art": images painted and viewed with the use of a cylindrical mirror, so that they looked weirdly distorted on the canvas but correct in the [mirror's] distorted reflection. (This byway of art history may be a useful defense when your friends and family give you odd looks for staring at fractal images color-cycling on a CRT.) The Inversion option performs a related transformation on most of the fractal types. You define the center point and radius of a circle; Fractint maps each point inside the circle to a corresponding point outside, and vice-versa. This is known to mathematicians as inverting (or if you want to get precise, "everting") the plane, and is something they can contemplate without getting a headache. John Milnor (also mentioned in connection with the Distance Estimator Method (p. 91)), made his name in the 1950s with a method for everting a seven- dimensional sphere, so we have a lot of catching up to do. For example, if a point inside the circle is 1/3 of the way from the center to the radius, it is mapped to a point along the same radial line, but at a distance of (3 * radius) from the origin. An outside point at 4 times the radius is mapped inside at 1/4 the radius. The inversion parameters on the <Y> options screen allow entry of the radius and center coordinates of the inversion circle. A default choice of -1 sets the radius at 1/6 the smaller dimension of the image currently on the screen. The default values for Xcenter and Ycenter use the coordinates currently mapped to the center of the screen. Try this one out with a Newton (p. 49) plot, so its radial "spokes" will give you something to hang on to. Plot a Newton-method image, then set the inversion radius to 1, with default center coordinates. The center "explodes" to the periphery. Fractint Version 20.04 Page 93 Inverting through a circle not centered on the origin produces bizarre effects that we're not even going to try to describe. Aren't computers wonderful? --- --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus

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EHNewt
by sciwise＠ihug.co.nz 26 Jan '16

26 Jan '16

An attempt at solving a second order non linear differential equation has produced this formula , using Euler Heun and Newton's method ; where : x method , with complex divisor %i*s , for a second order > non linear differential equation. > > Select zmag for outer . > > } > EHNewt{; EH Newton , > w1 = pixel, > sn=-1, > Pd = 1*(10^(-13)), > a5= 42.469607686999 , > b1= 23546.24999999999 , > b2= 9.343749999999999*(10^(8)) , > b3= 96.8 , > s=0.01 > p=0.39757, > h=0.71743, > x = 0.1, > y = 0, > tol = 1: > > u = y > w = ( sn*a5*y*y+sn*(b2*x + b3)*y +sn*( sn*b2*w1 + sn*b1)*x +sn*b1)/s > w = sn*log(w)/a5 > > a = x + p*u > b = y + p*w > > c = x + h*(u + b) > d = ( sn*a*( sn*b2*w1 +sn*b1 ) +sn*b*( b3 + a*b2 ) + sn*b1 + sn*a5*b*b)/s > d = y + h*(w + d) > d = sn*log(d)/a5 > > x = c > y = d > z = y > > tol = |u-y| > tol > Pd > > }

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W.David's post
by John Wilson 25 Jan '16

25 Jan '16

http://homepages.slingshot.co.nz/~alpersj/mandelbrot/ Hal, if you carry on as you described, you do indeed, end up with a Mandelbrot with a white center. It's a .pnp image, which can be saved as a .gif for manipulation in Fractint. John

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I missed David's web page's instructions the 1st time I viewed it
by Harold Lane 25 Jan '16

25 Jan '16

In David's recent post: ------ My soon-to-be son-in-law sent me this: http://homepages.slingshot.co.nz/~alpersj/mandelbrot/ -David W. Jones gnome@??? authenticity, honesty, community http://dancingtreefrog.com ------ I missed the page's instructions at upper left (they disappear) the 1st time I viewed it: "Use the arrow keys to pan, A and Z keys to zoom, S and X keys to change the threshold." The web page is "live" -- Javascript in your browser calculates the fractal essentially instantaneously -- and you can pan and zoom ("A") into it in real time... I discovered that if you hold down the threshold "S" key for long enough, the image does a kind of "inside out" transformation and eventually becomes an M-set with a white "lake." I'm not sure what the threshold feature is doing -- but, it's not a simple color map rotation. - Hal Lane ######################## # hallane(a)earthlink.net ######################## --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus

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Re: [Fractint] Finito
by David Jones 24 Jan '16

24 Jan '16

Took his ball and went home again. I guess to Bielefeld. (Thanks for the blog follow, John!) David W. Jones gnome(a)hawaii.rr.com authenticity, honesty, community http://dancingtreefrog.com On Jan 24, 2016 04:47, John Wilson <1stdiscus(a)gmail.com> wrote: > > Albrecht Niekamp and Bielefeld <https://en.wikipedia.org/wiki/Bielefeld> do > not actually exist. > > On 23 January 2016 at 23:39, Albrecht Niekamp <multifrac(a)t-online.de> wrote: > > > Archives included > > Albrecht

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Finito
by Albrecht Niekamp 24 Jan '16

24 Jan '16

Archives included Albrecht

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Re: [Fractint] Kinda fun despite wonky resolution and color shading
by David Jones 23 Jan '16

23 Jan '16

On Jan 23, 2016 11:21, Multifrac(a)t-online.de wrote: > > On 23.01.2016 06:32, david wrote: > > My soon-to-be son-in-law sent me this: > ; > Why posting such junk? It´s not even fractal. Hmm, actually, it's a rendering of the Mandelbrot set, so it is fractal. Low res and little or no color pallette. > If you don´t like what I´m doing you can just > say so or remain silent. My, sensitive are we? Has nothing to do with your fascinating and amazing achievements with DOS Fractint. Which I like very much, by the way. > Albrecht David W. Jones gnome(a)hawaii.rr.com authenticity, honesty, community http://dancingtreefrog.com

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Kinda fun despite wonky resolution and color shading
by david 23 Jan '16

23 Jan '16

My soon-to-be son-in-law sent me this: http://homepages.slingshot.co.nz/~alpersj/mandelbrot/ -- David W. Jones gnome(a)hawaii.rr.com authenticity, honesty, community http://dancingtreefrog.com

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Re: [Fractint] Another Niekamp animation by JoTz
by Harold Lane 21 Jan '16

21 Jan '16

----- JoTz said: ------ > Another Niekamp animation [links below]... Another great zoom, JoTz! I can't get over the fact that at every magnification, Albrecht's fractal formula provides a well-balanced scene with great detail and good coloring... Thanks Albrecht, JoTz! Btw, I like to watch JoTz's videos at 1/2 speed, so those great scenes don't go by so quickly -- so I can savor those nicely-arranged pixels... - Hal Lane ######################## # hallane(a)earthlink.net ######################## -----Original Message------------------------------------------------------------- From: Fractint [mailto:fractint-bounces+hallane=earthlink.net@mailman.xmission.com] On Behalf Of Harold Lane Sent: Wednesday, January 20, 2016 9:41 PM To: 'LLOYD GARRICK' <lgarr(a)colorado-hiking.net>; Albrechtx_Multifract!!! <Multifrac(a)t-online.de>; 'Fractint and General Fractals Discussion' <fractint(a)mailman.xmission.com> Subject: Re: [Fractint] <Albrecht> I´m asking myself is it makes any sense to go on... ----------- JoTz said: --------- > [Hal,] Please post to the group as I still do not have access: - Hal Lane ######################## # hallane(a)earthlink.net ######################## -----Original Message------------------------------------------------------------- From: LLOYD GARRICK [mailto:lgarr@colorado-hiking.net] Sent: Wednesday, January 20, 2016 9:04 PM To: Harold Lane <hallane(a)earthlink.net>; Albrechtx_Multifract!!! <Multifrac(a)t-online.de>; Fractint and General Fractals Discussion <fractint(a)mailman.xmission.com> Subject: Re: [Fractint] <Albrecht> I´m asking myself is it makes any sense to go on... . [Hal,] Please post to the group as I still do not have access: Another Niekamp animation; both AVI: 400Meg http://www.fractal-animation.net/special/PearlyGates1024.zip 200Meg http://www.fractal-animation.net/special/PearlyGates640.zip Comments welcome. --- 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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(Fractint] Fractal Trip
by Albrecht Niekamp 21 Jan '16

21 Jan '16

Fractal Trip ; Sometimes, - the Fractint users are aware of it -, I come up with something completely new to keep progress and curiosity alive. Today it´s the Fractal Trip: Starting from a zoom into the center of the parent view, I calculate maximum zooms - the zoombox at minimum size and exactly in the center. Starting this expereriment I did not know the result but was positively surprised, more then once on the way to the deepest possible zoom, number twelve. This means the images should be watched in their predefined sequence ranging from 70 to 82. The next to final zooms 80 and 81 have an identical x-axis but the y-axis has been slightly altered as interesting alternatives turned up, so there are three images with number80 and two with number 81. Number 82 already shows bigger pixels as it is the deepest possible zoom. ; Any feedback is welcome, I also regard it as an encouragement to go on. ; https://www.cubbyusercontent.com/pl/MultifracArchive/_67536d81761949e592b93… ; Path: MultifracArchive/New/Newgif Images 70-82 Path: MultifracArchive/New/Newpar\NEW.PAR ; Albrecht Das Wort für Welt ist Wald

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