Please do yourself a huge favor and take the free Win 10 upgrade. The deadline is approaching in July sometime. The 8.x set should never have been released. David W. Jones gnome@hawaii.rr.com authenticity, honesty, community http://dancingtreefrog.comOn May 17, 2016 15:59, Harold Lane <hallane@earthlink.net> wrote:

I'm not as happy with the anti-aliasing I've been able to do with tools on this Win 8.1 computer compared to those on my Win XP machine.  I'm still experimenting and I've improved it somewhat. 

Thanks for clicking the images to prevent resampling.

Jim's FOTX: http://www.emarketingiseasy.com/TESTS/FOTD/2016/F160516.jpg

Jim's "...obvious minibrot at the top center edge of the frame." "An order 7 minibrot with quadratic surroundings!?" http://www.emarketingiseasy.com/TESTS/FOTD/2016/F160516A.jpg

Hal's investigations: "Reaching for Infinity": http://www.emarketingiseasy.com/TESTS/FOTD/2016/F160516B.jpg

Wow!  In this zoom into "Reaching for Infinity," if you count the number of fat blue arms that extend most of the way to the edge of the image, and also include in your count the slightly shorter blue arms midway between them, you get 8. Now, count the number of yellow-green splats forming a slightly smaller circle inside the blue arms, and you get 7. Now, count the number of arms on the black minibrot/Mandeloid, and you get 6 (called "order 7".) There's a symmetry factor for everyone in this image!: http://www.emarketingiseasy.com/TESTS/FOTD/2016/F160516C.jpg

Jim says: "...raise the already huge imag(p1) parameter a few orders of magnitude and watch the order 7 minibrot gradually morph into a quadratic one."

// GIF animation // of imag (p1) raised in 11 steps from: 2x10^(10) to 2x10^(20) in steps of a factor of 10 greater each step in Jim's "...obvious minibrot at the top center edge of the frame.":  Not anti-aliased. http://www.emarketingiseasy.com/TESTS/FOTD/2016/F160516P.gif

Out the negative X-axis, the largest bud with an "attracting cycle of period 2" has islands: http://www.emarketingiseasy.com/TESTS/FOTD/2016/F160516S.jpg

And just to its left: http://www.emarketingiseasy.com/TESTS/FOTD/2016/F160516T.jpg

- Hal Lane

######################## # hallane@earthlink.net ########################

-----Original Message----- From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Jim Muth Sent: Monday, May 16, 2016 7:45 PM To: fractint <fractint@mailman.xmission.com> Subject: [Fractint] FOTX -- May 16, 2016

FOTD -- May 16, 2016 (Rating A-7,M-9)

Fractal visionaries and enthusiasts:

Today's image is strange.  The strangeness does not appear on the surface, which is a simple image of the large minibrot on the main stem of the Mandelbrot set.  But do not yet give up hope.  To see something strange indeed, check the obvious minibrot at the top center edge of the frame, on the filament extending from the northern bud of the large minibrot.

What is this we find?!  An order 7 minibrot with quadratic surroundings!?

Assuming that you have already seen the mysterious 'brot, how is it possible?  The minibrot is of order 7, nothing at all like the quadratic minibrot from which its filament extends.  In fact, everything deeper in the same parent fractal is of order 7, while everything closer to the surface has a quadratic nature.  The formula does it all.

As an extra surprise, raise the already huge imag(p1) parameter a few orders of magnitude and watch the order 7 minibrot gradually morph into a quadratic one.

Another bonus with this formula, which is several years old, is that it is possible to generate minibrots of fractional orders with none of the discontinuities that spoil scenes and minibrots created the easy Z^(2.5)+C way.

The day here at Fractal Central began clear and frosty.  It was reported that this morning's low of 34 was the coldest it has ever been in Central Pennsylvania this late in May.  But once the sun got to work later in the morning, the temperature reached a rather pleasant 68F 20C.  And yes, we do have kittens under the fractal back porch.  Their mother had them out exploring the fractal yard this afternoon.

Well, I guess that's it for now.  I'm sorry to hear that I should take it easy on the divisive philosophy for fear of causing too much off-topic debate.  But as I see it, according to the scientists who have spent their lives studying such things, the sub-atomic world and fractals are actually the same things -- the mental images created in people's minds by the underlying numbers, and it's hard to accept a real objective world or a real fractal world made of building blocks that are no more solid than mathematical abstractions.  If I'm wrong here, squelch the debate in the bud by showing where my thinking has gone astray.

If I see things getting too contentious on the list, I might start my own mailing list, where fractal philosophy will come first.  I hope not, since I'm working on a few very interesting new Fractint formulas.

The next FOTX will be posted in a couple days.  Until then, take care, and why does merely discussing reality cause such intense feelings?  Maybe it's not fractally correct.

Jim Muth jimmuth@earthlink.net

START PARAMETER FILE=======================================

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frm:FinDivBrot-2   { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc }

END PARAMETER FILE=========================================

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