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Test aiming into a minute "pore"...
...increasing difficulty maintaining symmetry,
which I suspect is due mainly to minute axial misalignment
between the "observer" and the 3D object...

<img src="{SMILIES_PATH}/damned.gif" alt="Damned" title="damned" /> ...although I can't discount the influence of chaotic instabilities becoming significant at high magnification
manifesting as a slight twist arising (I presume) from the central unresolved zone......

[Image: MandDE2.jpg]
Far fucking out!!!


hey Kalter
I'll  be back !!!

I love this thread

be patient

I am going to ride off into the sunset like John Wayne
with
ALL
the Universal Harmonic Codes deciphered.
and
I''l be back

[Image: john_wayne.jpg]
I did a pentagrid of the colorful one a few posts back
which just about catches me up to you.

The actual huge grid was too fussy, it had too much symmetry
and the rectangular template I posted earlier was better.
But the interior close up is cool.

We just lose too much resolution with Keith's image expansion program here.
It is far more detailed here at this end.




edit




I went back and sharpened TWICE!
This is better indeed but right at the edge of losing definition
from over sharpening
but definitely better than I had

[Image: nLCZQ.jpg]

<img src="{SMILIES_PATH}/cheers.gif" alt="Cheers" title="cheers" />
:uni: PHWEEET!!!
(cough)
Stars

This is why it behooves the viewer using Firefox to use the Zoom-it tool to reduce the display size. In this way, apparent sharpness is increased while eliminating artifacts, as well as allowing the image to be seen more in its entirety. In other words, it at least restores the image to its original state of compression....pre-THM......

Artistically...your symmetries approach incomprehensibility.
I wouldn't worry about being "too fussy".
<img src="{SMILIES_PATH}/hmm2.gif" alt="Hmm2" title="hmm2" /> My only critique might be that I see a kind of collage effect around certain sections. I don't know if there's a "pixel color alignment" tool in your software that's more precise than the usual "smooth" tactic.
First experiment with "Perlin Noise" color mapping...not too good...with pixellation......

[Image: Perlin1.jpg]
The last image won't work.

This image is wild but I can see a sharpness problem already:

[Image: MandDE2.jpg]


It certainly has a Face capacity .... but a mouth might be tough

supplying a small and large image to see how it looks

Psychedelic Mayan Glpyh 819


[Image: oezk8.jpg]


[Image: NCUzC.jpg]

[Image: Mand3D131.jpg]
those background colors are absolutely fascinating.

Some of the forefront detail really suffered though in the image.

Are these the sizes they give to you from the program?

Some of your earlier images didn't have the ...blur factor of images we get here
in this magnification program infused in this forum.
Whip

Look......OK......I hear what you're saying......

Right now you're pointing at 3 factors...
1) the appearance of the background
2) the appearance of the foreground
3) the appearance of earlier images

As I see it now, there seem to be 2 or more influences which may conflict...

These are the mathematical requirements to increase detail
as opposed to the ray tracing calculations needed to properly display that detail.
Earlier images usually incorporate much more default settings, so I need to retrace my steps.

Why does the background appear smoother than the foreground?
I don't know...
...there are what seem to be immense arithmetical voids on a microscopic scale
but which is  really a percolating soup of values
that confounds the ray tracing engine.

See how this one turns out...
...it's a zoom into a region of the previous image......

[Image: Mand3D132.jpg]
Back to basics...

I tried to maintain a uniform palette across the image to show a range of transitions between agate-like "background" textures and the "curdling" resulting in "detail".
The result, I think, is to illustrate that there is really a continuum of values which are more ore less truncated according to the doink-headdefining a 3D slice of a 4D Mandelbrot set. How much Time is allowed a loop to proceed?
10...100......1000 iteratiions???

[Image: Mand3D126.jpg]
Oh man

that is beautiful!

I will work on that one soon

here is one of our better ones

maybe imgur will give us a bigger image


[Image: 6KS5c.jpg]

I can't imagine how you derived that space altar design in the bottom of your last Weirstrass rendition!!!
It would make a great design for an archaeonomaly site.

This next is another exercise in attempting symmetry,
shifting palette to reduce rigidity and increase fluidity...

[Image: Mand3D133.jpg]

...and here's a zoom into the center of the above......

[Image: Mand3D134.jpg]
The altar design was facilitated by the availabiltiy of black space to manipulate with.
I cannot say what I do there because those are the unusual procedures
that make the grid rearrangements more versatile and unique.

I am still back on an earlier image a couple of posts ago.
This failed actually, and I will try again
but here are two images from the grid.
One is a reduced image and one is a larger close up of another part of the grid.

Facial features appear and I work those into form.
I don't know why the second one is a little less clear.
Over sharpening didn't help.

[Image: BaLJ6.jpg]



[Image: ovPO3.jpg]
Now, don't get me wrong......
I wasn't trying to get you to reveal proprietary information.
...it's just that I can't figure out what part of the image it came from...unless it has something to do with how you're using transitions between colored and black zones.
If so, then the black regions may not be actually the same as the true black background. I think if you look at the RGB values then they won't all be zeroed out. For instance, I detect a very subtle lightness variation in the space around the blue streams as opposed to the blackness on either side.
I guess it's like those blue particle streams mysteriously remind me of something I can't remember......

Also, when you get to my last image......
...ummm...yes...it is flawed......
The blackish blotches are because I was thinking about ergot infestation at the time,
and I was shifting the palette back and forth, watching the progression of the disease into the orange areas where it tended to migrate down the valleys...at the expense of the rest of the picture, however......

OK...what do you think about trying out some quaternion experiments???
I haven't used that formula since the Art & Madness thread, but I think what I've learned since might lead to some...
<img src="{SMILIES_PATH}/damned.gif" alt="Damned" title="damned" /> ...unusual results......
[Image: Mand3D135.jpg]
I took your close up and did a hex grid

here is an interior

yes
quaternion fractals would be fun,
I did a few of Paul Bourke's earlier in the Pentad thread.

I like this current batch that you have posted.
The surface textures are alive with tangibilty and sharp.

Add some black space and I can infiltrate galactic supernova.

The symmetry attempts you made were excellent,
especially since you didn't really flip or mirror... or did you somehow?

That big eye with that same sand dollar fractal is wild.
don't get too far ahead of me,
I can't keep up!

[Image: uZiTX.jpg]

Well...look at it this way...now you have more of a choice!!!

I'm not doing any post-processing, and I think an examination of what's occurring along any apparent axis of symmetry will display enough differences to show that everything is intrinsic to the original image. Right now I suspect that achieving classical  symmetry may be impossible because of (as near as I can tell...) factors involved with Riemannian geometry...ie. that the shortest distance between 2 points is along a curved line.
<img src="{SMILIES_PATH}/damned.gif" alt="Damned" title="damned" /> I suggest reading a Cthulhu Mythos story, The Hounds of Tindalos, by Frank Belknap Long...concerning the consequences of angular vs curved space-time.
search/curved vector
[Image: medium_e2.png]
http://physics.aps.org/articles/v1/35

So far, I haven't had any real success right now with quaternions.
Unfortunately I never saved any parameter files from early work...so it may be awhile......
I tried some Quaternion fractals off of the net.

The Mandelbulb has far more potential, but some of the quaternions are amazing.

The metallic silver close up that I supply is by Paul Nylander,
and he has great stuff at his links.

http://virtualmathmuseum.org/mathart/Ar ... index.html

http://www.bugman123.com/




Kalter, your better Mandelbulb fractals are certainly better than most of these here:

http://www.skytopia.com/project/fractal/mandelbulb.html

Perhaps submit some of yours.
Our enneagon cannot be beat.


This one from that above link however was quite special
[Image: IceCreamFromNeptune-med.jpg]



The large pentagonal grid of this is quite intense.
This quaternion fractal is by a guy at "fractal forums"
He had no name but just an avatar.
If you use google search for quaternion fractal and fractal forum you will find his stuff.

[Image: As96k.jpg]






I lost the master 5000 pixel grid to this by pressing the save button on the closeup
before saving the master grid.

Fractal Gothic Cosmosis architecture. .... oversharpened...

[Image: 64638.jpg]





The Paul Nylander Quaternion is quite special.
----reduced size full image of the actual Penternion will be in the Pentad thread----

[Image: AG1Wp.jpg]


I tried a master grid

penternion

pentaquaternion
whatever

The master grid failed with the need for massive repair surgery which is NOT EASY.

I tried one step too many and lost both perfect symmetry and resolution as well

here is a very reduced size penternion master grid:

Quaternion fractal by Paul Nylander <-----.
pentaquaternion grids C VS sept 2010

[Image: xETAS.jpg]




here is a close up from a prior seed grid template
[Image: 59i9Z.jpg]


there is one more in the Pentad thread of this series

Strange...for over the last week I've been thinking about how to get a metallic palette...and then you come up with Nylander's steel quaternion...ESP???

Like...what ray-trace parameters yield a sharp rayed glint off a polished surface?
...and there are a lot of subtle colored reflections from the ambient surroundings.
I could be wrong, but I don't think it's a texture file that being mapped on the surface... <img src="{SMILIES_PATH}/hmm2.gif" alt="Hmm2" title="hmm2" />
Do you think that he possibly achieved that metallic surface with Paint?

It is fabulous, and we saw another one similar that i posted a year ago.
a yellow one
with metallic surface,
but it was a Lyapunov fractal.

I will look for the image.

Quote:....and then you come up with Nylander's steel quaternion...ESP???...

It's the Jaguar, Kalter.

Look in the skies at Jupiter and the Moon.

All my work started with a dream 3 years or so ago now.

I was in a city and in that city was a park that no one else could see.

It had a fence too !

lol

Well, in that pristine spacetime warp of a pristine natural beauty park
were animals of every species,
all walking down to a lake side to drink water together in harmonious peace.

Then a large slender legged thinner cat
that looked like a cheetah with a lynx head that had tall pointed ears
walked very close by and looked at me.

This was a female.

She turned and kept walking, and behind her emerged the most magnificent huge
Jaguar
one could ever imagine.

He turned and looked at me, and a brilliant flash of Infinity
catapulted from his eyes into my mind.

Then he simply turned away and followed his mate.

The next morning I picked up a hand calculator and a pen and paper
and wrote the first equation
in Mayan Long Count planetary timelines:

585 Venus synod x 1.3333333~ { Khafre pyramid slope tangent } = 780 Mars synod.

And my life has never been the same since.

The next night I had the Star Gate dream,
but I won't burden you with that.

Suffice it to say that
Imagination
may have been the culprit here,
maybe even the accumulated effects of P. Semilanceata dimethyltryptamines over the years
may have stimulated such dreams...
but why pick up a calculator of the clear blue sky,
and just write that simple equation
as a springboard into everything I have done?

Cheers
I couldn't find that Lyapanov you posted...
I think it was black & gold???

Here's a bad attempt at a metallic appearance......
The last thing I did was add a slight layer of light pinkish fog, which interacted with different colors in the image to enhance the metal direction, although far from enough.......

[Image: Metallic12.jpg]

Anyway, as to the "sand dollar" artifacts in other images...
...those MAY POSSIBLY be 3D renditions of the spiral patterns seen in 2D Mandelbrot images. In that case, if you drastically cut back on iterations then the spiral takes on a radial grooved appearance.
Here's a short suggestive article about the relation between 2D and 3D Mandelbrot sets...
http://rj3sp.blogspot.com/2009/11/mande ... t-set.html
The actual resolution of these 3D images is abysmally low.
A 2D Mandelbrot requires at least around 100->200 iterations/pixel,whereas a 3D version may need as few as 6 iterations before plotting a point.
That isn't QUITE an accurate statement, but the idea is that 3D information becomes significant at much lower resolution than 2D...if that makes sense???

Dreaming...
Many times, before I crash, I will do an image search for material related to main things I have recently thought about. I've found that the subsequent dream will often reflect the previous image search content.
Try experimenting with jaguar/DMT type searches and then go dream.
For instance, there's a short video out there about a jaguar eating DMT containing leaves used in yage... http://www.google.com/url?sa=t&source=v ... pA&cad=rja

The first time I found a sand dollar, I thought it was a fern fossil!!!

[Image: Ash4.tif.JPG]
THE FOSSIL FERNS OF PETRIFIED FOREST NATIONAL PARK, ARIZONA
http://www.nature.nps.gov/geology/paleo ... _6/ash.htm

Look at specimen J above...
The morphology is suggestive, given the organic quality of the 3D M-set.
In that case it may be revealing to discern a "leaf stalk" of a given "sand dollar/fern", since this would indicate a connection to an unknown deeper fractal dimension of super-infinity...the exploration of which is limited only by available computer power......
This won't be gridable...and the HM resize turned out way too jagged compared to the original.
<img src="{SMILIES_PATH}/hmm2.gif" alt="Hmm2" title="hmm2" /> It's possible that turning up the resolution in ChaosPro was somehow the culprit......a real drag if I'm forced to abandon that parameter......
[Image: Mand3D140.jpg]
Globally, this is too random but smaller parts are interesting......

[Image: Mand3D141lobo.jpg]

[edit...replaced image with better rendition]
yes!

Outrageous!

I will try one in a couple days.

Good work!

The last one is beautiful.
If I don't over reprocess the grid work it might turn out fabulous.
You were right.
There was too much small detail that was not sharp enough for the regrids on that last image.
I did a large pentagrid,
and it is really cool but detail suffered as I had to sharpen image...3 times....
I might be over processing,
I will try to approach conservatively on the next one.
So it wasn't even worth posting,
it just did your image no justice.
OK...take a look at this original of my last image and then compare it to the above "improved" version......

[Image: Mand3D141.jpg]

The reason for the increased detail in the edit version is due to changing the "bailout" value from the default 1024 to only 4.
4 is the bailout value when computing the basic 2D M-set.

I didn't notice much difference in rendering time, and I really liked the more fluid effect and increased detail without introducing irritating sawtooth patterns.
And many interesting patterns are revealed within what before was mere shadow.
  I might have preferred a better lighted, more complex palette, I suppose......

Another subject related to the hidden order behind the is that of "orbits".
Before each point is plotted the values engage in a geometric dance before settling down to the bailout value.
Scroll down and read this about Mandelbrot orbits...and then try out the 2 simple applet versions...
http://math.hws.edu/xJava/MBold/index.html
Left click along the margin of the M-set to see the orbital pattern,
and then right click w/o moving the pointer to see the vector representation.
This probably explains the appearance of "sand dollar" artifacts, ripples, etc......
I'm a bit wasted tonite.
First alcohol in 2 or 3 months.
Last alcohol in 2 or 3 months.
I get absolutely no hang or burn from smoking.
I will be sorry tomorrow.
Had to tonite.
Finished a pdf and it was a 3 day affair.

I took this off the net.
Some-who-body some-where-wtf-I thank them

lol

image in full grid less than half size
[Image: lsxS5.jpg]

Cheers
Re...your enneagon in the Stargate Pentad thread......

[Image: rA4y6.jpg]

...is there any application of Lissajous patterns in understanding the basis of the multiple symmetries...as in the ratio of 9:5 ???
I did a search for freeware Lissajous pattern generators.
There are some out there, but I didn't test any.
Here's a Lissajous pattern generator applet with easy controls,
and 1000->99,999Hz range......
http://www.mathcats.com/explore/lissajo ... ajous.html
You can find other demos with an ELF range, but at least this one lets ratios be tested, and entering a very low sampling rate will show geometric shapes which <img src="{SMILIES_PATH}/dunno.gif" alt="Dunno" title="dunno" /> MIGHT be useful in grid work???

Now......about those bridge railings and lattices......
I THINK I have an inkling of what you're getting at.
OK...sooo...is your idea to grid the mathematical ratios inherent in a 3D view to generate a kind of "super-perspective" effect?
In that case, the bridge railings would act as calibration marks in a test image???
Whoa!

Damn ... ya can't unload

Lissajous pattern  Rofl

Quote:In that case, the bridge railings would act as calibration marks in a test image???

No and yes,
said Dr. Lao.

[Image: bslcT.jpg]



Quantum Quandry
is like
Dirty Laundry
said
Dr. Lao.

Dr. Lao had some fine home cooking,
I bet she knew how to sit on her groceries provocatively:

yummy, kind of an innocent Angie Dickinson
[Image: ywP8S.jpg]



Quote:In that case, the bridge railings would act as calibration marks in a test image???

yes, in that the select splice has to be augmented to create overall symmetry effect.
Invariably, there will be a convergence to a "harmonic" geometric scheme,
in which replicating geometry prevails,
regardless of true specific exactness into premier angles
such 30-6-90, or srqt5 based phi geometries, or replicating square root two rectangles.
ie
one can fudge an image easily
in 
"spin glass geometric frustration"
ha!

"Chew on those Chinese noodles",
said
Dr Lao.

OK
so in 2008 I released the Mars Pentad Time Pyramids pdf,
and in that is the:
Pentad Octagon.

Well one night after drinking with Dr. Lao in a love triangle with Barbara Eden there,
I took the Pentad Octagon,
and rotated it 90 degrees and overlaid it on the original image.
I then,
unexplainedly now,
mofobungo-ed around the the exterior in an artists concept,
but adhered to the geometry in the inner octagon created.

I drew the actually obvious connections to me,
that by chance
ended up being the interior
of the 5D demi-cube
which was a God
in ancient Hue-man history ............  Rofl

[Image: Plinkoseason37.jpg]


So in any case
the central octagon is the exact same geometry in my
hokey pokum geomo-smoke-em double Pentad Octagon.
Though my initial drawing is a bit askew,
it is there.
I called it a Star Gate geometry at the time. lol

[Image: 8fS6m.jpg]



[Image: A5jKl.jpg]




said
Dr Lao!
Vianova sees "...her groceries..."...

[Image: ywP8S.jpg]

I, on the other hand, see...

[Image: eizo-pin-up-calendar-2010-7.jpg?w=600]
Call this one "Jimi"...
Purple haze out across the stadium......

[Image: Mand3D124b.jpg]