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3D MANDLEBROT
<img src="{SMILIES_PATH}/hmm2.gif" alt="Hmm2" title="hmm2" /> ...sooo...you seem to be suggesting that a kind of "sub-genre of pareidolia" might be at play???
...as in the work of Arcimboldo......

[Image: arcimboldo11.JPG]
[Image: arcimboldo11a.jpg]
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Here's a color mapping test on a mandelbulb zoom......

...with depth of field parameter enabled...

[Image: colormaptest3.jpg]
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Your arcimboldo images did not load
but I really like that Mandelbrot zoom

I somewhat dissected and reassembled it....maybe too much...
but here is a hex grid,
a close up from within,
then another closeup in a revised color scheme


photobucket is on the lame so the images may not post right away or at all,
please let me know if they don't show up on other computers



[Image: kalt1a.jpg]



[Image: kalt1e.jpg]




[Image: kalt1c.jpg]
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V......if you rotate your middle grid closeup by 90 deg. CCW, then the eye interprets the shadows better and really increases the 3D aspect.
I imagine that an effect like intricately carved jade might be achieved.

Your program does a great job in smoothing the edges in my images.
Unfortunately I have to do some tweaking for a given rendition to eliminate any jaggies.
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Quote:our program does a great job in smoothing the edges in my images.


believe it or not it is the old MGI Photosuite that came with my Hewlett Packard 5 years ago


I had to try that Mandelbrot zoom again,
and I got a wannabe octagon here,
the image below that is a close up along another symmetry line.

[Image: kalt4a.jpg]


[Image: kalt6a.jpg]
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Turn your second octagon image by 90 deg. and it becomes a curtain pulled discretely across an ornately grilled window......
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Try rotating 90 deg. CW and then mirroring......

[Image: weirstrassecol1.png]

Shifted palette/size (better???)

[Image: weirstrassecol2.png]
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I had a hard time with that image for some reason.
I might have tried to do too much with it.
I will just put out at small hex here.
Maybe later I will try an octagon to shift gears.
Also, the image is wonderful but too waxy.

I will try again later, but I almost got a perfect hex here, just a hair off on the horizontal axis

[Image: zzz2c.jpg]
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AWESOME pictures KR & V.
Never invite a Yoda to a frog leg dinner.
Go ahead invite Yoda to a Frog leg dinner
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I got my first pentagonal image to pop!

I took one of my electric series images as a test image,
so this one may be a bit congested with too much multi linear visual impact.

I will call these Pentalectricity Grids.

[Image: pentalectricity.jpg]




[Image: pentalectricity1.jpg]


<img src="{SMILIES_PATH}/cheers.gif" alt="Cheers" title="cheers" />
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Quote:I had a hard time with that image for some reason.
I might have tried to do too much with it.
I will just put out at small hex here.
Maybe later I will try an octagon to shift gears.
Also, the image is wonderful but too waxy.

Yeah...I know what you mean...
As a last resort to the edges problem in my images, I tweaked up a depth adjustment enough to deal with that issue but then the overall image became "waxy".

Try this one......a little more plastic than waxy......

[Image: surftest3.jpg]
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Too mono colored....don't likey the plastissimo effect,
kinda like a pharmaceutical corporation nanopolymeric life form Cheers
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OK...here's the mono image using the same palette but using a different color map (using what are called Weierstrass functions)...unfortunately this new Chaospro version has the iteration count capped at a low count for Mandelbulbs, so I couldn't get any more detail...

[Image: weiersrass3.jpg]
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That is outrageous.
This looks like fun.

<img src="{SMILIES_PATH}/reefer.gif" alt=":uni:" title="reefer" />
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Psychedelic Entity

Dimethyltryptamorphosis

[Image: kalterface.jpg]


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One more psychedelic scifi fantasy then tomorrow I will try strict geometric symmetry

Planet Maker
Dimethyltrypamorphosis


[Image: kalterface2a.jpg]
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Whistle ...ewww-kaaay ???
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Quote:In mathematics,
the Weierstrass function is a pathological example of a real-valued function on the real line.
The function has the property that it is continuous everywhere
but differentiable nowhere.


I didn't quite understand the mathematics of the Weiershtuncken function,
but when I saw this I knew I was right anyways.

LOL


Quote:It turns out that the Weierstrass function is far from being an isolated example:
although it is "pathological", it is also "typical" of continuous wtf functions:

* In a topological sense:
it can be shown that the set of nowhere-differentiable wtf real-valued functions
on [0, 1] is dense in the wtf vector space
C([0, 1]; R) of all continuous real-valued wtf functions on [0, 1]
with
the
topology
of uniform convergence.

Cheers
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I didn't have any luck with the standard image supplied into hex grid symmetries.
So I went back to the sci fi fantasy I produced and tried a penta grid,
which I like because it uses Phi.

That last image of yours is so fantastic that it lends itself to symmetry replications
but only in a Weiershtuncten Harmonic Convergence in the geomesci-fi,
which in this case as you mentioned convolutions,
indeed,
it borders on interdimensional brain matter and symmetry synergy.



Pentaneurosynaptic Phi interior of pentagonal grid

[Image: zypentaswirl2.jpg]






even closer in

[Image: zypentaswirl2a.jpg]


<img src="{SMILIES_PATH}/cheers.gif" alt="Cheers" title="cheers" />
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i...i..is that orange decastar poisonous??? <img src="{SMILIES_PATH}/uhoh.gif" alt="Uhoh" title="uhoh" />

The decastar could use a kind of "orange peel" texture.........also I'm going to try to add a Lyapunov transformation to the Weierstrass color mapping to see if I can get spines to grow from the concentric circular features...like fractal Morgellons!!!

In the following example, the orange peel surface might be modulated by the basic wavelength of the curve while Lyapunov rays might emanate from the amplitude peaks...

[Image: 300px-WeierstrassFunction.svg.png]
Plot of Weierstrass Function over the interval [?2, 2].
The function has a fractal  behavior: every zoom (red circle) is similar to the global plot.

The keyword here is "similar"...BUT NEVER THE SAME!!!

http://www.daviddarling.info/encycloped ... curve.html
Quote:pathological curve
          ______________
A curve often specifically devised to show the falseness of certain intuitive concepts. In particular, the image of continuity as a smooth curve in our mind's eye severely misrepresents the situation and is the result of a bias stemming from an overexposure to the much smaller class of differentiable functions. A chief lesson of pathological curves is that continuity is a weaker notion than differentiability. Many pathological curves are fractals, such as Cantor Dust, including space-filling curves, such as the Peano Curve. The earliest known example is the graph of Weierstrass' Nondifferentiable Function.

The process can be seen in the generation of so-called "mountain fractals", in which any given section of the curve shows a similar rise/fall pattern resembling a mountain range.
Slightly incrementing a certain variable and then redrawing the curve X times yields this...

[Image: mountain.jpg]
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Mountain fractal looks interesting!

OK I took your last image that I had reconstructed into a Pentaneurosynaptic grid,
and I decided to challenge myself and see if I could create an enneagon or nonagon,
the 9 sided symmetry.
It couldn't have worked better,
and somehow,
....somehow the pentagonal symmetry replicated itself around the interior enneagon
with 9 pentagonal grids from the pentaneurosynaptic grid.
It just flowed together somehow like magic,
and this is a masterpiece in multiple geometries and symmetry reflection.

Enneagon
[Image: zyx2a1.jpg]




Interior close up....needs some clean up, but it can be fixed.
[Image: zyx3.jpg]

<img src="{SMILIES_PATH}/cheers.gif" alt="Cheers" title="cheers" />
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OK......I just got done studying your main nonagon/pentagon subset image.
<img src="{SMILIES_PATH}/hmm2.gif" alt="Hmm2" title="hmm2" /> The question I have is whether the symmetry of the pentagonal ring is more apparent than real, because there are asymmetries between the vertices of the pentagons???
I mean, if a line geometric pentagonal ring were superimposed on the color image then would there or not exist a divergence between outer vertices of adjacent pentagons?
It's hard to tell, because the inner and outer nonagons appear to be symmetrical with regard to their component features.
Is that because the nonagon angles merely introduce an overall periodicity which "overcomes" those of the pentagon?

I suppose these might sound like rudimentary questions, but I don't understand how symmetry is restored between the inner and outer nonagons. I would have thought the divergence would simply radiate and magnify as the transition between 9->5->9 is manifested.
Did you see these 9/5/9 patterns in your pentad work???
_________

Anyway, here's a resolution test......excuse the overly placid color mapping......

[Image: Mbulb1.jpg]
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I am not quite sure yet why it worked in the nonagon,
but you did spot the inconsistency along the axis lines between each of the 9 pentagons.
The nonagon has 9 triangles of 70 - 70 degrees in the corners - and 40 interior at the center.
It may have something to do with the nonagon triangle corner 70 degree angles,
being so close to the interior central 5 angles of a pentagon of 72 degrees each.
Thus if, in the original splice together of the pentagon tile...
each pentagon has a nice wide perimeter structure as these do,
then when cutting the splice for the nonagon triangle,
it just happened to align with a two degree differential allowing some ...
....flex in the quantum flux baby......once connected
ie
as you move out from the nonagon center area and move out along between two pentagons,
the connecting arm between the pentagons there
widens a pinch as you  go towards the exterior.
This still allows a complete nonagon replicating tile however.
But it still contains pentagonal geometry within the pentagons along a secondary ....stretch axis...
Stretch axis...or more like
Divergent axis....
creates multiples geometric symmetries by encasing one geometry within another geometry



Note as well the bisector from a nonagon corner to the center point of the axis line
from base line to center is 30 degrees!


This image below will show the "divergent axis" or stretch axis as the red line .
You can see the "double blue eye"  almost dead center in the image on that red axis line,
but the exact correlative features above right and left are single blue eyed.
This is because that reflection is off angle by 2 degrees?...but centered for symmetry.
Near the bottom of the red axis line {line does not go through it}
is a small  symmetrical hex with a pinched top that acts as a juncture connector,
and above that straight up is even larger hex  that is diverging or expanding in size.
The equilibrium point along that red axis line is probably half way between the two hexes
and that would be the gold colored X motif  on the axis line.

[Image: zyx2a2.jpg]
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This thread is a ten!
Never invite a Yoda to a frog leg dinner.
Go ahead invite Yoda to a Frog leg dinner
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I tried another Pentalectricity grid just to see if it would be cool.
Most of my electric series may be too congested.
Two close ups in a row.

[Image: pentalectricity6a.jpg]



[Image: pentalectricity6b.jpg]
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Rotatingheart
~~~~~ ** ~~~~~&nbsp; <br />[Image: bee.gif]<br />We make decisions or we make excuses ~~ it's always our choice.
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Thanks Sarafina!
it is always nice to hear that people appreciate the work by all parties here.

Kalter this image still employs one of the Mandelbulb fractals you supplied.
The combinations of geometries just works when you adjust your splice correctly.
You can essentially encase any geometry within another
in the "stretch axis" scheme, which essentially creates a "spreading axis" within the tile
...the divergent axis that spreads slightly allowing the encasement.

Pentahex

[Image: pentahex1a.jpg]




interior closeup
[Image: pentahex1b.jpg]
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WOW !!!

It's a good thing I lost my post last night because my point was rendered obsolete by your 5->6 images !!!

I WAS thinking that there was some sort of "barrier" between integer symmetries, but now
I see that each integer is expressed in certain sub-symmetries within the image.
1 is an  Axis which sets the  2 of a reflection.
3 is created by the intersections of X Y Z axes,
thus generating the 4 faces of a tetrahedron.

Dunno ...much less 6->7->8->9......???

......and for that matter, how the fractal nature of the information being mirrored contributes to the direction of a given vertex, meaning that the structure exists at unimaginably tiny mathematical levels.

[Image: Juliabulb1-1.jpg]

[Image: Juliabulb2.jpg]


[Image: Juliabulb3.jpg]
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The last image is the right size but that kind doesn't work because it is too pixellated.
The other two are too small.
I never use your whole image, often only 50-75% before replication.
In this case I was down to 30% of your image and so by the time it was done being expanded
the image was butchered and clarity was lost.
I need image two in the last post much larger.

here is a close up of interior from image one last post, in a different color scheme,
pentagrid interior

[Image: pentacolor1.jpg]
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Dunno

On the other hand, the weird forms evident in small sections is what interests me.
I was using the Julia plotting mode.
In contrast to 2D Julia curves which tend to too much sameness,
the 3D "Juliabulb" exhibits much more varied small scale structure.

I was wondering about how you were approaching dealing with these images.
I have been intending that you first try a simple mirror of the entire image
and THEN do a grid.
In that way, the underlying gargoyle will be revealed as the template guiding the grid.

Here's image 2 at original 1024X768 (dunno what the HM resize will be)......

[Image: Juliabulb2-1.jpg]
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Quote:I have been intending that you first try a simple mirror of the entire image
and THEN do a grid.

Well I didn't use the entire image, but I did take most of it and mirror....
on which axis?

In any case I actually did a lot of things I have never done before with this one,
which included isolated section enhancements,
one of which was at the end where the swirl is limited to the main pentagonal interior,
not to the whole image.
I did a lot of selective processing on this one.
I also just want to save a bit of time and just do a pentagonal grid,
as those are easiest for me.
I use a lot of little tricks in making these large grids.
the full size is about 4500 by 4500 approx.

[Image: pentabulb1.jpg]




close up interior
[Image: pentabulb1a.jpg]




close up number two
[Image: pentabulb1c.jpg]


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The main pentagonal image above makes me think of Yezidis for some unknown reason. I did a quick search to see if pentagrams figure in Yezidi religious art but found nothing particularly relevant......except that they worship a cosmic peacock called the Melek Taus......and Yezidis are called devil worshipers by moslems......so I dunno,it probably doesn't mean anything.

I'd like to see a different rendition where the broad curved red patches are brought close to the center to form a red flower.

[Image: 1677yezidi.jpg]
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Quote:I'd like to see a different rendition where the broad curved red patches are brought close to the center to form a red flower.




[Image: redhex.jpg]



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