3D MANDLEBROT

[Kalter Rauch]

[Vianova]

Are you sharpening images from your end?
If so , don't.
This one appears to be too pixelated to work with,
so I will try a test image of a section of a huge grid as a determinant.
It is a great image. I like it a lot. Perhaps you can redo it with less pixelation.
I don't understand why pixellation is coming out of a fractal program.
Does this program give you a 768 by 1024 or are you magnifying the image?






It is a dynamite one eh?
I did a lot of things to it.

Interesting, a lot of the pixellation disappears here.
But I still cannot sharpen  from here, what do you think the pixelation might be?

[Valentine]

The Deepest Mandelbrot-Fractal Zoom Ever Did—Bigger than any universe that’ll ever exist.

It's in Danish except for the title.
http://www.misterhonk.de/blog/8061/the- ... ver-exist/

[Kalter Rauch]

<img src="{SMILIES_PATH}/hmm2.gif" alt="" title="hmm2" /> I rendered my last image at 1024X768 and put it on photobucket with no resizing or sharpening at my end.
I guess it must be something I'm doing...maybe too many iterations is leading to a kind of grainy quality...I don't know.
I can't redo the image because the program doesn't allow it.
Will test......

[Vianova]

The Deepest Mandelbrot-Fractal Zoom Ever Did—Bigger than any universe that’ll ever exist.

It's in Danish except for the title.
http://www.misterhonk.de/blog/8061/the- ... ver-exist/
<img src="{SMILIES_PATH}/dunno.gif" alt="" title="dunno" />

Interesting thing about that video is that the predominant focus of ..penetration
or interdimensional travel into the Mandelbrot sequence
was along flip/mirror and mirror symmetries as a replicating function
expressed somehow by the original equation.

The equation has the number 228.....dunno, I look for math sequences,
228 is a multiple of 57 as is also the synod of Jupiter to Earth of 399 days = 7 x 57.
That synod is recently dissected mathematically by me, in relation to Phi geometry.
I am not quite sure of what they mean by using the letter e in the equation
or if that is part of the universal constant e.

[Kalter Rauch]

I am not quite sure of what they mean by using the letter e in the equation
or if that is part of the universal constant e.

"e" means "exponent.
1E0 or 10^0=1
1E1 or 10^1=10
1E2 or 10^2=100
1E3 or 10^3=1000
1E228 or 10^228 = Error...does not compute......

[Vianova]

yes, it makes sense but I have slopped in my capacity of replication anyways.
I took one of the earlier images,
and in attempts to replicate an enneagon {nine sides} I have wandered into God knows what.
Convolutymmetry.
Shit.
Back to the drawing board.
Until I ferret my mistakes out, I am stuck here for now
I had 3 hours of failures.
There is some septagonal symmetry {7 sides} in the central yellow lines...and overall
so this ended up vaguely septagonal.
I have "symmetry contamination" 
There are 7, 11, and 15 in the replicative arms possible therein.
This is failure 4.
and closeup.

EDIT

Failure4 and closeup deleted

LOL

Garbage bin
see next post

[Vianova]

I got rid of the garbage in the last post because I figured out my mistake.
The enneagon is a tough cookie man.

So here it is with an old image from our selection of mandelbulb fractals.

The Hexapentenneagon .... enneagon with encased pentagonal and hexagonal geometries

Ha!





in the close up here
if you focus on one the yellow brain like 3D features
then look just adjacent into the pentagonal area
the pentagonal areas look like flowing pools with a lotus blossom
between the yellow bulging brain like motifs

[Kalter Rauch]

...or sharper with depth of field turned OFF, but more pixellated......

[Vianova]

You need yellow as a color, the spectrum of what it offers is limited.
I can get yellow in some of the reverse color copies.
The dashed lines on the right side of your image had to be cropped out, they did not work at all,
and a lot of replication of areas within became necessary to create image space.
There was too much black space in your image as well.
I worked on this one for over two hours and I didn't like my result.
No enneagon for this one.

The full pentagonal grid was too blah, here is a  section





Interior close up reveals a nice area of joint section but that's about it

[Kalter Rauch]

[Vianova]

The Mandelbulb images look like lifeforms or the whole substance is alive.
The stuff on the right side of that image looks like the semi frozen mud in Hellas basin,
it has....movement.....it looks like it might also just explode in fractal expansion 
much like mushroom mycelia does when it blooms on a substrate.
So what are the mandelbulb....substrates?
just the mathematical formulas
or also the imagination's connection to Infinity?
From your other post in the other forum here,
the master
Alex Grey

[Kalter Rauch]

So what are the mandelbulb....substrates?
just the mathematical formulas
or also the imagination's connection to Infinity?

Funny you should mention that......

This morning after doing that last image I experimented with Weirstrass color mapping applied to that image.
This time I was greeted by what appeared to be an overall speckled pixellation effect.
But there seemed to be a pattern.
So I increased the iteration count from 13 to 60 and filled the screen with colored snow.
Then I applied a different, scaled monocolor palette, along with a cube root function added to the Weirstrass.
This caused the multicolored snow to resolve into a previously hidden layer of Mandelbulbs marked by the peaks indicated by the Weirstrass functions.
I'll try to post a sequence tomorrow...
...even though the wonder might just be due to my own ignorance......

<img src="{SMILIES_PATH}/reefer.gif" alt=":uni:" title="reefer" /> sooo anyway...despite the lack of any visual evidence to substantiate my findings,
I think I can say that fractal pixellation may, in many cases, be due to the presence of a local nexus of detail.

Consider this... https://www.fractalus.com/info/antialias.htm

[Kalter Rauch]

well, hell...ignore most of what I said above...
I think I just found a crude roundabout way of getting the same result as my original image.
<img src="{SMILIES_PATH}/dunno.gif" alt="" title="dunno" />

[Vianova]

[quote author="Kalter Rauch"]well, hell...ignore most of what I said above...
I think I just found a crude roundabout way of getting the same result as my original image.

the complexities therein seen visually revolve around simplicities inherent.
Harmonic code search is back door methodology into mathematics.
Just as Mandelbrot sets are eventually exampled in a Hidden Order,
the Hidden Order itself has basic simplicities inherent, and isn't necessarily that complex.
Phi and the golden rectangle, and the tetrahedral sqaure root two rectangle,
can replicate in their own harmonic fashion to infinity which is straight forward geometric expansion or progression.

So... crude, or simplistic, or back door, it is just there,
and if it gets you to the same result,
it is actually more efficient many times.

[Kalter Rauch]

I'm thinking of retracting my retraction...
BECAUSE...I forgot to include the magnification factor...
I FORGOT that I experimented with high magnifications of so-called "pixels".

Here's an intermediate stage...at an obscure slightly pixellated spot......

[Kalter Rauch]

I'm not TRYING to be obtuse......

OK Vianova...here's the original Weirstrass color mapping of the image you characterized as "frozen Hellas mud"...
You can see the problem with apparent "speckling"......



HOWEVER...you can tell that the "pixellation"
is due to tiny versions of the warped bullseye patterns.
So, in an effort to either get rid of...or better yet, USE them,
I zoomed into a tiny patch in the blue zone.



After the steps listed in the above post, I came up with this crude image......



Using a monocolor palette brings out more resolution.
This shows that the details, rough as they are,
are ALL composed of what had previously appeared
as a major visual annoyance of Weirstrass peaks/pixels!!!

[Vianova]

That's interesting, but you didn't have many problems with some of the images prior,
some of those came out great.
For some reason when your pixellated images are transferred here,
worked on by me,
then transferred to photobucket then to HM,
the pixellation reduces...I cannot figure that one out.
I used a soften feature on one of yours once as well.

I actually like that speckled image with color pattern.
It reminds me of focusing in close on the surface of a shiny black jade boulder on the beach
to try and look into the rock, so to say, by interpreting the surface composition,
and observe a very very sparse but evenly distributed tiny grit suspension
or more like dust particulate load overall.
That will be throughout the entire interior to a degree.
You want to find as pure of sample as possible, but all of it no matter what
will carry this suspension particulate.
Some of the shinest most beautiful ones at the beach carry obvious suspension particulate,
to even a grit factor.

So I will call your speckles.....suspension particulate,
and I will see if I can play with that image.

[Vianova]

That is amazing.

For some reason when your pixellated images are transferred here,
worked on by me,
then transferred to photobucket then to HM,
the pixellation reduces...I cannot figure that one out.

here is a quick prototype with your image.
This is all I can do today, I am bushed and was on the road almost all day yesterday

The first image is unsharpened at my computer here.
The second image sharpened here on my computer
looks like hell with that pixelated particulate load,
super amplified to almost noisy distortion.
But when I transfer it here it looks better than the first one.
What does it look like for your end?
Which image is better to your eye to work with?

[Vianova]

OK I ate some cinnamon bread smothered in Tahini so I have a pinch of energy to do a quick
pentagrid and opposite color closeup.







I might try sharpening them form here later when I have time,
but gotta catch some of this day and water the shrooms.

[Kalter Rauch]

I liked the 2nd one better, as far as resolution...
...but for my taste it was a too washed out colorwise.
:uni: OK......here's another fuzzy experiment to refine this Weirstrass color mapping......
I found out that I have a choice of 3 Weirstrass functions...P, Zeta, and Sigma.
I had been previously/unknowingly using the P function.
This one is mapped according to the Zeta function... http://mathworld.wolfram.com/Weierstras ... ction.html .
Once again, ALL the image pixels are due to Weirstrass peaks, and from the same bit of blue in the big image...using the same palette so the pattern origin may be considered.
Recall the "mountain" graph mentioned some pages earlier.
The density of peaks increases with the overall iteration count but still according the basic fractal curve.

[Vianova]

I looked at that wolfram link on Weierstrusselshtuncken Zeta peaks

<img src="{SMILIES_PATH}/stars.gif" alt="" title="stars" />

LOL

but I did like the coefficients formulas on the patterning of the fractions c4 c5 c6 c7 c8,
I sure wish they showed c9 if such exists.
concisely to not bore you with lengthy math progression,
the denominators of c6 and c8 coefficient fractions are 39 and 7293
in which 7293 / by 39 = 187 exact,
with 187 a very important numeric sequence in my convergence dynamics of universal constants.
Essentially in floating decimal application: Phi x Pi / by {e} = 1.87
exact at 1.8700074

It is what I call a major coincidence hit, a convergence dynamic.
Also 39 is a fine harmonic in of itself
18 x 39 = Dresden Codex astronomical constant 702
19 x 39 = solfeggio 741
20 x 39 = Mars 780 day synod
21 x 39 = important Mayan astro glyph 819
etc

[Kalter Rauch]

Well, then you might find something interesting in these pages about the other 2 Weierstrass functions besides Zeta... http://mathworld.wolfram.com/Weierstras ... ction.html
Here's the P function... http://mathworld.wolfram.com/Weierstras ... ction.html ...peaks are expressed in clusters of 2, 3...or even funnel-like......
And this is the Sigma function... http://mathworld.wolfram.com/Weierstras ... ction.html

Links in these pages at the bottom go to plotting applets.
http://functions.wolfram.com/webMathema ... strassZeta
http://functions.wolfram.com/webMathema ... ierstrassP
http://functions.wolfram.com/webMathema ... trassSigma

It looks like the parameters can be plugged into ChaosPro.

[Vianova]

Enneagon, German 1604




1665





Lisi's E8

[hrm]

Lisi's E8

Surf's uP!


Hey you think that the Squares (large and small) and the rectangles
and their placement are representational of points of an individuals
interior emotional geographical landscape in the Enneagon?

What does the measurement scale at the bottom right pertain to?
Degrees?

Is this 9 vertices and 36 edges of the 8-simplex...sorta erased?

Hey does this mean I'm a many sided polygon or just a regular nonagon?


It's a very cool picture

[Vianova]

now jump back up to the top of the above image..... that purple alien looking gobbly thing <img src="{SMILIES_PATH}/rofl.gif" alt="" title="rofl" />

[hrm]

[Wook]

http://www.youtube.com/watch?v=SPIK9wUX ... re=related
Uriah Heep - Look At Yourself

[Kalter Rauch]

The "Enneagon, German 1604" is an idealized design for a fortress.
The wavy lines around the structure is a moat.
...that's what I get from the image info ("festung" means fort)

"normal" orbital coloring, w/ iterations sacrificed to reduce pixellation......

[Vianova]

festung --- fort, excellent, thanks. How odd to use the 9 sided model. Fascinating.
I like this image, and I think I can adapt and enhance the coloring to offer more variety.
I will work on it on the next couple of days.
Some of that has a pinch of Paul Bourke's quaternion fractals look in the image,
which I did regrids of in the Pentad thread.
Some of those Mandelbulbs invoke a psychedelic type of mental response/reaction.
LSD sometimes creates olfactory and taste hallucinations.
I feel like I can almost taste those fractals sometimes, like you could sometimes "taste LSD"
as a background permeation of a virtual oceanic soaking of psychedelic substance
in every pore and cell of your existence.
Like the energy just permeates and soaks your entirety to the taste buds by visual stimulation.

[Kalter Rauch]

..enhance the coloring to offer more variety."

I found out how to save parameter files, so if this version doesn't work I can go back and make any changes.
Unfortunately I accidentally tweaked the size and position a little on this version,
but I CAN go back to the original red/orange/blue par. file...for a different palette or whatever...

[Vianova]

The problem for me is that I have to delete black space from your image there,
limiting image size.
I am using the first one that is.
I am going to switch to the second one after all.

But I will work with this one a bit, slowly,
maybe one every two days till I get the big grid to work with.

Image size is limited and you will see here, as I would have to expand that in odd replications
to get to a 2000 by 2000 image let's say, to work into a giant geometric grid.
Also I am quite liberal with altering the image within the image in your fractals,
and many times it works miraculously without a visual trace of evidence,
but sometimes it reveals itself.
You won't see it in this size image.
can your image sizes be increased to like 1800 by 2400?

fantasy image 1

[Kalter Rauch]

I haven't tried any other storage site except for photobucket, and they limit image uploads to 1024X768 for free accounts.
The only way I can meet your size specification is to pay for it, which I don't want to do.

OK...so...you don't want any black zones or aliasing artifacts...
or plasticene flowers towering over your head......
Fair enough......
But we're getting into a grey zone when it comes to palette choice.
I have to be guided by the way my aesthetic sense responds to how it's coming together.