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Crystals are the less fractal patterns that nature can form. Straight lines, cubes, trianglular shapes etc...crystals are too euclidian, and not irregular enough. That is why they look so apealing to our eye.
But crystals can also display beautiful fractal patterns and self similarities, take a look at this fluorite from Illinois, I find it outstanding !.

(http://nocache-nocookies.digitalgott.com/gallery/8/2605_06_10_11_9_35_01.jpeg)

Hi Prokofiev,

Agreed! Crystals are absolutely fascinating from a fractal perspective. I don't remember if you have visited the crystal museum when we were at the CIJM fair in Jussieu, it was absolutely stunning to see what Nature is capable of!

cheers

bib

I am sure that if you write an IFS algorithm at low iters and some random mangling about sizes and rotations you obtain a very similar image. :beer:

I remember some similar stuff in a famous 3D program anyway (Bryce?). :alien:

Yes, I have seen this little museum in Jussieu 3 or 4 times, including during our CLJM fair together. The nicest collection in France.
A real shock. The first time, I just wanted to show the kids some "nice stones". Once inside, I kept on answering "oh, just 2 minutes more, please", as they were asking desperately "Daddy, can we go now ?" every minute. I was hooked.  :D

Another Fluorite with infinite cubic details at all scales. It was for sale on Ebay. Far too expensive for me...
(http://nocache-nocookies.digitalgott.com/gallery/8/2605_07_10_11_11_02_37.jpeg)

Want one more ?  :D Wow ! some of the cubic details are really tiny !
(http://www.phidelity.com/photos/d/105829-2/DSC_0004.JPG)

Like the first example much more than the others.
It is a clear example how less can be more
It is a rule that easily can be used when producing bulbs for the galleries here, though often enough, it is not so easy to make things simpler

I just tried. Much room for improvement (some of the bigger cubes are way too pure), but I certainly think it is possible.

In order to get a picture similar to the first one, you would have to use a raytracer with a fancy shader mixing sub-surface scattering with metallic shading. And probably a lot of patience :-)


(Structure Synth with internal raytracer)

Not bad !
Remember fluorites are made of cubes, not rectangles.

If you reduce the size variability probably it returns good :) - or force both dimensions to be equal (but the result should look less realistic) anyway you are a wiz :D Luca

Another fluorite from the Musquiz mine in Mexico. This location is famous for its fluorites with fractal patterns.
Its quality and transparency are exceptionnal !
Its price is exceptionnal as well...
(http://nocache-nocookies.digitalgott.com/gallery/8/2605_10_10_11_10_20_52.jpeg)

Continuing my selection of fractal crystals, here is an unusual calcite piece, showing surprizing parallel square blades, at all scales !   :o
(http://nocache-nocookies.digitalgott.com/gallery/8/2605_15_10_11_3_21_27.jpeg)

This one is for sale on eBay. Wonderful steps at all scales again !
Reasonable starting price.
I'll try a bid or two .... I hope it doesn't go too high !
I cross my fingers... :)
(http://nocache-nocookies.digitalgott.com/gallery/9/2605_18_10_11_5_07_21.jpeg)

I missed it :-(.

Nature, and Euclid are often underestimated like this, and then the proposer has to contradict themselves when new discoveries are revealed .

These image are stunning, and should make you question your basic assumptions everyday!

Continuing my selection of fractal crystals  :D
Here is a bismuth crystal displaying beautiful fractal patterns in 3 dimensions.
Such crystals are very rare in nature and not that spectacular.
Most but of them, like this one, are synthetic and grown in labs. The colors are the result of surface oxydation.
The fractal pattern is formed by growing straight and suddenly forming right angles at random.
As a result, they form, most of the times, spirals at many scales.
Enjoy !
(http://nocache-nocookies.digitalgott.com/gallery/9/2605_28_10_11_11_20_58.jpeg)

 :thumbsup1: Wonderful. Reminds me of Kali's fortress, somewhat.

Love it!

Can I eat it?

Very intresting and beautiful, never see such crystal before! Where i can find such crystals?

Great photos! I like the straight lines in the spiral patterns.

Just look for "bismuth crystal" on ebay.

Beautiful tiny crystals of cuprite (a copper mineral). A breathtaking fractal structure !  :surprised:

(http://www.mineral-forum.com/message-board/files/supermacro07_192.jpg)
(http://www.mineral-forum.com/message-board/files/macro514_183.jpg)

Wow, that second image looks astonishingly like a standard hypercomplex (aka bicomplex) Julia Set !!

And what about this one ? Doesn't it remind you of something ?
Kaleidoscopic IFS ! Of course !
It is a kind of black garnet.
(http://www.mineral-forum.com/message-board/files/8131m_andradite3_111.jpg)

What started me off in fractals was the notion that plants and trees in particular derived their shape from a combination of biology and spatial constraints,that is a space that the leaf and branch could fit into, rather as the roots are shaped by the cavities between soil particles. But your images show that this spatial shape is intrinsic. The internal dynamics of the crystals form the shape.

For a living organism i would automatically presume internal "vital" dynamisms, but crystals show this vitality is inherent in all matter, not just biological.

Sierpinski Octahedron Menger hybrid :)

Another nice find.
Pyrite crystals normaly tend to be very simple: I have one which is just a big perfect cube. So simple it looks like it was man made.
But, wow, this pyrite has become mad !  :hmh: Can anybody guess what parameters were used, here, by mother Nature ?
(http://nocache-nocookies.digitalgott.com/gallery/9/2605_02_12_11_2_26_40.jpeg)

I found some crystals like that in M3D  O0

Hint: Rotated Mixpinski interior view. Enjoy  :angel1:

Excellent find Jeremie !  :dink:

What about this one ?
What parameters, do you think ?
(http://www.alpinismeetmineraux.fr/mineralogie/macro/macro3/supermacro337.jpg)
Well...no. It is a real photograph of a real crystal !
Not convinced ?
Then look at this enlarged photo here : http://www.alpinismeetmineraux.fr/mineralogie/macro/macro3/supermacro336.jpg (http://www.alpinismeetmineraux.fr/mineralogie/macro/macro3/supermacro336.jpg)

@Prokofiev, you HAVE to test the new dIFS function in Mandelbulb3D. I am sure it can give fantastic crystals.

You can not get every ifs with difs, it semms to be very limited not like in Incendia. I will look it a bit closely ;)

I agree it sems more limited than Incendia of course, anyway it's a great new feature and I trust you will bring fantastic additions!

Hum, Jesse used a mystical coding and I need to understand
Anyway imo we can add the heightfield in that form, would be cool

Stay tuned Jeremie :D

With a straightforward escape-time algorithm (as in Mandelbulber and Masndelbulb3D) you cannot even get all linear/affine IFS rendered "correctly" because of the potential overlap problem with respect to the bailout volumes on each iteration.
To render 3D IFS using the escape-time method requires the full IFS tree to be rendered for each point on each ray if using distance estimation, this may sound like a huge overhead but in practice for linear IFS one can use Hart's intersection method rather than distance estimation - unfortunately because of the difficulties with respect to non-linear functions it's very difficult to render non-linear IFS and of course certain function have no proper inverse therefore to produce the "correct" result with transforms involving such functions is AFAIK impossible even using distance estimation.
I wrote a formula for Ultra Fractal that does 2D IFS using the escape-time method that allows non-linear transforms but the results for flames using non-linear morphs can't usually be replicated and in any case producing the required "hits" value for true flame colouring is also very difficult (though I don't think it's quite impossible).
I also wrote a 3D formula for IFS that uses Hart's intersection method for intersecting the viewing rays with the bounding volumes - again just a different version of the escape-time method - but that only allows linear IFS as it doesn't currently include an option to use distance estimation.
Both these formulas can be found in "mmf4.ufm" as "Escape-time IFS" and "3D IFS" respectively. Both also include various conditional modifiers that allow user-controlled restrictions with respect to the transforms used within the IFS tree.
"mmf4.ufm" itself can be found in the Ultra Fractal Formula database here:
http://formulas.ultrafractal.com/

Hmmm - just noticed that "dIFS"  is referring to something Jesse has just added to Mandelbulb3D - so the above may be "out of date" with respect to that program as I'm not quite sure what "dIFS" is exactly - it could be a version of Hart's direct intersection routine ?

Some research i have been doing into Justus Gunther Grassmann, father of Hermann Grassmann has thrown some light onto the importance of crystals (http://www.persee.fr/web/revues/home/prescript/article/rhs_0151-4105_1989_num_42_1_4136) in Raumlehre development.

For me the important thing is the ideas of the nature of sppace that were developed by those who studied crystals, but it was Jusus who began to marry the ethical, psychological and subjective processing of these attributes or observables into a coherent theory of space, based on current but unusual ideas of Schliermacher and Schmid,called Raumlehre (http://my.opera.com/jehovajah/blog/2012/01/13/http-www-persee-fr-web-revues-home-prescri). Fundamental to this idea was Justus concept of syntesis which was about combinatoric laws and repetition of those laws at larger and larger scales of synthesis. The underlying fractal nature of crystal development was thus apprehended in one of its basic "laws" self similarity, and "almost" self similarity.

It is these notions of his father that Hermann Grassmann developed fully, well as much as he could without help and synergistic research collaborations in his "Ausdehnungslehre ,eine Wissenschaft...." of 1844, and 1862 and in various scientific writing in between.

Thus Benoit Mandelbrot had a rich background of uncoordinated theory to synthesise from when he decided to study this field and call it Fractal Geometry. His profound insights, but especially his famous mandelbrot set image welded together what so many had so nearly achieved, and made accessible philosophical ideas and scientific philosophy about the nature of force fields in space.

Because Grassmann was fundamentally hijacked by Gibbs, and kept as a guilty secret by Abstract geometrists, and frankly rated as too abstract for most to follow, the link to his ground breaking and foundation laying work is obscured.

I have attempted to study it in the original German, and find it is very clear and understandable! Too me it pee;s away the "fehlerhaft" of ideas presented to us about space and in particular "vectors". Suffice it to say that it is worth looking into the "mirror" of the Ausdehnungslehre, especially when one realises it is a tool not a description. Strecken are but one possible application of this tool!

This observation is key. Stuff, materials and their structures just iterate, iterate and iterate. Perhaps life has just seen some more (focussed) iterations than crystals. I almost dare to say crystals are the "missing link" between life and non-living. Which means, there is no boundary but only a link. If life really was "something else" then why does it consist of the same basic stuff of about 99,9...% of the universe?

So if both the basic stuff, and also the basic method of evolving/growing is the same, then what makes the difference? Very hard to categorize things when there are no boundaries. But then again, we know that species have no hard boundaries. But over time they do differentiate, so we can give 'm separate names like dogs or wolves. Is it the same for life and non-living matter ... ?

@youhn
The viruses form a recognised boundary between living and non living entities in biological taxonomies. But beyond viruses are Bacteriophages.
In these structures we see the models coalesce both crystalline and organic structures.

The key point for me is that these are model structures, not " reality" . They are humanity's best guesses, from a mechanical, or even field dynamical point of view.

The whole universe is a great " mystery", and some of us have the privilege of expositing that to others in an entertaining and educational way that increases their creative capacity and ability to develop technological innovations that could benefit all!
But the choking hand of greed strangles these newborns at birth!

At the end of it all I feel privileged to have witnessed the most complex model we have devised feed into real advancements in adjusting to" the wheel works" of the universe, as Tesla put it.

On the spiritual( that is consciousness) side I find no grounds for a materialistic assertion that it is an emergent property of matter. But that it is the cause of all is also groundless!
We are left with the facts and the Myths that we create to make sense of this incredible experiential continuum that I for one acknowledge. And the great paradigm shift in my thinking has been the fractal topological dynamic of fluids.

As a stab at connecting that " verbiage" to everyday experience I would draw your meditative attention to magnetic behaviour.

I have gone into this at length elsewhere on the Internet, but here the pure fractal topology and computational modelling by Fractal generators is what I focus on.

would you mind adding a link? I'd like to read into that.


yep, I share a similar view. though I think chrystals are too unreactive. As Jehovajah says, add fluid dynamics (as in "life needs fluid water") and you get fast evolution of chemicals.
Pretty sure you'll like this one :):
https://www.youtube.com/watch?v=sPZmfxpEPY0&list=PLuBeCwzDtE8JltcK9AADCbgGy1-BiB1Kv&index=61

@Chillhelmer

http://magneticuniverse.com/discussion/129/a-sound-magnetic-base/p1

This link is to a forum thread that I initiated but which fortunately attracted other contributors  with interesting observations.

You hopefully will forgive my many annoying typos, and feel free to query , comment or request clarification . Also, I am here to learn so do not fail to impart what you have learned from experience. Book learning is valuable, but I like experimental data and observation best of all. Xxx