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Author Topic: Is there a limit in exploring 3D fractals?  (Read 5643 times)
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bib
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« Reply #15 on: December 07, 2010, 12:21:43 AM »

Participating in exhibitions organized by mathematical associations, specialized scientific art galleries or with the partnership of universities is already a good start to have fractal art more widely recognized. For sure it's a good vehicle to enable new generations to gain interest in mathematics, but it's turning in closed loop. To break this circle and touch a wider public, I think the critical mass effect can only be reached when fractal art is simply part of modern art exhibitions, not only scientific art. And that should take much longer...
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David Makin
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« Reply #16 on: December 07, 2010, 04:09:35 AM »

Participating in exhibitions organized by mathematical associations, specialized scientific art galleries or with the partnership of universities is already a good start to have fractal art more widely recognized. For sure it's a good vehicle to enable new generations to gain interest in mathematics, but it's turning in closed loop. To break this circle and touch a wider public, I think the critical mass effect can only be reached when fractal art is simply part of modern art exhibitions, not only scientific art. And that should take much longer...

The key is to increase the awareness of the nature of Fractal Art from a purely creative standpoint as well as the mathematical/algorithmic.
When introducing students to fractal math it's virtually impossible for them to miss the visual/artistic potential of the images that the mathematics conjures up and for schools it adds probably the strongest way ever of linking Art and Math together.
Last year I did a talk to a mixture of Art and Math students at the local college and I'd say that interest was pretty evenly distributed between the two disciplines and I think that's something likely to be repeated generally.
As to modern art exhibitions, I'd hope that Fractal Art will eventually appeal to a considerably larger proportion of the general populace than a lot of the work currently being exhibited in such.
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JodyVL
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« Reply #17 on: June 22, 2011, 06:37:27 PM »

Hi guys...

I've studiously read through all the posts in this thread and found it all to be be very very interesting. But often, I found myself thinking "oh my god, what what what?"  huh? ... To quote some of you:


Quote
Another variation in my UF formula is that I added standard escape-time IFS style transforms which can be mixed with the other formula types

"3D/4D forms such as quaternon/hypercomplex/bicomplex"
"complicated 3D formulas actually involving 3D transcendental functions."

I have also enjoyed looking at a hybrid of the standard Trig (real) ( Float power:: 7.4659, z-multiplier: -0.5) with a Bulbox that's pretty much default, each 1 iteration.  It's all wicker-y and has twisty stuff and a couple of other features

because of the number of types of conformal transformations available in 3-dimensions is limited (rotations, scaling, inversion, and translation).

the most "sophisticated" 3D factal rendering is being done by those using L-Systems (or at least L-Systems converted to a form of IFS) and that there are other fractal forms (DLA, plasma/fBm,attractors) that work in 3D+.
Also the 4D forms extending from the 3D Mandelbulb have yet to be fully investigated, I fully expect some of those to be more mathematically "consistent" than the 3D, maybe even finding a true "field" ?

You know?  tongue stuck out

So I'd like to know if any of you could point me in the right direction... I'd like to understand the maths behind 3D Mandelbrot/fractals (already have the 2D maths down, mostly grin ). Once I understand it all, I'll be creating a Tutorial on my own blog. (My goal is to put all the fractal newbie stuff in one place, my blog, as I learn it all myself).

I have been searching for some answers myself but truly, most sites always assume some previous advanced maths knowledge.

Thanks smiley ... Oh and, I'm posting here to get the attention of all you wise men  cheesy .. Let me know if I need to start a new thread somewhere instead.
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SonoKAI
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« Reply #18 on: June 28, 2011, 03:25:03 AM »

Well, there are infinite* equations out there, the possibilities ARE endless.
And it also depends on which numbers you use in the effect you want. In some cases, the Mandelbulbs or Mandelboxes, when you plot in a certain number you can actually see the Infinity effect the brocolli takes on it's own. grin
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LhoghoNurbs
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« Reply #19 on: August 21, 2011, 07:55:48 PM »

I'm in a hurry now (and I admit I did not read all the opinions in the thread) - So my hyperquick two cents on this topic is that I kind of share the worries expressed by the original poster.

For example, when I started my exhibition few years ago, I wanted to have 30-40 posters with 2D fractals. The first 4-5 came up quickly, but every next poster took more and more time. I spent exponentially increasing time for finding a new fractal position for the next poster. The 15th one took almost two weeks of nonstop browsing in the Mandelbrot set. I got the impression that all shapes that I saw were variants of already found shapes.

So, my exhibition had only 16 posters (15 posters with fractals and 1 cover poster) - I simply gave up finding new shapes.

I do agree, that even in 3D we will reach (or have reached) the state where drastically new shapes appear quite rare, but at the same time I believe that some new breakthrough will open another world of fractal shapes...
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