Roquen
Iterator
Posts: 180


« Reply #75 on: September 09, 2014, 07:22:42 AM » 

The flip side is that having a preconceived notion of what it should look like might be steering you in the wrong direction.



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kram1032


« Reply #76 on: September 09, 2014, 11:59:23 AM » 

indeed. For one thing, why would it have a 4fold symmetry?
Though basically all we need would be to geometrically separate each bulb of the mandelbrot, rotate it around its local axis, and instance it a couple (symmetric) times around its motherbulb. If we somehow can describe this process geometrically and efficiently, we would get exactly that movie except with arbitrary detail.



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Kalles Fraktaler


« Reply #77 on: September 09, 2014, 12:59:56 PM » 

I was hoping that the relation between the center of the circles in the 2D Mandelbrot and solutions of the expanded z=z ^{2}+c polynoms could give any hint to create the shape preconceived by Marco Vernaglione. But maybe I am only spoiling the thread, sorry. A function that would result in Marco Vernaglione's shape would only be interesting if the iterations are too low to determine if points are in the mset or not, which results in spirals etc. If the iteration is enough it would only result in prefect spheres. So Marco Vernaglione's shape is probably not even interesting. It is fascinating though, that the polynoms quickly get ridiculous high degrees and that the circles of deep minibrots represent solutions of mind blowing high degree polynoms. We know the solutions, because we know the location of the circle, but we have no idea of the polynom! We know the answer but not the question But that is perhaps another topic...



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quaz0r
Fractal Molossus
Posts: 652


« Reply #78 on: September 10, 2014, 12:23:11 PM » 

i think if people were honest when they talk about the true grail what they really mean is a truly aesthetic grail, not a truly mathematical grail. basically a preconceived idea of sort of rotating a 2D mandelbrot to produce something like what karl just posted, which is visually geometrically pleasing. in the time that ive been interested in fractals ive always thought the mandelbox is far more pure and grailish as a 3D fractal than any attempts at projecting a 2D mandelbrot into 3D will ever be, both in the simplicity of the math and the resultant beauty and complexity of the object it produces. if the mset is the 2D grail, i think we already have a native 3D grail in the mandelbox. that being said, its always exciting to see people trying to explore new territory


« Last Edit: September 10, 2014, 12:29:43 PM by quaz0r »

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cKleinhuis


« Reply #79 on: September 10, 2014, 12:58:18 PM » 

ive always thought the mandelbox is far more pure and grailish as a 3D fractal than any attempts at projecting a 2D mandelbrot into 3D will ever be, both in the simplicity of the math and the resultant beauty and complexity of the object it produces. if the mset is the 2D grail, i think we already have a native 3D grail in the mandelbox. that being said, its always exciting to see people trying to explore new territory this is exactly my opinion, the mandelbox could serve as THE 3d fractal holy grail, its simplicity is unbeaten, it does not even induce those althougnotsocomplex "complex" numbers and works by just plain multidimensional real number mathematics



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Alef


« Reply #80 on: September 10, 2014, 05:06:36 PM » 

Mandelbox isn't so much explorable and haven't all that mathematical mumbo jumbo behind Probably David could publicate this in some scientical journal, there are folks whou are recieving goverment grants and making publications for much less creative things about the fractals. This thing are perfectly symmetrical, but maybe too much. Even with more bulbs it would be pretty boring in the respect of exploring and don't gives feeling about the mandelbrot set with all of the imperfect lightnings and seahorses.


« Last Edit: September 10, 2014, 05:13:04 PM by Alef »

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Kalles Fraktaler


« Reply #81 on: September 11, 2014, 12:05:47 PM » 

The beauty of the 2D Mandelbrot is because we can colorize points based on how fast we can determine that they are not in the set. If we only look at the points that are inside the set, they form boring circles and a few cardioids. So it might be that the idea of a 3D Mandelbrot is fundamentally wrong?



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youhn
Fractal Molossus
Posts: 696
Shapes only exists in our heads.


« Reply #82 on: September 11, 2014, 01:27:16 PM » 

Seen in space, the mandelbrot set is all about "the spaces in between", like the empty space of a mould that would be filled with matter to form the actual product. What about mass and the real world instead of the math? We are also about ... 99% or something of empty space. The closer you look, the less there is. Also seen in time (iteration time) it's all about the journey, not the destination. In the burning ship iteration bands often end in nothing (no miniship or whateven, just singularity). But in the mandelbrot it all approaces the boundary (is this a real boundary ?!). So I would think that the DE method for the 3D mandelbulb is correct. I just don't understand how the formula in 3D was formed. So not very sure on the questions maybe not to be asked.



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quaz0r
Fractal Molossus
Posts: 652


« Reply #83 on: September 12, 2014, 06:24:35 AM » 

it seems to me that the boundary of the mset is more than just somewhat analogous to reality, but in fact perfectly analogous to reality, more 100% than 99%. the closer you look at reality it seems to be comprised of the "boundaries" of the "orbits" of "energies". some arrogant humans might like to argue that there is a point at which you cant go any smaller, such as the planck length, but would anyone really try to argue that it is simply a perfect "solid" at such a point? a bunch of perfectly "solid" indivisible planck marbles? also considering that the colloquial notion of "solid" is rendered all but entirely empty and meaningless in the context of defining reality as closer to what it really is, the interaction of the boundaries of the orbits of some mysterious cosmic energies that never die.



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Kalles Fraktaler


« Reply #84 on: September 12, 2014, 10:02:28 AM » 

some arrogant humans
But I don't know if I think for example Steven Hawking is arrogant in this topic...



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Roquen
Iterator
Posts: 180


« Reply #85 on: September 12, 2014, 10:22:05 AM » 

All evidence shows that things only occur in discrete chunks. The mathematics of reals and the associated notions of infinity and infinitesimal are pure abstraction (imaginary things). Logically they can't exist either because they imply an infinite amount of information per item...so an infinite amount of infinite.



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quaz0r
Fractal Molossus
Posts: 652


« Reply #86 on: September 12, 2014, 10:24:59 AM » 

just because he is intelligent does not mean he is not arrogant. possessing intelligence beyond the average person does not somehow exempt you from the pitfalls of human emotions and desires such as arrogance and the desire to command authority. indeed extreme intelligence often goes hand in hand with human failings like arrogance and the desire to command authority. the hallmark of a truly wise individual is the capacity to say "I don't know," or "The following is my best guess, though we cannot know for sure at this time."



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quaz0r
Fractal Molossus
Posts: 652


« Reply #87 on: September 12, 2014, 10:40:33 AM » 

All evidence shows that things only occur in discrete chunks. The mathematics of reals and the associated notions of infinity and infinitesimal are pure abstraction (imaginary things). Logically they can't exist either because they imply an infinite amount of information per item...so an infinite amount of infinite.
in other words "all the evidence" boils down to "Infinity does not exist because it wouldn't make sense to me," and the variation on that, "Infinity does not exist because I wouldn't be able to calculate it." this perfectly and succinctly illustrates the unfortunate world view even lots of brilliant minds rigidly adhere to.


« Last Edit: September 12, 2014, 10:42:47 AM by quaz0r »

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Sockratease


« Reply #88 on: September 12, 2014, 10:56:38 AM » 

it seems to me that the boundary of the mset is more than just somewhat analogous to reality, but in fact perfectly analogous to reality, more 100% than 99%. the closer you look at reality it seems to be comprised of the "boundaries" of the "orbits" of "energies". some arrogant humans might like to argue that there is a point at which you cant go any smaller, such as the planck length, but would anyone really try to argue that it is simply a perfect "solid" at such a point? a bunch of perfectly "solid" indivisible planck marbles? also considering that the colloquial notion of "solid" is rendered all but entirely empty and meaningless in the context of defining reality as closer to what it really is, the interaction of the boundaries of the orbits of some mysterious cosmic energies that never die.
The notion of a smallest possible unit of measure does not imply solidity, just what it says  a smallest possible unit of measure. Perhaps beyond that we may pass through to some other weird dimension like in Star Trek's "Subspace" but that does not exist in our Universe (it is outside our universe) so the concept of a smallest possible unit remains valid even though it is possible to pass beyond that limit. But the only thing we can be certain about regarding the infinite is that we can never prove it one way or another, so we all have to either take a side and choose to believe it or not, or of course take the third option and choose not to decide. I choose to disbelieve the notion as anything more than an abstraction. All evidence shows that things only occur in discrete chunks. The mathematics of reals and the associated notions of infinity and infinitesimal are pure abstraction (imaginary things). Logically they can't exist either because they imply an infinite amount of information per item...so an infinite amount of infinite.
in other words "all the evidence" boils down to "Infinity does not exist because it wouldn't make sense to me," and the variation on that, "Infinity does not exist because I wouldn't be able to calculate it." this perfectly and succinctly illustrates the unfortunate world view even lots of brilliant minds rigidly adhere to. I see it more as "Infinity does not exist because it is inconsistent with Quantum Theory, Logic, and The Nature of Reality!" I have long held that Infinity is a very useful Mathematical Construct, but it has no corollary in Reality. Of course, it's possible that Quantum Theory is wrong and the Monster really does exist, but the two are mutually exclusive in my view.


« Last Edit: September 12, 2014, 11:10:41 AM by Sockratease, Reason: grammatically incorrect »

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quaz0r
Fractal Molossus
Posts: 652


« Reply #89 on: September 12, 2014, 11:19:26 AM » 

The notion of a smallest possible unit does not imply solidity of measure, just what it says  a smallest possible unit of measure. Perhaps beyond that we may pass through to some other weird dimension like in Star Trek's "Subspace" but that does not exist in our Universe (it is outside our universe) so the concept of a smallest possible unit remains valid even though it is possible to pass beyond that limit.
good point! an important distinction. But the only thing we can be certain about regarding the infinite is that we can never prove it one way or another, so we all have to either take a side and choose to believe it or not, or of course take the third option and choose not to decide.
indeed! ideally activities such as "belief" and "taking sides" would occur outside of science. I see it more as "Infinity does not exist because it is inconsistent with Quantum Theory, Logic, and The Nature of Reality!" I have long held that Infinity is a very useful Mathematical Construct, but it has no corollary in Reality.
the problem with this type of argument in my view is that it evolves from an underlying assumption that a fundamental, immutable property of reality and the universe is that it cannot possibly hold any properties which a homo sapien living on earth in the 21st century AD cannot comfortably understand and calculate with his maths. if we were being perfectly honest, i think this belongs more in the aforementioned "belief" and "taking sides" range of activities which, again, would ideally occur outside of science.


« Last Edit: September 12, 2014, 11:23:19 AM by quaz0r »

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