Fractal-oscillation attraction

[KALSTER]

First, a quote from the Wiki page on Fractals:

 

A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."

 

A fractal often has the following features:

It has a fine structure at arbitrarily small scales.

It is too irregular to be easily described in traditional Euclidean geometric language.

It is self-similar (at least approximately or stochastically).

It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).

It has a simple and recursive definition.

 

And an example:

 

The Mandelbrot set is a famous example of a fractal.

 

A closer view of the Mandelbrot set.

 

Now, imagine a 3D version of a fractal created by an oscillating disturbance at its centre. The oscillation means that the orientation of the fractal (into its mirror image) changes with a certain frequency and that the speed at which the newly created fractal moves away from its source is governed by the medium of propegation it finds itself in. The shape, size and type of the fractal is determined by the particular shape, size and type of the disturbance. It is possible for the shape of two fractals to be equal in every way except for the orientation being in the opposite direction (i.e. it points outward instead of inward).

 

My question is: Is it possible for the interaction between these two fractals, equal except for orientation, to exert an attractive force on each other? Would two of the exact same fractals then exert a repulsive force on each other?

[KALSTER]

From the Wiki page on Fractals:

 

"Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels. Coastlines may be loosely considered fractal in nature."

 

The images in the OP was only to get a casual reader an idea of what a fractal is.

 

I was thinking of fractals in the form of self-similar reducing eddies in a medium, that is, reducing as the energy is dissipated with distance by forming multitudes of smaller and similar eddies (if that makes sense). This hypothetical medium would have no internal friction as one would expect from water, say.

By oscillating I mean that they form mirror images of each other along an axis running through the source, roughly in the same manner a sine-wave would.

 

So assuming that nature can not be infinitely reduced (the space-time fabic for instance), I guess this fractal would have to terminate after a certain number of instances. Maybe even straight down to the planck length.

 

For simplification, think of a wave-form being emitted around an axis of symmetry, similar to a sine wave, but instead of the regular positive and negative curves, you have (alternating between each side of the axis) spirals/eddies curling in the direction of the disturbance. This single arm comes into contact with the arm of another disturbance. The direction of rotation of the spirals/eddies will clash head-on with the spirals/eddies of the other arm. Now extrapolate this to a 3D situation with large numbers of arms from the two disturbances interacting with each other. The disturbances should be attracted to each other, no?

 

Just to be clear: I am not making any claims, just doing a mind experiment.

 

Any takers?

[KALSTER]

I was reading through the wiki article on Superfluidity and came across this gob-smacking passage:

 

"A more fundamental property than the disappearance of viscosity becomes visible if superfluid is placed in a rotating container. Instead of rotating uniformly with the container, the rotating state consists of quantized vortices. That is, when the container is rotated at speed below the first critical velocity (related to the quantum numbers for the element in question) the liquid remains perfectly stationary. Once the first critical velocity is reached, the superfluid will very quickly begin spinning at the critical speed. The speed is quantized - i.e. it can only spin at certain speeds."

 

This is exactly the type of stuff I was thinking and wondering about! Could the medium I am considering produce such vortices? Can vortices have a fractal nature, even if only stochastically? Could an oscillating source create the kind of vortices I am looking for?

 

Is there some kind of simulation engine where I can feed it variables and see what happens anywhere available?

[foodchain]

Any takers?

 

Well if I get what you are talking about even slightly would that be something along the lines of motion from say the most infinitesimal scale up to the largest in a continuum type of sense? Like a flower unfolding or something?

[KALSTER]

motion from say the most infinitesimal scale up to the largest in a continuum type of sense?

More or less, but it has to be coherent, i.e. the shape has to be constant to at least a predictable degree.

[KALSTER]

I made this same thread on another forum and it got Really Interesting over there!