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# Fractal?

chasbeen
So the Mandelbrot is the most well known.
It has self similarity and goes on for good.

Now imagine a circle surrounded by 6 circles.
Have you noticed this before?

All the circles are the same size and all 7 circles (Including the one at the centre)
are touching each others circumference with no overlap or gap.

Go inside any of the 7 circles and put another 7 circles inside that.
These circles have dimensions exactly one third of the first set of circles.

I could not find this in any discussion on Fractals mentioning this structure.

Do you think it is a fractal?
Ankhanu
Not sure this can be mathematically derived...
kelseymh
 chasbeen wrote: So the Mandelbrot is the most well known. It has self similarity and goes on for good. Now imagine a circle surrounded by 6 circles. Have you noticed this before? All the circles are the same size and all 7 circles (Including the one at the centre) are touching each others circumference with no overlap or gap. Go inside any of the 7 circles and put another 7 circles inside that. These circles have dimensions exactly one third of the first set of circles. I could not find this in any discussion on Fractals mentioning this structure. Do you think it is a fractal?

Yes, it's just a variation on the Sierpinski triangle. The fact that the enclosed circles have r = R/3 of the larger circle is trivial: that's how they are constructed.
Bikerman
LOL...I spent an hour with a pencil and paper to work that out - thanks Michael - I concur.
kelseymh
 Bikerman wrote: LOL...I spent an hour with a pencil and paper to work that out - thanks Michael - I concur.

Ah, sorry it took you so long The centers of the six circumscribed circles form a hexagon surrounding the central one. The three across the middle are in a line, and since they all touch, the diameter of each one is trivially just 1/3 the distance across all three.
Afaceinthematrix
It sounds like a variation of the Apollonian gasket although it will have a different Hausdorff dimension.
chasbeen
So In went ahead with a web page. I called it Fractal Navigation.
It's a way of navigating around some examples on my website

http://www.irunmywebsite.com/raphael/rapdevexold.php
zaxacongrejo
the universe is fractal
zaxacongrejo
the universe is fractal
always the same shape for start
Bikerman
Err...no, it just isn't.
zaxacongrejo
hi i just notice your post now
 Quote: Err...no, it just isn't.

ok help to understand why it isnt?
kelseymh
zaxacongrejo wrote:
hi i just notice your post now
 Quote: Err...no, it just isn't.

ok help to understand why it isnt?

Observational data. On the largest scales, the universe exhibits a filamentary structure. On smaller scales (clusters and superclusters of galaxies), it is strongly clumped, and not filamentary at all. On even smaller scales (single galaxies), it is essentially uniform density spheres, with small disk-shaped or elliptical objects (the visible galaxies of stars and gas) embedded within them.
zaxacongrejo
ok there you go and why?
kelseymh
 zaxacongrejo wrote: ok there you go and why?

SonLight
zaxacongrejo, any fractal has patterns that are repeated at different scales. A mathematically pure fractal repeats the patterns at all scales, from the smallest to the largest.

The universe has stars, galaxies, clusters etc. and some of these have similarities on different scales. But the degree of similarity is nowhere near enough to consider it a fractal, or even like a fractal.

Consider the Solar system, an example of a fairly typical stellar system. It has most of its mass at the center, and most of the mass that is left over is in large objects (planets). This is very unlike what we see on the scale of galaxies or clusters, where mass is more spread out, and distribution of mass is generally more even the larger the scale.

Our Milky Way galaxy is again typical of many galaxies at approximately the same scale. It is a spiral galaxy, essentially a spinning disk. Nowhere is there any larger-scale object that is composed of smaller gravitationally-bound objects oriented in a similar manner.

Even at very small scales, we have atoms consisting of a heavy nucleus surrounded by orbiting electrons. This has been likened to the solar system. While there are analogies, there are so many differences that is couldn't begin to be considered fractal-like even if there were repetitions on many scales. The binding force of the atom is electromagnetic, not gravitational. There are precise patterns and energy levels that have no analog in a stellar system. Electrons can easily be shared with other nuclei, which never happens with planets.
zaxacongrejo
 Quote: Even at very small scales, we have atoms consisting of a heavy nucleus surrounded by orbiting electrons. This has been likened to the solar system. While there are analogies, there are so many differences that is couldn't begin to be considered fractal-like even if there were repetitions on many scales. The binding force of the atom is electromagnetic, not gravitational. There are precise patterns and energy levels that have no analog in a stellar system. Electrons can easily be shared with other nuclei, which never happens with planets.

Hi
You have understand my point

 Quote: Even at very small scales, we have atoms consisting of a heavy nucleus surrounded by orbiting electrons. This has been likened to the solar system. While there are analogies

Have a look here

http://www.fractaluniverse.org/v2/?page_id=2
asnani04
Quite interesting to know this.
Bikerman
I thought I smelled a rat.
This is Plasma Cosmology hiding behind a fractal disguise - the plasma merchants are obviously desperate to cling to their discredited hypothesis.
Bah, humbug and bollox is what I think. The BB theory, which this speculative approach both states, and actually requires, to be wrong has been verified to an astonishing degree of accuracy by the COBE and WMAP data.
Plasma cosmology is something I looked at a while back and concluded that it is simply electrical/electronic engineers feeling left-out and wanting a grand-unified theory which features their field rather than the models from basic physics/cosmology. My opinion has not changed - and the fact that two of the leading lights in this 'field' - Lange (Berkeley) and Matsumoto (Nagoya) - had their theoretical underpinning, and whole raison-d'etre for PP, pulled out from under them by COBE in 1992 indicates to me that this is a dying field, though the corpse is obviously still twitching slightly.....