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?
Not sure this can be mathematically derived...
LOL...I spent an hour with a pencil and paper to work that out - thanks Michael - I concur.
It sounds like a variation of the Apollonian gasket although it will have a different Hausdorff dimension.
the universe is fractal
always the same shape for start
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.
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.....