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### #Actualsamoth

Posted 07 February 2014 - 04:16 AM

If sierpiński carpet is a fractal i see no reazon for this to be not fractal ;\

That is like saying: If a circle is round, I see no reason why a square should not be.

A Sierpinski carpet (or triangle) has the "stereotypical look" of a fractal, which your image just doesn't have. Note that looking like a fractal doesn't make an image a fractal, but not looking like one at all rules it out pretty safely.

If you look at a Sierpinski triangle starting at level 1, it has the look of a filled triangle where an upside-down triangle has been cut out (it works if you start with the level-0 triangle too, but I find the similarity more striking if you start at one subdivision). That exact same pattern is visible in each of the three smaller filled triangles around that cut-out triangle, and in each of the three even smaller triangles inside these, and so on. You can repeat this ad infinitum, and it will always look the same.

If you look at your image, there are circles and rings, and yes they are somewhat similar, arranged in a somewhat repeating texture. But that's where it stops. If you zoom into one of the circles, it doesn't turn out being an orb with many smaller circles and rings. It's just a circle.

This, too, is a regular, repeating pattern, but it is not fractal:

we should ask some mathematician good in fractals, for answer why  ifsierpiński is a fractal this  ball is not ;\

Well, one mathematician already gave an explanation a dozen or so posts above.

### #2samoth

Posted 07 February 2014 - 04:16 AM

If sierpiński carpet is a fractal i see no reazon for this to be not fractal ;\

That is like saying: If a circle is round, I see no reason why a square should not be.

A Sierpinski carpet (or triangle) has the "stereotypical look" of a fractal, which your image just doesn't have. Note that looking like a fractal doesn't make an image a fractal, but not looking like one at all rules it out pretty safely.

If you look at a Sierpinski triangle starting at level 1, it has the look of a filled triangle where an upside-down triangle has been cut out (it works if you start with the level-0 triangle too, but I find the similarity more striking if you start at one subdivision). That exact same pattern is visible in each of the three smaller filled triangles around that cut-out triangle, and in each of the three even smaller triangles inside these, and so on. You can repeat this ad infinitum, and it will always look the same.

If you look at your image, there are circles and rings, and yes they are somewhat similar, arranged in a somewhat repeating texture. But that's where it stops. If you zoom into one of the circles, it doesn't turn out being an orb with many smaller circles and rings. It's just a circle.

This, too, is a regular, repeating pattern, but it is not fractal.

we should ask some mathematician good in fractals, for answer why  ifsierpiński is a fractal this  ball is not ;\

Well, one mathematician already gave an explanation a dozen or so posts above.

### #1samoth

Posted 07 February 2014 - 04:12 AM

If sierpiński carpet is a fractal i see no reazon for this to be not fractal ;\
That is like saying: If a circle is round, I see no reason why a square should not be.

A Sierpinski carpet (or triangle) has the "stereotypical look" of a fractal, which your image just doesn't have. Note that looking like a fractal doesn't make an image a fractal, but not looking like one at all rules it out pretty safely.

If you look at a Sierpinski triangle starting at level 1, it has the look of a filled triangle where an upside-down triangle has been cut out (it works if you start with the level-0 triangle too, but I find the similarity more striking if you start at one subdivision). That exact same pattern is visible in each of the three smaller filled triangles around that cut-out triangle, and in each of the three even smaller triangles inside these, and so on. You can repeat this ad infinitum, and it will always look the same.

If you look at your image, there are circles and rings, and yes they are somewhat similar, arranged in a somewhat repeating texture. But that's where it stops. If you zoom into one of the circles, it doesn't turn out being an orb with many smaller circles and rings. It's just a circle.

we should ask some mathematician good in fractals, for answer why  ifsierpiński is a fractal this  ball is not ;\

Well, one mathematician already gave an explanation a dozen or so posts above.

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