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### #Actualfir

Posted 07 February 2014 - 04:48 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:

Probably when increasing the palette frequency inifinitely you will get infinite level of depth in such circle patterns - you ignore this thing or you do not understand? Im not sure but maybe there can be stated that if you will get any small rectangle area you will find a circles in it (though maybe some vaves may be much  smaller than dominant one

for me i may repeat it seem this is not worse fractal than sierpiński carpet

I wonder if 3d version of it could be obtained? maybe someone will know? (this is maybe more 2d than 3d and i wonder if real spheric

3d versiion surface is obtainable and which formula?)

PS Alvaro could ypu maybe rise up the visuals by inventing more colorfull palette here (more like unbird did)? (I cannot work on this today but would be curious if this could be more colorfull)

### #1fir

Posted 07 February 2014 - 04:44 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:

Probably when increasing the palette frequency inifinitely you will get infinite level of depth in such circle patterns - you ignore this thing or you do not understand? Im not sure but maybe there can be stated that if you will get any small rectangle area you will find a circles in it (though maybe some vaves may be much  smaller than dominant one

for me i may repeat it seem this is not worse fractal than sierpiński carpet

I wonder if 3d version of it could be obtained? maybe someone will know? (this is maybe more 2d than 3d and i wonder if real spheric

3d versiion surface is obtainable and which formula?)

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