Koch snowflake and planck length

AI Thread Summary
The discussion centers on the Koch snowflake's infinite perimeter and its implications regarding physical objects and fractals. It is established that the Koch curve, being a mathematical construct, cannot exist as a physical object due to atomic composition limitations in the universe. While the infinite perimeter is theoretically possible in mathematics, real-world fractals, like coastlines, have finite lengths. The conversation also highlights the distinction between scale-invariant fractals, which lack physical representation, and scale-dependent fractals, which can model real-world structures effectively. Ultimately, the relevance of fractals lies in their ability to provide useful mathematical models for approximating physical phenomena.
fromage123
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surely if you keep adding smaller and smaller sides to the snowflake they will become even smaller than the Planck length and so how can the perimeter be infinite- or is the infinite perimeter only theorteically possible with maths, but not actaully acheivable?
 
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fromage123 said:
surely if you keep adding smaller and smaller sides to the snowflake they will become even smaller than the Planck length and so how can the perimeter be infinite- or is the infinite perimeter only theorteically possible with maths, but not actaully acheivable?

The Koch curve cannot be a physical object because in our universe every physical object is composed of atoms.

The Koch curve is a mathematical object that actually has infinite length.
 
but why can't the snowflake be made of space or energy itself directly (theoretically?)
and if it it is as you say- that it cannot exist as a phyical object what is the point in fractals if in reality they do not have infinite perimeter? (since all the 'real' examples of fractals such as coastlines will in actual fact have a finite length)
 
fromage123 said:
but why can't the snowflake be made of space or energy itself directly (theoretically?)
It can, but then it would no longer be a "fractal".

and if it it is as you say- that it cannot exist as a phyical object what is the point in fractals if in reality they do not have infinite perimeter? (since all the 'real' examples of fractals such as coastlines will in actual fact have a finite length)
The same point as any mathematical model of a physical situation- by using the right mathematical model we can get arbitrarily good approximations to what is "physically" happening. If a physical situation involves distances near the Koch length, then "fractal geometry" or any geometry using continuous segments is no long the "right" mathematical model.
 
fromage123 said:
... what is the point in fractals if in reality they do not have infinite perimeter?

One may add that you can distinguish between scale-invariant fractals, that do not have a physical representation, and then scale-dependent fractals where the fractal dimension depends on the scale. The later is very much applicable to real world structures. See for instance [1] for some more details.

[1] http://en.wikipedia.org/wiki/Fractal_dimension
 

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