Koch snowflake and planck length

[fromage123]

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?

 

[pwsnafu]

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.

 

[fromage123]

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)

 

[HallsofIvy]

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.

 

[Filip Larsen]

... 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