The discussion centers on the Koch snowflake and its implications regarding infinite perimeter and physical representation. Participants assert that while the Koch curve is a mathematical construct with infinite length, it cannot exist as a physical object due to atomic composition in the universe. The conversation highlights the distinction between scale-invariant fractals, which lack physical representation, and scale-dependent fractals, which are relevant to real-world structures. Theoretical considerations of fractals are emphasized, particularly in relation to physical models and approximations.
PREREQUISITESMathematicians, physicists, and anyone interested in the intersection of mathematics and physical reality, particularly in the study of fractals and their applications in modeling complex structures.
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?
It can, but then it would no longer be a "fractal".fromage123 said:but why can't the snowflake be made of space or energy itself directly (theoretically?)
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.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:... what is the point in fractals if in reality they do not have infinite perimeter?