The concept of fractals is quite fascinating. Fractals are, in contrast with Euclidean geometry where everything has a definitive shape ( square, circle ), based on the observation that although most natural objects (clouds, coastline etc) do not have a definitive shape they still have some sort of regularity amidst the irregularity.
Wiki defines fractals as "rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole".
Fractal calculations are based recursively progressing equations that use the feedback from the previous iteration.
One example is in calculating the length of an irregular boundary. The basic idea is to start with a larger unit of measurement and gradually reduce the yardstick. The length will naturally increase as we pick a smaller unit. The change in length can be approximated as a algebraic function based on the pattern of the changes in length and this will give a much closer approximation of the length.
Now for the million dollar question....
We can find the length if rate of increase in length is lesser than the rate in reduction in the unit of calculation. What if this is not the case. What happens if the length grows at a faster rate.
Is it possible. Does this mean that we can in fact have an infinite boundary over a finite area?
