Question

Circles of various dimension with reference to original circle

Answer 1

One method we have been using to measure fractal dimension is the method of covering. There are other methods for measuring dimension. One that is useful for objects with dimension less than or equal to two involves measuring the total area of the object present inside circles of different radii. For a surface in a plane, the area increases as the square of the radius: A = $ \pi$R2. The power 2 of R tells us-again!-that a disk is 2-dimensional.

Check results of the formula A = $ \pi$R2 by counting the number of cells inside circles of different radii in the Figure. For each circle, count all the cells inside that circle, not just those between that circle and the next smaller circle. Enter your results