Question

In an experiment to determine the fractal dimension of crumpled newspaper, mass and radius were plotted on log-log paper. Selecting two points on the line-of-best fit, the vertical distance between the points was 44 mm and the horizontal distance between the points was 30 mm. Calculate the fractal dimension.

Answer 1

fractal dimension is 0.1092

Step-by-step explanation:

given data

vertical distance V = 44 mm = 0.044 m

horizontal distance H = 30 mm = 0.030 m

to find out

fractal dimension

solution

we will apply here fractal dimension formula that is

logV = ( 1 - fractal dimension) logH ...................a

put here all value in equation a

we get

fractal dimension = 1 -
`(logV)/(logH)`

fractal dimension = 1 -
`(log0.044)/(log0.030)`

fractal dimension = 1 -
`(-1.35654732351 )/(-1.52287874528 )`

fractal dimension = 0.1092217

so fractal dimension is 0.1092