Answer: the stream frontage has a fractal dimension between 1.67 and 2
Step-by-step explanation: The equation utilized to compute the fractal dimension of stream frontage is expressed as follows: D = (log N) / (log 1/s), where N represents the total count of constituent units and 1/s denotes the scaling factor.
At the scale of 10 meters, it has been determined that N equals one and the reciprocal of s equals one. At the scale of 1 meter, the sample size (N) is equal to 25, while the sampling interval (1/s) is equivalent to 0.1, which is obtained by dividing it by 10. At a distance of 10 centimeters, the number of observed particles is equivalent to 250 and the reciprocal of the standardized sensitivity value is 0.01. By employing the applicable formula, the fractal dimension can be computed as follows:
The equation can be expressed as D, which is equal to the logarithm of N divided by the logarithm of the reciprocal of s, represented as log 1/s.
At the 10-meter scale, it can be observed that D possesses a value of 0. This signifies that, within the scope of measurement, D does not exhibit any discernible magnitude.
At a scale of 1 meter, the value of D is approximately equal to 1.67.
The value of D on a 10 centimeter scale is equivalent to 2.