In this section, applications are within this range 0 <H< 1 and we use 2D fBm Hölder different functions (polynomial [49–51] and exponential [49–51]) that take as input the points (x, y) of the dataset and provide as output the desired regularity; these functions are used to show the dataset singularities:

(a)A polynomial of degree n is a function of the form

H 1 ( x,y )= a n x n y n + a n1 x n1 y n1 ++ a 2 x 2 y 2 + a 1 xy+ a 0 ( 11.12 )

where a0, ..., n are constant values.

(b)The general definition of the exponential function is[52]

H 2 ( x,y )= L 1+ e k( x x 0 y ) ( 11.13 )

where e is the natural logarithm base, x0

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