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

Get Computational Methods for Data Analysis now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.