| Fraclab GUI | |
0 : Input type
1 : Input name
2 : Box sizes
3 : Regression
4 : Others
The input type can not be changed in this window for it is choosen in the Fraclab main menu. However, we explain here the meaning of this option:
In the main window, the user can choose between "Signal or grayscale image", "Binary image" and "List of points".
R^n.
Signal or grayscale image
This type of input is the more common in Fraclab. It is also the more simple of use for the computation of the graph of a function.
The input is an array of values. These values are those of a function, and the dimension of the graph of the function is computed.
The function is supposed to be defined on [0,1] if the input is a signal (and [0,1]^(n-1) in higher dimensions).
For example, if you want to compute the box dimension of the graph of the function sin(2*Pi*t) for t in [0,1], your input may be sin(2*Pi*[0:10^(-4):1])
(This dimension is obviously 1, but this isn't the question)
It is also possible to perform this computation in any higher dimension.
For example, if you compute the box dimension of a grayscale image, the bright pixels are seen as peaks and the dark pixels as valleys. This option corresponds to the use of boxdim_classique
Binary image
This type of input is the easiest to understand. Your input is a black and white image (i.e. a matrix of 0 and 1), and the box dimension of the white pixels is computed: a box is non-empty if it contains at least one white pixel.
The image is supposed to be supported in [0,1]^2 (Or [0,1]^n if n ~= 2)
It works not only on images, but also with any higher (or lower) dimension array. This option corresponds to the use of boxdim_binaire
sin(2*Pi*t) for t in [0,1], your input may be [[0:10^(-4):1]',sin(2*Pi*[0:10^(-4):1])']
It is possible to perform this computation in any other dimension : a subset of R^n is described with a matrix with n columns. This option corresponds to the use of boxdim_listepoints
This is the name of the input. If you want to change the input, click on the new input in the main window, and then on the "Refresh" button. The "Refresh" button also gives back every field its default value.
Aspect ratio
The more natural way of performing the computation is to use square boxes. In this case, keep the default value of Aspect Ratio. However, you may want to use rectangular boxes. Then, the field "Aspect Ratio" is usefull.
It defines the sides of a reference box. All boxes will be homothetic to this first one. The k-th coordinate of "Aspect ratio" is the length among the k-th direction of this reference box. When choosing the value of "Aspect Ratio", don't forget that the definition set of a signal in Fraclab in supposed to be [0,1]
Normalize data
If choosen, this option brings all coordinates of the input points between 0 and 1 with an affine transformation before performing the computation.
max size, min size, #of box sizes and progression These fields allow you to define a vector "size". Max size is the biggest size, Min size the smallest and #of box sizes the number of box sizes to be computed.
If progression is "linear", then the sizes will be linearly spaced. If it is "Power law", the sizes will be exponentially spaced.
If "Aspect Ratio" has its default value, then the boxes are squares and size(i) is the side of the i-th box.
As a rule, the length among the k-th direction of the i-th box is "Aspect Ratio"(k)*size(i).
See Also
boxdim_classique,
boxdim_binaire,
boxdim_listepoints,
fl_regression