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 Fractal Dimension 

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FDSURFFT computes fractal dimension (slope) of surface image im and draw rose plots of slope and intercept.



Its based on the traditional box-counting method for finding the fractal dimension of an image. The code is just for beginners for getting an idea of how the box-counting is done.



IFS fractal dimension calculation using box-counting method.



Returns the Haussdorf fractal dimension D of an object represented by the binary image I. Nonzero pixels belong to an object and 0 pixels constitute the background.

Algorithm:

1 - Pad the image with background pixels so that...



This matlab scprit calculates fractal dimension and intercept of a 3D volume along each redial line using Fourier analytical technique. Directionally averaged fractal dimension, intercept and Hedgehog plots of fractal dimension and intercept of...



THIS ALGORITHM COMPUTES FRACTAL DIMENSION USING SEMI-VARIANCE TECHNIQUE. IT HELPS TO ASSESS THE DIRECTIONALITY OF THE TEXTURE PATTERN IN AN IMAGE. SEMI-VARIANCE ALONG HORIZONTAL DIRECTION IS DEFINED AS THE SUMMATION OVER ALL PIXELS N, OF THE...



[DIMENSION STANDARD_DEV] = fractalvol(DATA) calculates the fractal dimension of the 1 dimensional random walk, DATA. DATA is assumed to be a function of its indices.
Finds fractal volatility by embedding in the unit square and box
...



I found this equation in Wikipedia page for "List of fractals by Hausdorff dimension".
The problem is how to calculate the scaling coefficients for any given IFS fractal.
You can see the heuristic I used in the code.
It...



[VINDX FRACDIM V_SIGMA COVERSIZE] = varIndx(LOW,HIGH)

LOW is a column vector of the lowest price in the bar (second, minute,
etc).
HIGH is a column vector of the highest price in the bar.

VINDX is the variation...



BOXCOUNT Box-Counting of a D-dimensional array (with D=1,2,3).

The Box-counting method is useful to determine fractal properties of a
1D segment, a 2D image or a 3D array. If C is a fractal set, with fractal dimension DF < D,...



A file ReadMe explains everything in the folder.



Calculate HFD method1 uses HFDCALC() which in turn uses split() method2 uses HFD_LCALC()
Please read readme and HDF_sumanth.pdf files in the present zip file.



SWG() is a multipurpose, segment generation tool based on input, window size, overlap size
SWG() along with FFT() can be used to implement STFT

In the present implementation,
using SWG(), window based HFD is done on a sample data



It draws Apollonian Gasket Fractal for any n using Descartes theorem.

This is not the standard way though. It simply randomly finds 3 tangent circles at each iteration and tries to add new circles. The good thing is it can start w/ any...



It draws the central region of Apollonian Gasket fractal using IFS description.



Dragon IFS Fractal



Tetration Fractal.



This fractal created by converting logic statements into equations using fuzzy logic operators:

X: X is as true as Y is true

Y: Y is as true as X is false

See: Scientific American Magazine, February 1993, "A...



Random fractal curve (non-deterministic).



Multi-threaded Mandelbrot Fractal.