# DNA Fractal Beginning of Finger Print Detection

By , 8 Aug 2011

## Introduction

A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity. Roots of mathematically rigorous treatment of fractals can be traced back to functions studied by Karl Weierstrass, Georg Cantor and Felix Hausdorff in studying functions that were analytic but not differentiable; however, the term fractal was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.[2]

A fractal often has the following features:[3]

• It has a fine structure at arbitrarily small scales.
• It is too irregular to be easily described in traditional Euclidean geometric language.
• It is self-similar (at least approximately or stochastically).
• It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
• It has a simple and recursive definition.

## Nonrandomness Fractal

Intuitively, nonrandomness means that a sequence has "structure." More mathematically, it means a nonuniformity of subsequences[6]. If a sequence of numbers is used to produce an attractor, and that attractor has visually observable structure then we have revealed some underlying structure in the sequence of numbers, or some nonuniformity of subsequences. The Sierpinski triangle is very random but if we use an algorithm which is controlled by a poor (not very random) random number generator, the attractor displays nonuniformity (i.e., visually observable subsets or features).

Since a DNA sequence can be treated formally as a string composed from the four letters "a," "c," "g," and "t" (or "u"), it is an obvious candidate for testing the CGR to see whether in fact visually interesting features were present.

Specifically, we experimented with several DNA sequences, as follows: Instead of "rolling a 4-sided die,"(a way that we using for creating Sierpinski triangle)use the next base (a, c, g, t/u) to pick the next point. Each of the four corners of the square is labelled "a," "c," "g," or "u;" if a "c," for example, is the next base, then a point is plotted half way between the previous point and the "c" corner.
Example: The first 6 bases of the GenBank sequence
HUMHBB (human beta globin region, chromosome 11) are "gaattc":

• The first "g" is plotted halfway between the center of the square and the "g" corner.
• The next base, "a," is plotted halfway between the point just plotted and the "a" corner.
• The base "a" is plotted half way between the previous point and "a" corner.
• Next, "t" is plotted half way between the previous point and the "t" corner, etc.

Plotting these six bases, we obtain Fig. 1.

(the g-quadrant). A smaller copy of this "scoop"Fig. 1.

CGR of the first six bases of HUMHBB. As with the initial points of the Sierpinski triangle, little significance is visible. However, if we continue for the entire 73,357 bases of HUMHBB, we obtain Fig. 2.

Fig. 2. CGR of human beta globin region on chromosome 11(HUMHBB) (73,357 bases).

The CGR of HUMHBB is a good example of the point of this visualization technique, for it illustrates a number of the characteristics of CGRs in general.

## Question

Maybe you ask yourself what this algorithm is for !!!??? Exactly, I will use this algorithm for recognising finger print. I will put it here soon. ;)

## Reference

Chaos and Fractals - A Computer Graphical Journey. Ten Year Compilation of Advanced Research

 IRSOG Engineer Iran (Islamic Republic Of) Member
IRSOG
Programing & working on fractal and chaos;)

I say "I Rely Solely On God"

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 Fractal Dimension for 2d images zeebedee 31 Mar '13 - 1:17
 I am new to this topic so pls bear with me whilst i catch up with everyone else.   I have 2 images of the same tree/bush blowing in the wind. I take the difference of these 2 images and a distinctive/repeating pattern emerges. I would like to know if it is possible to calculate the fractal dimension of this image. The goal is to determine whether motion caught between 2 images is a tree/bush blowing in the wind or something else based on the fractal dimension value.   I am using C#.   Any suggestions or pointer would be great.   thanks Sign In·View Thread·Permalink
 Re: Fractal Dimension for 2d images IRSOG 31 Mar '13 - 6:32
 Re: Fractal Dimension for 2d images zeebedee 31 Mar '13 - 8:28
 DNA Fractal Beginning of Finger Print Detection Rob Ford 2 15 Aug '11 - 1:22
 My vote of 2 toantvo 8 Aug '11 - 16:27
 IMHO, you should explain the way you implement in the source code it better than you only introduce algorithm theory. I vote number 2 and looking forward you rewrite this article better. When you done I will re-vote for you. Sign In·View Thread·Permalink
 Re: My vote of 2 Ali Tavakoli 9 Aug '11 - 1:25