Fractal Definition and 85 Threads

Currently, as far as I know, the two main ways to express any given point on a plane is through either cartesian plane or polar coordinates. Both of which requires an ordered pair of two numbers to express a point. However, I wonder if there exists such a system that could express any given...

I found these papers, the first is that galaxies are fractal based on observation Fractal Analysis of the UltraVISTA Galaxy Survey Sharon Teles (1), Amanda R. Lopes (2), Marcelo B. Ribeiro (1,3) ((1) Valongo Observatory, Universidade Federal do Rio de Janeiro, Brazil, (2) Department of...

Hi all, Whats the significance/application of square fractal grid turbulence studies?

Attempt The interval sketch is obviously a line from 0, 1. F1 would cut the interval line by a third similar to the Cantor set. F2 would cut the interval line by a third and then there is a transformation that moves to the point (1/3, 1/3). F3 would cut the interval line by a third and then...

Gerd Binnig, Nobel laureate in physics in 1986, proposed in his article "The fractal structure of evolution" [1] that everything in the universe, including its laws, had changed and became what we have got today through a process which mixes some concepts from darwinian evolution and fractal...

This should maybe go in the Beyond The Standard Model forum but since it's a paper about quantum cosmology I'll put it here. Feel free to move it if it's too speculative but that's exactly my question. That is: if it is... Perusing "The Area of a Rough Black Hole" - -...

So, I recently heard about the Golden ratio fractal phase conjugation and I was wondering if it could possibly explain the solar system formation. Meaning, if you can imagine a torus energy dynamic shape (with the sun in the middle) maybe it could be explained by this theory?

I was trying to find some sort of pattern in the triangle (below) to graph it or find some equation, and I thought maybe measuring something would be a good idea. I was okay just calculating the area for the first few iterations, but then I got confused on how I was supposed to represent like...

So I had a topic which I would like to fact check from an informed scientific source. Basically there is an argument about whether or not an object that naturally exists in a fourth dimensional space, would by default have more than countably infinite times the energy of a 3 dimensional Object...

Hello, Definitely excited to be apart of this community. I hope to broaden my understanding of physics - both from the questions of the inquisitive and the answers the bold believe to hold true.

How fractals have weird dimension definitions.

In looking at the definition of a Hausdorff dimension of a space S = inf{d>0: inf{Σirid: there is a cover of S by balls with non-zero radii} =0} where i ranges over a countable set, it would appear that it would be acceptable to take the index set to be finite, but I am not sure how you would...

I have been learning about the idea of "dimension" of a shape in terms of how its "mass" scales down when we cut it into self-similar parts. For example, However, the term "dimension" is closely linked with the idea of degree of freedom. So my question is, is there any sense in which the...

What are the differences between Sierpinski/Vicsek fractals?

There are two subjects which pop up a lot as having physical examples (or, more precisely, where their approximations have), but many (not all) of them seem rather indirect or forced. For example: [1] phi (the Golden ratio) or 1/phi: (a) trivia: sunflowers and pineapples giving the first few...

Does there exist a binary fractal tree… (reference: http://ecademy.agnesscott.edu/~lriddle/ifs/pythagorean/symbinarytree.htm ) …whose leaves (endpoints) lie on a circle and are equidistant? Consider a binary fractal tree with branches decreasing in length by a scaling factor r (0 < r < 1) for...

Regarding the recent discovery by Ken Ono and colleagues of the fractal structure of partition numbers for primes: a great lever of intuition would be to see a diagram, or any presentation of the numbers that reveals this fractal structure. Perhaps the fractal structure is somehow hidden in a...

Hi there, so recently we had professor's assistant covering our class and he decided to talk about Fractal Dimensions. Maybe its just the concept or his explenation but we all left the class bewildered to say the least. Could someone clarify for me, how do we refer to the number of dimensions...

So the quality of my over-the-air digital TV reception has been getting worse over the past few months. Probably the digital TV antenna that I'm using is getting old and starting to degrade. Last night I resorted to trying different reflector combinations to try to boost the signal for the...

There's a question that's been in my mind for quite a while but I cannot figure out what the answer is. I't probably an ill posed question but I will ask it anyway: 1.- Do we know what the dark-matter statistical distribution in our Universe is (at large scales)? 2.- In case we do, could...

On an exam we just took, we were asked to find the dimension of a set using the box counting technique. So choose an epsilon, and cover your object in boxes of side length epsilon, and count the minimum number of boxes required to cover the object. Then use a smaller epsilon and and count the...

The code is as followed: function fern() AI = [0 0 ; 0 0.16]; AII = [ 0.85 0.04 ; -0.04 -0.85 ] ; AIII = [ 0.2 -0.26 ; 0.23 0.22 ] ; AIV = [-0.15 0.28 ; 0.26 0.24 ];BI = [ 0 ; 0]; BII = [ 0 ; 1.6]; BIII = [ 0 ; 1.6]; BIV = [0 ; 0.44]; N = 10000; I = 50; H = zeros(N,2); for n=1...

For my work, I need to check my calculations with an example of a fractal object. I searched on the internet, there are some examples of fractals with their hausdorff dimensions, but no boundary terms related. Also found some 1-d examples, but I need d>3 dimensional objects since my calculations...

It never goes crazy and starts doing it's own unpredictable number pattern or sequence, right? Thanks in advance.

Hey, I am working on a project where I need to take several time series of various lengths and identify common features. So, for example, a period of 100 days may exhibit the same features as a period of 10 days -- the system is self-similar in this way. In order to compare these series of...

Here is Dr Jonathan Tallant a famous math phlosopher Fractal Binary is a type of math that uses waves in performing it's calculations. Frequency Bits, (Numbers), are generated as waves. These positive and negative waves are then added and subtracted together 'at the same time', waves have a...

What are some of your favorite fractal art? http://lava360.com/wp-content/uploads/2010/10/fractal-world11.jpg

Hi, I am trying to understand why do the two versions of Hausdorff (fractal) dimension are actually the same.I refer to the definition by coverings and the definition by ratio of two logarythms. http://en.wikipedia.org/wiki/Hausdorff_measure...

Hi, Can someone give me a link to a clear and relatively basic and short matirial introducing the notion of fractal dimension (Hausdorff dimension)? Thank's in advance.

Sierpiń́ski's fractal and calculating the total "blank" space Homework Statement Connect the midpoints of the sides of an equilateral triangle to form 4 smaller equilateral triangles. Leave the middle small triangle blank, but for each of the other 3 small triangles, draw lines connecting the...

Hi all, I'm trying to self-learn about chaos, fractal, or anything that correspondence to random analysis (maybe with some material from statistical physics). Anyone know what the best textbook for these fields?

Back in november I asked the forum about this fractal: http://en.wikipedia.org/wiki/File:Phi_glito.png At the time I couldn't figure out how to make it. Since then I've figured it out. I used MS Excel. I'm not completely satisfied though. There are some gaps between the major...

I understand how to calculate the capacitance of an isolated conductor, say a sphere, and I know that the associated formula involves the surface area of the conductor. Does all of this make the assumption that the surface in question is convex, or at least "non-concave"? More specifically, what...

Homework Statement Hey all, this is for a laboratory. I need to determine the fractal basin boundaries for a magnetic pendulum swinging chaotically about 3 other magnets underneath. I was able to plot a single path for the pendulum in Mathematica, but now I need to expand my code to...

Hello, I had a question about data which is represented by a fractal distribution. I know that the linear regression lies in the plot of log(N) vs. log(x) for which the ratio represents the fractal dimension as the limit of x going to infinity. However, how would one get the representative...

Riemann's zeta function "fractal" because of Voronin? I am not sure which rubric this belongs to, but since the zeta function is involved, I am putting it here. I noticed a comment (but was in too much of a hurry to remember the source) that, because of the "universality" of the Riemann zeta...

Homework Statement I am doing an experiment to determine the fractal dimension of hand compressed aluminium spheres. I cut a square of foil of some length ##L## and known thickness, ##t##. I do this a few times, varying ##L##. The radius of the hand compressed spheres, $$r =...

I've been fooling around in MS Excel trying to reconstruct this fractal: I haven't had any issues here making it. I totally understand the algorithm for generating the left turn/right turn ordering. What I really want to know is how this version is generated: Original image...

C++ Recursion to print a "fractal pattern" I guess I really don't understand how to create a initial case for my recursion Can some advice to where I would need to change the code ___________The problem: Create a recursive function to draw this pattern, given a maximum number of stars (which...

Is universe a 3 dimensional fractal...? Hi all, Yesterday I was reading on fractals (2 dimensional). It was interesting to know leaves etc are examples of fractals ( for example : fern). So I thought if there is a possibility for 3 dimensional fractal. And as in any case which is distorted...

Do you know why a simple set used for construction of the Mandelbrot's fractal results in a jaw dropping shape?

Hi, I'm not sure if this is the right place for this...if it isn't if I could be redirected/if a moderator could move my post to the right place I would greatly appreciate it. In any case, I am trying to understand fractal dimensions. I read through wikipedia's description and I believe I...

First post! I'm investigating chaos in non linear coupled spring oscillators. After generating a poincare' map of said system i wanted to see if the map was fractal. i proceeded to use a box counting method in order to calculate a fractal dimension. I generated a plot of log(number of...

Hey Everyone, I just wanted to ask for a bit of help on this research assignment I have to do. I have to show how Fractal Geometry contributes to the theory that Mathematics was invented. I have been looking into fractal dimensions and the fact that the dimensions we have labelled (1,2 and 3)...

Hi, I have been looking for fractal behavior in a data set. I've used the box method to determine fractal dimension by looking at the inverse of box size and the number of boxes needed to enclose the object. These two variables seem to be fairly accurately predicted by a power law...

Homework Statement I have a problem trying to code these two programs, one is related to the obtain the fractal dimension of the Koch curve by using the method of the box counting dimension and also using the Grassberger-Procaccia algorithm Homework Equations For the box counting...

The very first time I ever heard about fractals was in my junior year in high school in my Algebra II class when we were studying complex numbers. I was fascinated by these wonderous objects and I've had many questions about them ever since. Though two of my main questions have always been...

Hello, after reading something about fractals, I was wondering if it is possible to find invariants on fractal entities. For example in 3D Euclidean space we know that curvature and torsion uniquely define a regular curve: they are invariant to rigid motions. In fractal geometry and in...

In attempting to arrive at a fair critique of Alexander de Seversky's "Combat Plane" concept, I discovered something unexpected about the "Combat Box" formation developed in late 1942 by then-Colonel Curtis LeMay. In particular, the numerical and spatial organization of the Combat Box...

Homework Statement 13.2 A quadratic Julia set has the form z(n+1)=z(n)^2+c The special case where c=-.123+.745i is called Douday's rabbit fractal. Follow example 13.1, and create an image using this value of c. For the Madelbrot image, we started with all z-values equal to 0...