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7
votes
2answers
412 views

Sierpinski carpet with GraphData

Is this graph in the list among the so-called "standard" structures used in GraphData? However, I have not found, yet, anything like "Carpet" or "Sponge" in the ...
8
votes
1answer
152 views

How to make a Nebulabrot?

A Nebulabrot is a generalization of the Buddhabrot, a fractal rendering technique related to the Mandelbrot set that sort of looks like a meditating buddha. The Buddhabrot rendering technique was ...
7
votes
1answer
201 views

Plotting iterated function system images

I'm new not only to this forum, but to Mathematica in general, evidently. I'm running into an issue, and my best attempts at Googling solutions (and trying the search box for this forum) came up with ...
5
votes
0answers
170 views

Wavelet Transform Modulus Maxima (WTMM) method

Has anyone already coded the Wavelet Transform Modulus Maxima (WTMM) method for computing the singular spectrum using multi fractal formalism in Mathematica? The goal is to analyse 1D, 2D and 3D ...
7
votes
2answers
1k views

Manipulating plot of random iterated function system fractal

I'm generating the Sierpinski Gasket by implementing a chaos game in Mathematica. What I'd like to do is create an interactive manipulation with a slider, whereby moving it forward, plots all the ...
0
votes
0answers
53 views

How to efficiently find period orbits in a series defined by recurrence relation?

I have a series defined as $z_{n+1} = z_n^2 + c$, which is the series for the Mandelbrot set. I have defined it, in order to plot the set, as ...
8
votes
2answers
446 views

Interactive Mandelbrot Zoomer?

I want to combine Manipulate with ManbelbrotSetPlot just to get Mathematica to give me a quick and dirty Mandelbrot Zoomer. I want to be able to single/double click on a section, and have it zoom in ...
1
vote
0answers
73 views

Do not like quality of graphics when exported by Mathematica 9

I have been using Mathematica 9 to generate images of fractals for some time, and I noticed an uncomfortable phenomenon when I export the fractal image into a PDF. The lines get thick so that the ...
3
votes
0answers
158 views

Minimalistic code challenge on Apollonian gaskets

I've been recently fascinated by the beauty, symmetry and mathematical richness of the Apollonian gaskets. So I felt myself challenged to see if it was possible to generate one in Mathematica with ...
1
vote
1answer
174 views

Combining Mandelbrot and Monte Carlo

I'm trying to combine plotting a Mandelbrot set with Monte Carlo randomization to plot an equation using random points for complex number z, for the function $z^3-2z+2=0$. Below is the code I have ...
2
votes
1answer
141 views

3D Vicsek Fractal Notebook

Can I get a link to a notebook that explores this fractal structure? I am specifically asking for a url to a Mathematica notebook that generates and / or visualizes this type of fractal. If that ...
4
votes
3answers
464 views
6
votes
1answer
136 views

What are the arguments supplied to ColorFunction in MandelbrotSetPlot?

On the document of MandelbrotSetPlot, it said: With ColorFunction->f, where f is a function, the argument of f is a real number in proportional to the number of ...
3
votes
0answers
174 views

Fractals or other patterns in the quadruple linked pendulum

This will seem like a physics question, but I'm looking for something to do in Mathematica specifically. I've successfully modeled a quadruple linked pendulum by setting up the ODEs and solving them ...
3
votes
1answer
252 views

How to plot a Circles-and-Squares fractal

The Circles-and-Squares fractal is produced by iteration of the equation $\quad \quad z_{n+1}=z_n^2\ ({\rm mod}\; m)$ which results in a Moiré-like pattern: Source: Wolfram MathWorld In ...
0
votes
0answers
36 views

Is there a reliable way to compute the Hurst Dimension of a time series [duplicate]

The Mathematica function FindProcessParameter exists but may be unreliable: FindProcessParameters for Fractional Brownian Motion Returns Error Is there a simple algorithm that can be done in ...
7
votes
1answer
397 views

Computing the Hurst exponent or fractal dimension of fractional Brownian motion

The Hurst exponent is related to the fractal dimension by noticing that the fractal dimension $D$ is equal to $2-H$, where $d$ is the intrinsic dimension and $H$ is the Hurst exponent, for 1-D ...
4
votes
6answers
1k views

Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do?

The Mandelbrot set is defined by complex numbers such as $z=z^2+c$ where $z_0=0$ for the initial point and $c\in\mathbb C$. The numbers grow very fast in the iteration. ...
0
votes
1answer
184 views

Better code for two variable fractal interpolation functions

I am trying to write code for 2-variable fractal interpolation functions using two iterated function systems and two starting functions (both $y(x)=x$) which creates a sequence of piecewise defined ...
0
votes
1answer
147 views

multiple generators for iterative construction of fractal

The code below is an attempt to use more than one generator (in this case two) to generate a fractal using the standard iterative procedure involving generators. Only the first two stages of the ...
3
votes
1answer
186 views

Optimization of power tower fractal generator [closed]

I tried to optimize the code for generating power tower fractals from here. As the author suggested, I tried to memorize the points already tested in a list. Here is my code : ...
4
votes
1answer
288 views

How do I built a zoomable Koch curve?

I'm new to Mathematica and my goal is to write a simple program in order to demonstrate self-similarity of the Koch curve by zooming in. Here is a good example of what I mean (it's a Java applet). I ...
-4
votes
1answer
519 views

How to generate this fractal-like 3D distribution of points in Mma 7.0?

I would like to produce some 3D distributions of points using Mathematica 7.0, that look like the picture below : How could I do that ? What are your suggestions ? What Mma 7 codes could do a ...
45
votes
4answers
2k views

Speeding up this fractal-generating code

I used the code below (which is a sample from this gist containing more similar code) in my answer to my own question about Mandelbrot-like sets for functions other than the simple quadratic on ...
11
votes
3answers
2k views

Poor rendering of fractals

Could someone explain why I get those ugly graphics .. ..trying to use fractals in mathematica 8 ? I'd also like to know if it is possible to draw 2D fractals in Mathematica My configuration ...
47
votes
1answer
3k views

Measuring fractal dimension of natural objects from digital images

This is a useful topic. A college physics lab, medical diagnostics, urban growth, etc. - there is a lot of applications. On this site by Paul Bourke about Google Earth fractals we can get a high ...
2
votes
1answer
290 views

calculating a sequence of functions using iteration

I am trying to compute a sequence of functions using iteration and keep running into problems trying to use built in looping commands because of the recursive nature of the definition. The code below ...
12
votes
2answers
586 views

How can I compile this function

I want to simplify my function f1 to f2, but f2 can't be compiled. How can I make it ...
21
votes
4answers
3k views

How to draw Fractal images of iteration functions on the Riemann sphere?

Prof. McClure, in the work "M. McClure, Newton's method for complex polynomials. A preprint version of a “Mathematical graphics” column from Mathematica in Education and Research, pp. 1–15 (2006)", ...
40
votes
9answers
8k views

Generating a Sierpinski carpet

I am trying to draw a Sierpinski_carpet. I have code that works, but I think there is a more elegant way to do than my way. Maybe I couls use Tuples or ...
25
votes
5answers
4k views

Making fractals with Mathematica

I recently saw this post on math.stackexchange and was curious as to how to generate the image in Mathematica. I tried the following naive approach; however, it is extremely slow. ...