# Tagged Questions

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319 views

### Converting a Sierpinski tetrahedron to a Graph

I need a representation of a 3D Sierpinski gasket in a form of a graph to perform some simulations on. The 2D version is included in GraphData[], but the 3D one is ...
504 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 data....
267 views

### Fractal basins of attraction in a Magnetic Pendulum

I am trying to write a Mathematica program that realizes a graphical approximation of the basins of attraction in a Magnetic pendulum subject to friction and gravity, in which the three magnets are ...
659 views

### Revolution of Koch Snowflake

How do I plot a shape made from revolving the Koch Snowflake? I try to use RevolutionPlot3D[f, {t, t1}], but I think there is no $f$ for the Koch Snowflake.
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### 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 ...
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### Random walk on a Sierpinski gasket

I am trying to simulate a random walk on a Sierpinski gasket. The best strategy i could come up with is to use Nearest point function to determine the next possible step of my walker. But this creates ...
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### Fractal plotting for the Collatz fractal

I have the following equation: f[z_] := 1/4 (2 + 7 z - (2 + 5 z) Cos[Pi*z]) I want to map this on the imaginary plane such that if it converges under iterations ...
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### Coordinates of the centers of the triangles composing a Koch snowflake [duplicate]

How do I obtain the coordinates of the centers of triangles composing the Koch snowflake?
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### How to introduce two successive points inside the FixedPointList for each cycle?

If we want to draw the attraction basins of an iteration function of the following type $$x_{k+1}=x_k-\frac{f(x_k)}{\frac{f(x_k)-f(w_k)}{x_k-w_k}},$$ where $w_k=x_k+b f(x_k)$, $b\in R-\{0\}$, we can ...
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### 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 ...
361 views

### Mandelbrot set—efficiently iterate over a list of initial points

OP edit: This is a Mathematica-specific question about an approach it attempted for a fractal visualization problem described HERE. I'm using the Mandelbrot set there and here as an example, but the ...
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### Basins of attraction of equilibrium points

The Henon-Heiles potential is the following V = 1/2*(x^2 + y^2) - y*(1/3*y^2 - x^2); which has four equilibrium points ...
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### How to plot fractals created with Newton's method [duplicate]

I'm quite a beginner using Mathematica. I'd like to plot the fractals of higher degree polynomials. I have an example for z^3 - 1 which looks like this: ...
498 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 ...
284 views

### I change a single constant and the simple script suddenly takes forever to complete

I writed a code to display the Dragon Curve fractal, and I reached my goal. The algorithm works by taking the previous two points and then adding the following one by making a 90 degrees turn left or ...
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### 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 ...
429 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 ...
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 ...
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### 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 ...
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### 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 ...
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### Do not like quality of graphics when exported by Mathematica 9 [closed]

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 ...
315 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 ...
255 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 ...
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### 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 ...
534 views

### How to draw a polygon with hue color like this one (Koch snowflake)?

I know how to construction Koch snowflake ...
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### 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 ...
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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 ...
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### FindProcessParameters for Fractional Brownian Motion Returns Error

I have the following data: ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
203 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 ...
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### 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 : ...
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### 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 ...
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### 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 ...
3k 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 Math....
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### 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 is:...
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### 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 (...
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### 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 ...